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Difficulties may arise when analyzing longitudinal data using mixed-effects models if nonparametric functions are present in the linear predictor component. This study extends semiparametric mixed-effects modeling in cases when the response variable does not always follow a normal distribution and the nonparametric component is structured as an additive model. A novel approach is proposed to identify significant linear and non-linear components using a double-penalized generalized estimating equation with two penalty terms. Furthermore, the iterative approach intends to enhance the efficiency of estimating regression coefficients by incorporating the calculation of the working covariance matrix. The oracle properties of the resulting estimators are established under certain regularity conditions, where the dimensions of both the parametric and nonparametric components increase as the sample size grows. We perform numerical studies to demonstrate the efficacy of our proposal. [ABSTRACT FROM AUTHOR]

In practical survival analysis, the situation of no event for a patient can arise even after a long period of waiting time, which means a portion of the population may never experience the event of interest. Under this circumstance, one remedy is to adopt a mixture cure Cox model to analyze the survival data. However, if there clearly exhibits an acceleration (or deceleration) factor among their survival times, then an accelerated failure time (AFT) model will be preferred, leading to a mixture cure AFT model. In this paper, we consider a penalized likelihood method to estimate the mixture cure semiparametric AFT models, where the unknown baseline hazard is approximated using Gaussian basis functions. We allow partly interval‐censored survival data which can include event times and left‐, right‐, and interval‐censoring times. The penalty function helps to achieve a smooth estimate of the baseline hazard function. We will also provide asymptotic properties to the estimates so that inferences can be made on regression parameters and hazard‐related quantities. Simulation studies are conducted to evaluate the model performance, which includes a comparative study with an existing method from the smcureR package. The results show that our proposed penalized likelihood method has acceptable performance in general and produces less bias when faced with the identifiability issue compared to smcure. To illustrate the application of our method, a real case study involving melanoma recurrence is conducted and reported. Our model is implemented in our R package aftQnp which is available from https://github.com/Isabellee4555/aftQnP. [ABSTRACT FROM AUTHOR]

AbstractMixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are increasingly common in various fields. Despite their widespread use and successful applications, these models suffer from over-parameterization, making them not suitable for even moderately sized matrix-variate data. To address this issue, we introduce a sparse model-based clustering approach for three-way data. Our approach assumes that the matrix mixture parameters are sparse and have different degrees of sparsity across clusters, enabling the induction of parsimony in a flexible manner. Estimation relies on the maximization of a penalized likelihood, with specifically tailored group and graphical lasso penalties. These penalties facilitate the selection of the most informative features for clustering three-way data where variables are recorded over multiple occasions, as well as allowing the identification of cluster-specific association structures. We conduct extensive testing of the proposed methodology on synthetic data and validate its effectiveness through an application to time-dependent crime patterns across multiple U.S. cities. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

A critical aspect of modeling binomial response data is selecting an appropriate link function, as an improper choice can significantly affect model precision. This paper introduces the skew–t link model, an extension of the skew–probit model, offering increased flexibility by incorporating both asymmetry and heavy tails, making it suitable for asymmetric and complex data structures. A penalized likelihood-based estimation method is proposed to stabilize parameter estimation, particularly for the asymmetry parameter. Extensive simulation studies demonstrate the model's superior performance in terms of lower bias, root mean squared error (RMSE), and robustness compared to traditional symmetric models like probit and logit. Furthermore, the model is applied to two real-world datasets: one concerning women's labor participation and another related to cardiovascular disease outcomes, both showing superior fitting capabilities compared to more traditional models (with probit and the skew–probit links). These findings highlight the model's applicability to socioeconomic and medical research, characterized by skew and asymmetric data. Moreover, the proposed model could be applied in various domains where data exhibit asymmetry and complex structures. [ABSTRACT FROM AUTHOR]

We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also validated. The problem that the true values lie on the boundary is solved by our previous results applicable to singular models, besides, penalized estimation and non-ergodic statistics. To overcome non-identifiability, we consider a suitable penalty such as the non-convex Bridge and the adaptive Lasso that stabilize the asymptotic behavior of the estimator and shrink inactive parameters. Then the estimator converges to one of the most parsimonious values among all the true values. The oracle property can also be obtained even if likelihood ratio tests for model selection are labor intensive due to singularity of models. Examples are: a superposition of parametric proportional hazard models and a counting process having intensity with multicollinear covariates. [ABSTRACT FROM AUTHOR]

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the parameter space or where even identifiability fails. For that, we propose a more general local approximation of the parameter space (at the true value) than previous studies. This estimation theory is comprehensive in that it can handle penalized estimation as well as quasi-maximum likelihood estimation (in the ergodic or non-ergodic statistics) under such non-regular models. In penalized estimation, depending on the boundary constraint, even the concave Bridge estimator does not necessarily give selection consistency. Therefore, we describe some sufficient condition for selection consistency, precisely evaluating the balance between the boundary constraint and the form of the penalty. An example is penalized MLE of variance components of random effects in linear mixed models. [ABSTRACT FROM AUTHOR]

Additive partial linear models with symmetric autoregressive errors of order p are proposed in this paper for modeling time series data. Specifically, we apply this model class to explain the weekly hospitalization for respiratory diseases in Sorocaba, São Paulo, Brazil, by incorporating climate and pollution as covariates, trend and seasonality. The main feature of this model class is its capability of considering a set of explanatory variables with linear and nonlinear structures, which allows, for example, to model jointly trend and seasonality of a time series with additive functions for the nonlinear explanatory variables and a predictor to accommodate discrete and linear explanatory variables. Additionally, the conditional symmetric errors allow the possibility of fitting data with high correlation order, as well as error distributions with heavier or lighter tails than the normal ones. We present the model class and a novel iterative process is derived by combining a P-GAM type algorithm with a quasi-Newton procedure for the parameter estimation. The inferential results, diagnostic procedures, including conditional quantile residual analysis and local influence analysis for sensitivity, are discussed. Simulation studies are performed to assess finite sample properties of parametric and nonparametric estimators. Finally, the data set analysis and concluding remarks are given. [ABSTRACT FROM AUTHOR]

Model-based clustering analysis of functional data often has normality assumption. This article considers clustering non Gaussian functional data. We propose a novel non Gaussian functional mixed-effects model without the prior information and clustering number. We use transformation functions to accommodate non Gaussian functional data. Smoothing spline ANOVA and cubic B-spline approximate unknown fixed effects and random effects, respectively. A penalized likelihood is used to estimate unknown parameters, and the consistency and asymptotic normality is provided after that. We take simulations for different measurement error distribution assumptions and adopt the air quality of Italian city data. Both simulation and actual data analysis show that the proposed method performs well and has a better clustering effect. [ABSTRACT FROM AUTHOR]

AbstractIn many applications of multivariate longitudinal mixed models, it is reasonable to assume that each response is informed by only a subset of covariates. Moreover, one or more responses may exhibit the same relationship to a particular covariate for example, if they are capturing the same underlying aspect of an individual physical, mental, and emotional health. To address the above challenges, we propose a method for simultaneous clustering and variable selection of fixed effect coefficients in multivariate mixed models. We achieve this in a computationally scalable manner via a composite likelihood approach: separate mixed models are first fitted to each response, after which the model estimates are combined into a single quadratic form resembling a multivariate Wald statistic. We then augment this with fusion- and sparsity-inducing penalties based on broken adaptive ridge regression. Simulation studies demonstrate that the proposed composite quadratic estimator is similar to or better than several existing techniques for fixed effects selection in (univariate) mixed models while being computationally much more efficient. We apply the proposed method to longitudinal panel data from Australia to quantify how an individual’s overall health, assessed via a set of eight composite scores, evolves as a function of various demographic and lifestyle variables. [ABSTRACT FROM AUTHOR]

The cause-specific hazard Cox model is widely used in analyzing competing risks survival data, and the partial likelihood method is a standard approach when survival times contain only right censoring. In practice, however, interval-censored survival times often arise, and this means the partial likelihood method is not directly applicable. Two common remedies in practice are (i) to replace each censoring interval with a single value, such as the middle point; or (ii) to redefine the event of interest, such as the time to diagnosis instead of the time to recurrence of a disease. However, the mid-point approach can cause biased parameter estimates. In this article, we develop a penalized likelihood approach to fit semi-parametric cause-specific hazard Cox models, and this method is general enough to allow left, right, and interval censoring times. Penalty functions are used to regularize the baseline hazard estimates and also to make these estimates less affected by the number and location of knots used for the estimates. We will provide asymptotic properties for the estimated parameters. A simulation study is designed to compare our method with the mid-point partial likelihood approach. We apply our method to the Aspirin in Reducing Events in the Elderly (ASPREE) study, illustrating an application of our proposed method. [ABSTRACT FROM AUTHOR]

In capture-recapture problems, when individuals are categorized into different groups and individuals within each group are suspected to be captured with equal probability, the finite mixture of Poisson distributions is commonly employed to address heterogeneity in capture probabilities. In this study, we propose a penalized likelihood estimation method to estimate population sizes and demonstrate that the penalized likelihood ratio statistic asymptotically follows a standard chi-square distribution. To detect the presence of heterogeneity, we introduce a retooled EM test statistic that asymptotically follows a mixture of chi-square distributions. Our numerical investigations reveal that the proposed maximum penalized likelihood estimator offers increased stability, while the penalized likelihood ratio interval estimator shows enhanced accuracy compared with existing approaches. By carefully selecting an adaptive tuning parameter, the EM test achieves a better balance between the type I error and power than the goodness-of-fit and AIC-based tests. Finally, we apply the proposed method to three real-life datasets: street prostitute data, H5N1 influenza data, and opiate user data. [ABSTRACT FROM AUTHOR]

Conventional supervised learning usually operates under the premise that data are collected from the same underlying population. However, challenges may arise when integrating new data from different populations, resulting in a phenomenon known as dataset shift. This paper focuses on prior probability shift, where the distribution of the outcome varies across datasets but the conditional distribution of features given the outcome remains the same. To tackle the challenges posed by such shift, we propose an estimation algorithm that can efficiently combine information from multiple sources. Unlike existing methods that are restricted to discrete outcomes, the proposed approach accommodates both discrete and continuous outcomes. It also handles high-dimensional covariate vectors through variable selection using an adaptive least absolute shrinkage and selection operator penalty, producing efficient estimates that possess the oracle property. Moreover, a novel semiparametric likelihood ratio test is proposed to check the validity of prior probability shift assumptions by embedding the null conditional density function into Neyman's smooth alternatives (Neyman, 1937) and testing study-specific parameters. We demonstrate the effectiveness of our proposed method through extensive simulations and a real data example. The proposed methods serve as a useful addition to the repertoire of tools for dealing dataset shifts. [ABSTRACT FROM AUTHOR]

In this paper, a Markov Regime Switching Model of Conditional Mean with covariates, is proposed and investigated for the analysis of incidence rate data. The components of the model are selected by both penalized likelihood techniques in conjunction with the Expectation Maximization algorithm, with the goal of achieving a high level of robustness regarding the modeling of dynamic behaviors of epidemiological data. In addition to statistical inference, Changepoint Detection Analysis is performed for the selection of the number of regimes, which reduces the complexity associated with Likelihood Ratio Tests. Within this framework, a three-phase procedure for modeling incidence data is proposed and tested via real and simulated data. [ABSTRACT FROM AUTHOR]

The use of social contact rates is widespread in infectious disease modeling since it has been shown that they are key driving forces of important epidemiological parameters. Quantification of contact patterns is crucial to parameterize dynamic transmission models and to provide insights on the (basic) reproduction number. Information on social interactions can be obtained from population-based contact surveys, such as the European Commission project POLYMOD. Estimation of age-specific contact rates from these studies is often done using a piecewise constant approach or bivariate smoothing techniques. For the latter, typically, smoothness is introduced in the dimensions of the respondent's and contact's age (i.e. the rows and columns of the social contact matrix). We propose a smoothing constrained approach—taking into account the reciprocal nature of contacts—introducing smoothness over the diagonal (including all subdiagonals) of the social contact matrix. This modeling approach is justified assuming that when people age their contact behavior changes smoothly. We call this smoothing from a cohort perspective. Two approaches that allow for smoothing over social contact matrix diagonals are proposed, namely (i) reordering of the diagonal components of the contact matrix and (ii) reordering of the penalty matrix ensuring smoothness over the contact matrix diagonals. Parameter estimation is done in the likelihood framework by using constrained penalized iterative reweighted least squares. A simulation study underlines the benefits of cohort-based smoothing. Finally, the proposed methods are illustrated on the Belgian POLYMOD data of 2006. Code to reproduce the results of the article can be downloaded on this GitHub repository https://github.com/oswaldogressani/Cohort_smoothing. [ABSTRACT FROM AUTHOR]

A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of the domain. The proposed method is referred to as sparse and smooth functional clustering (SaS-Funclust) and relies on a general functional Gaussian mixture model whose parameters are estimated by maximizing a log-likelihood function penalized with a functional adaptive pairwise fusion penalty and a roughness penalty. The former allows identifying the noninformative portion of the domain by shrinking the means of separated clusters to some common values, whereas the latter improves the interpretability by imposing some degree of smoothing to the estimated cluster means. The model is estimated via an expectation-conditional maximization algorithm paired with a cross-validation procedure. Through a Monte Carlo simulation study, the SaS-Funclust method is shown to outperform other methods that already appeared in the literature, both in terms of clustering performance and interpretability. Finally, three real-data examples are presented to demonstrate the favourable performance of the proposed method. The SaS-Funclust method is implemented in the R package sasfunclust, available on CRAN. [ABSTRACT FROM AUTHOR]

In clinical studies, one often encounters time-to-event data that are subject to right censoring and for which a fraction of the patients under study never experience the event of interest. Such data can be modeled using cure models in survival analysis. In the presence of cure fraction, the mixture cure model is popular, since it allows to model probability to be cured (called the incidence) and the survival function of the uncured individuals (called the latency). In this paper, we develop a variable selection procedure for the incidence and latency parts of a mixture cure model, consisting of a logistic model for the incidence and a semiparametric accelerated failure time model for the latency. We use a penalized likelihood approach, based on adaptive LASSO penalties for each part of the model, and we consider two algorithms for optimizing the criterion function. Extensive simulations are carried out to assess the accuracy of the proposed selection procedure. Finally, we employ the proposed method to a real dataset regarding heart failure patients with left ventricular systolic dysfunction. [ABSTRACT FROM AUTHOR]

In a semi-competing risks model in which a terminal event censors a non-terminal event but not vice versa, the conventional method can predict clinical outcomes by maximizing likelihood estimation. However, this method can produce unreliable or biased estimators when the number of events in the datasets is small. Specifically, parameter estimates may converge to infinity, or their standard errors can be very large. Moreover, terminal and non-terminal event times may be correlated, which can account for the frailty term. Here, we adapt the penalized likelihood with Firth's correction method for gamma frailty models with semi-competing risks data to reduce the bias caused by rare events. The proposed method is evaluated in terms of relative bias, mean squared error, standard error, and standard deviation compared to the conventional methods through simulation studies. The results of the proposed method are stable and robust even when data contain only a few events with the misspecification of the baseline hazard function. We also illustrate a real example with a multi-centre, patient-based cohort study to identify risk factors for chronic kidney disease progression or adverse clinical outcomes. This study will provide a better understanding of semi-competing risk data in which the number of specific diseases or events of interest is rare. [ABSTRACT FROM AUTHOR]

Misclassified current status data arise when the failure time of interest is observed or known only to be either smaller or larger than an observation time rather than observed exactly, and the failure status is examined by a diagnostic test with testing error. Such data commonly occur in various scientific fields, including clinical trials, demographic studies and epidemiological surveys. This paper discusses regression analysis of such data with the focus on variable selection or identifying predictable and important covariates associated with the failure time of interest. For the problem, a penalized maximum likelihood approach is proposed under the Cox proportional hazards model and the smoothly clipped absolute deviation penalty. More specifically, we develop a penalized EM algorithm to relieve the computational burden in maximizing the resulting, complex penalized likelihood function. A simulation study is conducted to examine the empirical performance of the proposed approach in finite samples, and an illustration to a set of real data on chlamydia is also provided. [ABSTRACT FROM AUTHOR]

Standard likelihood penalties to learn Gaussian graphical models are based on regularizing the off‐diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit sample variances. We show that such standardization can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood, L0$$ {L}_0 $$ and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an L1$$ {L}_1 $$ penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference. [ABSTRACT FROM AUTHOR]

We revisit the generalized hyperbolic (GH) distribution and its nested models. These include widely used parametric choices like the multivariate normal, skew‐t$$ t $$, Laplace, and several others. We also introduce the multiple‐choice LASSO, a novel penalized method for choosing among alternative constraints on the same parameter. A hierarchical multiple‐choice Least Absolute Shrinkage and Selection Operator (LASSO) penalized likelihood is optimized to perform simultaneous model selection and inference within the GH family. We illustrate our approach through a simulation study and a real data example. The methodology proposed in this paper has been implemented in R functions which are available as supplementary material. [ABSTRACT FROM AUTHOR]

We consider here penalized likelihood-based estimation and model selection applied to econometric time series models, which allow for nonnegativity (boundary) constraints on some or all of the parameters. We establish that joint model selection and estimation result in standard asymptotic Gaussian distributed estimators. The results contrast with nonpenalized estimation, which, as is well-known, leads to nonstandard asymptotic distributions that depend on the unknown number of parameters on the boundary of the parameter space. We apply our results to the rich class of autoregressive conditional heteroskedastic (ARCH) models for time-varying volatility. For the ARCH models, simulations show that penalized estimation and model selection works surprisingly well, even for models with a large number of parameters. An empirical illustration for stock-market return data shows the ability of penalized estimation to select ARCH models that fit nicely the empirical autocorrelation function, and confirms the stylized fact of long-memory in such financial time series data. [ABSTRACT FROM AUTHOR]

Motivated by an empirical analysis of stock reaction to COVID-19 pandemic, we propose a generalized mediation model with high-dimensional potential mediators to study the mediation effects of financial metrics that bridge company's sector and stock value. We propose an estimation procedure for the direct effect via a partial penalized maximum likelihood method and establish its theoretical properties. We develop a Wald test for the indirect effect and show that the proposed test has a χ 2 limiting null distribution. We also develop a partial penalized likelihood ratio test for the direct effect and show that the proposed test asymptotically follows a χ 2 -distribution under null hypothesis. A more efficient estimator of indirect effect under complete mediation model is also developed. Simulation studies are conducted to examine the finite sample performance of the proposed procedures and compare with some existing methods. We further illustrate the proposed methodology with an empirical analysis of stock reaction to COVID-19 pandemic via exploring the underlying mechanism of the relationship between companies' sectors and their stock values. [ABSTRACT FROM AUTHOR]

In practice, multivariate skew normal mixture (MSNM) models provide a more flexible framework than multivariate normal mixture models, especially for heterogeneous and asymmetric data. For MSNM models, the maximum likelihood estimator often leads to a statistical inference referred to as "badness" under certain properties, because of the unboundedness of the likelihood function and the divergence of shape parameters. We consider two penalties for the log-likelihood function to counter these issues simultaneously in MSNM models. We show that the penalized maximum likelihood estimator is strongly consistent when the putative order of the mixture is equal to or larger than the true order. We also provide penalized expectation-maximization-type algorithms to compute penalized estimates. Finite sample performance is examined through simulations, real data applications, and comparison with existing methods. [ABSTRACT FROM AUTHOR]

Finite mixture of regressions (FMR) are commonly used to model heterogeneous effects of covariates on a response variable in settings where there are unknown underlying subpopulations. FMRs, however, cannot accommodate situations where covariates' effects also vary according to an "index" variable—known as finite mixture of varying coefficient regression (FM‐VCR). Although complex, this situation occurs in real data applications: the osteocalcin (OCN) data analyzed in this manuscript presents a heterogeneous relationship where the effect of a genetic variant on OCN in each hidden subpopulation varies over time. Oftentimes, the number of covariates with varying coefficients also presents a challenge: in the OCN study, genetic variants on the same chromosome are considered jointly. The relative proportions of hidden subpopulations may also change over time. Nevertheless, existing methods cannot provide suitable solutions for accommodating all these features in real data applications. To fill this gap, we develop statistical methodologies based on regularized local‐kernel likelihood for simultaneous parameter estimation and variable selection in sparse FM‐VCR models. We study large‐sample properties of the proposed methods. We then carry out a simulation study to evaluate the performance of various penalties adopted for our regularized approach and ascertain the ability of a BIC‐type criterion for estimating the number of subpopulations. Finally, we applied the FM‐VCR model to analyze the OCN data and identified several covariates, including genetic variants, that have age‐dependent effects on OCN. [ABSTRACT FROM AUTHOR]

In clusterwise regression analysis, the goal is to predict a response variable based on a set of explanatory variables, each with cluster-specific effects. In many real–life problems, the number of candidate predictors is typically large, with perhaps only a few of them meaningfully contributing to the prediction. A well–known method to perform variable selection is the LASSO, with calibration done by minimizing the Bayesian Information Criterion (BIC). However, existing LASSO-penalized estimators are problematic for several reasons. First, only certain types of penalties are considered. Second, the computations may sometimes involve approximate schemes. Third, variable selection is usually time consuming, due to a complex calibration of the penalty term, possibly requiring several multiple evaluations of an estimator for each plausible value of the tuning parameter(s). We introduce a two–step approach to fill these gaps. In step 1, we fit LASSO clusterwise linear regressions with some pre–specified level of penalization (Fit step). In step 2 (Selection step), we perform covariate selection locally, i.e. on the weighted data, with weights corresponding to the posterior probabilities from the previous step. This is done by using a generalization of the Least Angle Regression (LARS) algorithm, which permits covariate selection with a single evaluation of the estimator. In addition, both Fit and Selection steps leverage on an Expectation Maximization (EM) algorithm, fully in closed forms, designed with a very general version of the LASSO penalty. The advantages of our proposal, in terms of computation time reduction, and accuracy of model estimation and selection, are shown by means of a simulation study, and illustrated with a real data application. [ABSTRACT FROM AUTHOR]

Length-biased failure time data occur often in various biomedical fields, including clinical trials, epidemiological cohort studies and genome-wide association studies, and their analyses have been attracting a surge of interest. In practical applications, because one may collect a large number of candidate covariates for the failure event of interest, variable selection becomes a useful tool to identify the important risk factors and enhance the estimation accuracy. In this paper, we consider Cox's proportional hazards model and develop a penalized variable selection technique with various popular penalty functions for length-biased data, in which the failure event of interest suffers from interval censoring. Specifically, a computationally stable and reliable penalized expectation-maximization algorithm via two-stage data augmentation is developed to overcome the challenge in maximizing the intractable penalized likelihood. We establish the oracle property of the proposed method and present some simulation results, suggesting that the proposed method outperforms the traditional variable selection method based on the conditional likelihood. The proposed method is then applied to a set of real data arising from the Prostate, Lung, Colorectal and Ovarian cancer screening trial. The analysis results show that African Americans and having immediate family members with prostate cancer significantly increase the risk of developing prostate cancer, while having diabetes exhibited a significantly lower risk of developing prostate cancer. [ABSTRACT FROM AUTHOR]

This paper compares several methods for constructing weekly nowcasts of recession probabilities in Italy, with a focus on the most recent period of the Covid-19 pandemic. The common thread of these methods is that they use, in different ways, the information content provided by financial market data. In particular, a battery of probit models are estimated after extracting information from a large dataset of more than 130 financial market variables observed at a weekly frequency. The accuracy of these models is explored in a pseudo out-of-sample nowcasting exercise. The results demonstrate that nowcasts derived from probit models estimated on a large set of financial variables are, on average, more accurate than those delivered by standard probit models estimated on a single financial covariate, such as the slope of the yield curve. The proposed approach performs well even compared with probit models estimated on single time series of real economic activity variables, such as industrial production, business tendency survey data or composite PMI indicators. Overall, the financial indicators used in this paper can be easily updated as soon as new data become available on a weekly basis, thus providing reliable early estimates of the Italian business cycle. [ABSTRACT FROM AUTHOR]

In supervised learning, the gap between the truth label and the model output is always portrayed by an error function, and a fixed error function corresponds to a specific noise distribution that provides for model optimization. However, the actual noise usually has a much more complex structure. To be better fit for it, in this paper, we propose a robust noise model that embeds a mixture of Gaussian (MoG) noise modeling strategy into a baseline classification model, which is selected as the Gaussian mixture model (GMM) here. Further, to facilitate the automatic selection of the number of mixture components, we apply the penalized likelihood method. Then, we utilize an alternative strategy to update the parameters of the noisy model and the basic GMM classifier. From the meta-learning perspective, the proposed model offers a novel approach to defining the hyperparameters from the error representation. Finally, we compare the proposed approach with three conventional and related classification methods on the synthetic, two benchmark handwriting recognition datasets and the Yale Face dataset. In addition, we embed the noise modeling strategy into the semantic segmentation task. The numerical results validate that our approach achieves the best performance and the efficiency of MoG noise modeling. [ABSTRACT FROM AUTHOR]

The cognitive diagnosis model (CDM) is an effective statistical tool for extracting the discrete attributes of individuals based on their responses to diagnostic tests. When dealing with cases that involve small sample sizes or highly correlated attributes, not all attribute profiles may be present. The standard method, which accounts for all attribute profiles, not only increases the complexity of the model but also complicates the calculation. Thus, it is important to identify the empty attribute profiles. This paper proposes an entropy-penalized likelihood method to eliminate the empty attribute profiles. In addition, the relation between attribute profiles and the parameter space of item parameters is discussed, and two modified expectation–maximization (EM) algorithms are designed to estimate the model parameters. Simulations are conducted to demonstrate the performance of the proposed method, and a real data application based on the fraction–subtraction data is presented to showcase the practical implications of the proposed method. [ABSTRACT FROM AUTHOR]

In order to deal with data of great complexity, the need to develop new methods for variable selection has emerged. Among the new methods, methods based on penalty functions have received great attention. These methods can be used in complex data problems since they shrink a subset of coefficient estimates to zero, thus removing the associated variables from the model, which allows the identification of the subset of the most relevant explanatory variables and, consequently, drastically reduces the computational burden. In this work we analyse the problem of variable selection in mixtures of linear mixed models. In order to do it, we compare the performance of a penalized likelihood approach for variable selection via the Expectation-Maximization and the Classification Expectation-Maximization algorithms through a simulation study and a real-world application. [ABSTRACT FROM AUTHOR]

Pearson's system is a rich class of models that includes many classical univariate distributions. It comprises all continuous densities whose logarithmic derivative can be expressed as a ratio of quadratic polynomials governed by a vector β$$ \beta $$ of coefficients. The estimation of a Pearson density is challenging, as small variations in β$$ \beta $$ can induce wild changes in the shape of the corresponding density fβ$$ {f}_{\beta } $$. The authors show how to estimate β$$ \beta $$ and fβ$$ {f}_{\beta } $$ effectively through a penalized likelihood procedure involving differential regularization. The approach combines a penalized regression method and a profiled estimation technique. Simulations and an illustration with S&P 500 data suggest that the proposed method can improve market risk assessment substantially through value‐at‐risk and expected shortfall estimates that outperform those currently used by financial institutions and regulators. [ABSTRACT FROM AUTHOR]

An advantage of the standard mixture cure model over an usual survival model is how it accounts for the population heterogeneity. It allows a joint estimation for the distribution related to the susceptible and non‐susceptible subjects. The estimation algorithm may provide ±∞$$ \pm \infty $$ coefficients when the likelihood cannot be maximized. This phenomenon is known as Monotone Likelihood (ML), common in survival and logistic regressions. The ML tends to appear in situations with small sample size, many censored times, many binary or unbalanced covariates. Particularly, it occurs when all uncensored cases correspond to one level of a binary covariate. The existing frequentist solution is an adaptation of the Firth correction, originally proposed to reduce bias of maximum likelihood estimates. It prevents ±∞$$ \pm \infty $$ estimates by penalizing the likelihood, with the penalty interpreted as the Bayesian Jeffreys prior. In this paper, the penalized likelihood of the standard mixture cure model is considered with different penalties (Bayesian priors). A Monte Carlo simulation study indicates good inference results, especially for balanced data sets. Finally, a real application involving a melanoma data illustrates the approach. [ABSTRACT FROM AUTHOR]

We propose a semiparametric regression defined from the generalized odd log-logistic Maxwell distribution under the cubic spline with linear and nonlinear effects for censored and uncensored data. The parameter estimates for this regression are determined using penalized likelihood. Global influence diagnostics and quantile residuals are addressed in new standards. Several Monte Carlo simulations investigate the consistency of the estimates. The usefulness of the new regression is illustrated by means of two applications to real data. [ABSTRACT FROM AUTHOR]

Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This article investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approximation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference. [ABSTRACT FROM AUTHOR]

Covariance estimation for high-dimensional datasets is a fundamental problem in machine learning, and has numerous applications. In these high-dimensional settings the number of features or variables p is typically larger than the sample size n. A popular way of tackling this challenge is to induce sparsity in the covariance matrix, its inverse or a relevant transformation. In many applications, the data come with a natural ordering. In such settings, methods inducing sparsity in the Cholesky parameter of the inverse covariance matrix can be quite useful. Such methods are also better positioned to yield a positive definite estimate of the covariance matrix, a critical requirement for several downstream applications. Despite some important advances in this area, a principled approach to general sparse-Cholesky based covariance estimation with both statistical and algorithmic convergence safeguards has been elusive. In particular, the two popular likelihood based methods proposed in the literature either do not lead to a well-defined estimator in high-dimensional settings, or consider only a restrictive class of models. In this paper, we propose a principled and general method for sparse-Cholesky based covariance estimation that aims to overcome some of the shortcomings of current methods, but retains their respective strengths. We obtain a jointly convex formulation for our objective function, and show that it leads to rigorous convergence guarantees and well-defined estimators, even when p> n. Very importantly, the approach always leads to a positive definite and symmetric estimator of the covariance matrix. We establish both high-dimensional estimation and selection consistency, and also demonstrate excellent finite sample performance on simulated/real data.

When the data are stored in a distributed manner, direct applications of traditional statistical inference procedures are often prohibitive due to communication costs and privacy concerns. This article develops and investigates two communication-efficient accurate statistical estimators (CEASE), implemented through iterative algorithms for distributed optimization. In each iteration, node machines carry out computation in parallel and communicate with the central processor, which then broadcasts aggregated information to node machines for new updates. The algorithms adapt to the similarity among loss functions on node machines, and converge rapidly when each node machine has large enough sample size. Moreover, they do not require good initialization and enjoy linear converge guarantees under general conditions. The contraction rate of optimization errors is presented explicitly, with dependence on the local sample size unveiled. In addition, the improved statistical accuracy per iteration is derived. By regarding the proposed method as a multistep statistical estimator, we show that statistical efficiency can be achieved in finite steps in typical statistical applications. In addition, we give the conditions under which the one-step CEASE estimator is statistically efficient. Extensive numerical experiments on both synthetic and real data validate the theoretical results and demonstrate the superior performance of our algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of simultaneous variable selection and estimation in the random‐intercepts model with the first‐order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra‐class correlation, and the first lagged response to address the serial correlation, which are two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring correlation among random effects and initial responses can lead to biased regularized estimates. Furthermore, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of dynamic random‐intercepts models leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low‐ and high‐dimensional settings and evaluate regularized estimators' performances by conducting simulation studies and analyzing a real dataset. Supporting information is available online. [ABSTRACT FROM AUTHOR]

This article concerns maximum penalized likelihood estimation in misspecified generalized linear models with independent and identically distributed observations. A new method for simultaneous model selection and estimation with bias reduction is proposed in the framework. A discontinuous penalized likelihood function is used, and an approximate method to solve the discontinuous optimization problem is introduced. The proposed method has model selection consistency in a sparse regression setting in which the dimension of predictors is fixed and the sample size increases. The efficiency of the proposed method is illustrated through a finite simulation study. [ABSTRACT FROM AUTHOR]

Time‐varying covariates can be important predictors when model based predictions are considered. A Cox model that includes time‐varying covariates is usually referred to as an extended Cox model. When only right censoring is presented in the observed survival times, the conventional partial likelihood method is still applicable to estimate the regression coefficients of an extended Cox model. However, if there are interval‐censored survival times, then the partial likelihood method is not directly available unless an imputation, such as the middle point imputation, is used to replaced the left‐ and interval‐censored data. However, such imputation methods are well known for causing biases. This paper considers fitting of the extended Cox models using the maximum penalised likelihood method allowing observed survival times to be partly interval censored, where a penalty function is used to regularise the baseline hazard estimate. We present simulation studies to demonstrate the performance of our proposed method, and illustrate our method with applications to two real datasets from medical research. [ABSTRACT FROM AUTHOR]

In this paper, we present a new regularized image reconstruction method for positron emission tomography (PET), where an adaptive weighted median regularizer is used in the context of a penalized-likelihood framework. The motivation of our work is to overcome the limitation of the conventional median regularizer, which has proven useful for tomographic reconstruction but suffers from the negative effect of removing fine details in the underlying image when the edges occupy less than half of the window elements. The crux of our method is inspired by the well-known non-local means denoising approach, which exploits the measure of similarity between the image patches for weighted smoothing. However, our method is different from the non-local means denoising approach in that the similarity measure between the patches is used for the median weights rather than for the smoothing weights. As the median weights, in this case, are spatially variant, they provide adaptive median regularization achieving high-quality reconstructions. The experimental results indicate that our similarity-driven median regularization method not only improves the reconstruction accuracy, but also has great potential for super-resolution reconstruction for PET.

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a sequence of smooth, unconstrained subproblems. These subproblems are generated and solved via the proximal distance version of the majorization-minimization principle. The resulting algorithm executes rapidly, gracefully handles settings where the number of parameters exceeds the number of cases, yields a positive-definite solution, and enjoys desirable convergence properties. Empirically, we demonstrate that our approach outperforms competing methods across several metrics, for a suite of simulated experiments. Its merits are illustrated on international migration data and a case study on flow cytometry. Our findings suggest that the marginal and conditional dependency networks for the cell signalling data are more similar than previously concluded. [ABSTRACT FROM AUTHOR]

Practitioners as well as some statistics students often blindly use standard software or algorithms to get maximum likelihood estimator (MLE) without checking the validity of existence of such an estimator. Even in simple situations where data comes from mixtures of Gaussians, global MLE does not exist. This note is intended as a teachers corner, highlighting existential issues related to MLE for mixture models, even when the components are not necessarily Gaussian. [ABSTRACT FROM AUTHOR]

Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where they tend to be over-parameterized. As a consequence, different solutions have been proposed, often relying on matrix decompositions or variable selection strategies. Recently, a methodological link between Gaussian graphical models and finite mixtures has been established, paving the way for penalized model-based clustering in the presence of large precision matrices. Notwithstanding, current methodologies implicitly assume similar levels of sparsity across the classes, not accounting for different degrees of association between the variables across groups. We overcome this limitation by deriving group-wise penalty factors, which automatically enforce under or over-connectivity in the estimated graphs. The approach is entirely data-driven and does not require additional hyper-parameter specification. Analyses on synthetic and real data showcase the validity of our proposal. [ABSTRACT FROM AUTHOR]