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This article is concerned with model averaging for de-noise linear models, in which some covariates are not observed, but their ancillary variables are available. The least-squares-based estimation procedure is used to estimate the unknown regression parameter in each candidate model after the calibrated error-prone covariates are obtained. Then a Mallows-type weight choice criterion is constructed. When all candidate models are misspecified, the model averaging estimator is asymptotically optimal in the sense that achieving the lowest possible squared error. On the other hand, when the true model is included in the set of candidate models, the model averaging estimator of the regression parameter is root n consistent. The finite sample performance of our model averaging estimator is evaluated by some simulation studies. The proposed procedure is further applied to real-data analysis. [ABSTRACT FROM AUTHOR]

We propose an extension of the double autoregressive (DAR) model: the sign-double autoregressive (SDAR) model, in the spirit of the GJR-GARCH model (also named the sign-ARCH model). Our model shares the important property of DAR models where a unit root does not imply non stationarity and it allows for asymmetry, as other alternatives in the literature such as the GJR-GARCH or asymmetric linear DAR and dual-asymmetry linear DAR models. We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the context of the SDAR model. Furthermore, it is shown by simulations that the asymptotic properties also apply in finite samples. Finally, an empirical application shows the usefulness of our model specially in periods of supply/demand crises of oil disruptions, where spikes of volatility are very likely to be predominant. [ABSTRACT FROM AUTHOR]

Abstract.In this article, we research the asymptotic properties of least squares estimation for fractional Brownian bridge with linear drift dXt=α(θ−Xt)T−tdt+dBtH,  0≤tX0 = x0, where α>0,θ∈R and γ≜αθ are unknown parameters, BH is fractional Brownian motion with Hurst index H∈(1/2,1), as well as T > 0. Based on the continuous-time observation, we obtain the estimators α̂,γ̂ and θ̂ for α, γ, and θ. Depending on the value of α, we can have the strong consistency or not as t→T. Since these estimates do not formally depend on the value of θ, we also get the rate of these convergences when the consistency holds in both θ≠0 and θ = 0 case. This work extends the results of Es-Sebaiy and Nourdin (2013) studied in the case where θ = 0 is known. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating an unknown parameter vector θ ∈ R n , given noisy observations Y = θ θ T / n + Z of the rank-one matrix θ θ T , where Z has independent Gaussian entries. When information is available about the distribution of the entries of θ , spectral methods are known to be strictly sub-optimal. Past work characterized the asymptotics of the accuracy achieved by the optimal estimator. However, no polynomial-time estimator is known that achieves this accuracy. It has been conjectured that this statistical-computation gap is fundamental, and moreover that the optimal accuracy achievable by polynomial-time estimators coincides with the accuracy achieved by certain approximate message passing (AMP) algorithms. We provide evidence towards this conjecture by proving that no estimator in the (broader) class of constant-degree polynomials can surpass AMP. [ABSTRACT FROM AUTHOR]

Ridge regression is an effective tool to handle multicollinearity in regressions. It is also an essential type of shrinkage and regularization methods and is widely used in big data and distributed data applications. The divide and conquer trick, which combines the estimator in each subset with equal weight, is commonly applied in distributed data. To overcome multicollinearity and improve estimation accuracy in the presence of distributed data, we propose a Mallows-type model averaging method for ridge regressions, which combines estimators from all subsets. Our method is proved to be asymptotically optimal allowing the number of subsets and the dimension of variables to be divergent. The consistency of the resultant weight estimators tending to the theoretically optimal weights is also derived. Furthermore, the asymptotic normality of the model averaging estimator is demonstrated. Our simulation study and real data analysis show that the proposed model averaging method often performs better than commonly used model selection and model averaging methods in distributed data cases. [ABSTRACT FROM AUTHOR]

With the advent of modern devices, such as smartphones and wearable devices, high-dimensional data are collected on many participants for a period of time or even in perpetuity. For this type of data, dependencies between and within data batches exist because data are collected from the same individual over time. Under the framework of streamed data, individual historical data are not available due to the storage and computation burden. It is urgent to develop computationally efficient methods with statistical guarantees to analyze high-dimensional streamed data and make reliable inferences in practice. In addition, the homogeneity assumption on the model parameters may not be valid in practice over time. To address the above issues, in this paper, we develop a new renewable debiased-lasso inference method for high-dimensional streamed data allowing dependences between and within data batches to exist and model parameters to gradually change. We establish the large sample properties of the proposed estimators, including consistency and asymptotic normality. The numerical results, including simulations and real data analysis, show the superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

To learn the subgroup structure generated by multidimensional interaction, we propose a novel multiview subgroup integration technique based on tensor decomposition. Compared to the traditional subgroup analysis that can only handle single-view heterogeneity, our proposed method achieves a greater level of homogeneity within the subgroups, leading to enhanced interpretability and predictive power. For computational readiness of the proposed method, we build an algorithm that incorporates pairwise shrinkage-encouraging penalties and ADMM techniques. Theoretically, we establish the asymptotic consistency and normality of the proposed estimators. Extensive simulation studies and real data analysis demonstrate that our proposal outperforms other methods in terms of prediction accuracy and grouping consistency. In addition, the analysis based on the proposed method indicates that intergenerational care significantly increases the risk of chronic diseases associated with diet and fatigue in all provinces while only reducing the risk of emotion-related chronic diseases in the eastern coastal and central regions of China. [ABSTRACT FROM AUTHOR]

This paper focuses on the estimation of parameters in linear models with fixed regressors and exchangeable errors, especially, these errors are assumed to be a subset of an infinite exchangeable sequence. We propose a modified M-estimation to estimate the slope parameter, which outperforms the traditional M-estimation when the random errors are exchangeable. The modified M-estimation utilizes a design point centralization technique, leading to a more suitable estimator with improved theoretical properties. To establish the asymptotic properties of the modified M-estimator, we also develop a weighted central limit theorem for exchangeable sequences, which is of independent interest. Regarding the intercept, we prove that there is no consistent estimator for the intercept when the exchangeable errors have non-zero covariance, and we propose an unbiased estimator for the intercept as a viable compromise. Based on our theoretical findings, we develop a simulation-based approach to approximate the confidence set of the slope, and we establish a prediction model specifically designed for linear models with exchangeable errors. Additionally, we illustrate the finite sample performance of the proposed method through various numerical simulations and a real data application. [ABSTRACT FROM AUTHOR]

Inequality (concentration) curves such as Lorenz, Bonferroni, Zenga curves, as well as a new inequality curve – the D curve, are broadly used to analyse inequalities in wealth and income distribution in certain populations. Quantile versions of these inequality curves are more robust to outliers. We discuss several parametric estimators of quantile versions of the Zenga and D curves. A minimum distance (MD) estimator is proposed for these two curves and the indices related to them. The consistency and asymptotic normality of the MD estimator is proved. The MD estimator can also be used to estimate the inequality measures corresponding to the quantile versions of the inequality curves. The estimation methods considered are illustrated in the case of the Weibull model, which has many applications in life sciences, for example, to fit the precipitation data. In econometrics it is also considered to fit incomes, especially in the case when a significant share of population have low incomes, for example, in less developed countries or among low-paid jobs. [ABSTRACT FROM AUTHOR]

In this paper, we focus on model selection problem for conditional density function when response variables are right-censored with censoring indicators missing at random. We propose three model selection criteria based on the Kullback–Leibler divergence and define corresponding parametric estimators. At the same time, we construct Wald test statistics of hypothesis testing on the parameters. Under suitable conditions, the consistency of proposed criteria as well as asymptotic distributions of estimators and test statistics are established. Also, simulation study and real data analysis are conducted to evaluate finite-sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

The symmetric nonlinear regression model encompasses a wide class of models like the nonlinear normal, Student-t, and power exponential regression models, among others. We provide a simple closed-form expression, in matrix form, for the second-order skewness of the maximum likelihood estimators of the regression parameters, as well as a simple expression for the second-order skewness of the maximum likelihood estimator of the scale parameter in the symmetric nonlinear regression model. The matrix formula involves simple operations on matrices and vectors, which is quite suitable for computer implementation. We present Monte Carlo simulations to verify the behaviour of the second-order skewness in small-sized samples in this class of regression models. Real data applications are also considered to show the practical importance of our results. [ABSTRACT FROM AUTHOR]

The Bradley-Terry model is a common model for analyzing paired comparison data. Under differential private mechanism, there is a lack of asymptotic properties for the parameter estimator of parameters in this model. In this article, we show that the moment estimators of the parameters based on the differential private degree sequence with Laplace noise is uniformly consistent and asymptotically normal. Simulations are provided to illustrate asymptotic results. [ABSTRACT FROM AUTHOR]

Abstract.We study the probability tail properties of Inverse probability weighting (IPW) estimators of the average treatment effect (ATE) when there is limited overlap between the covariate distributions of the treatment and control groups. Under unconfoundedness of treatment assignment conditional on covariates, such limited overlap is manifested in the propensity score for certain units being very close (but not equal) to 0 or 1. This renders IPW estimators possibly heavy tailed, and with a slower than n rate of convergence. Historically estimators are either based on the assumption of strict overlap, i.e., the propensity score is bounded away from 0 and 1; or they truncate the propensity score; or trim observations based on a variety of techniques based on covariate or propensity score values. Trimming or truncation is ultimately based on the covariates, ignoring important information about the inverse probability weighted random variable Z that identifies ATE by E[Z] = ATE. We propose a tail-trimmed IPW estimator whose performance is robust to limited overlap. In terms of the propensity score, which is generally unknown, we plug-in its parametric estimator in the infeasible Z, and then negligibly trim the resulting feasible Z adaptively by its large values. Trimming leads to bias if Z has an asymmetric distribution and an infinite variance, hence we estimate and remove the bias using important improvements on existing theory and methods. Our estimator sidesteps dimensionality, bias and poor correspondence properties associated with trimming by the covariates or propensity score. Monte Carlo experiments demonstrate that trimming by the covariates or the propensity score requires the removal of a substantial portion of the sample to render a low bias and close to normal estimator, while our estimator has low bias and mean-squared error, and is close to normal, based on the removal of very few sample extremes. [ABSTRACT FROM AUTHOR]

Consider the following generalized linear model (GLM) y i = h (x i T β) + e i , i = 1 , 2 , ... , n , where h(.) is a continuous differentiable function, { e i } are independent identically distributed (i.i.d.) random variables with zero mean and known variance σ 2 . Based on the penalized Lq-likelihood method of linear regression models, we apply the method to the GLM, and also investigate Oracle properties of the penalized Lq-likelihood estimator (PLqE). In order to show the robustness of the PLqE, we discuss influence function of the PLqE. Simulation results support the validity of our approach. Furthermore, it is shown that the PLqE is robust, while the penalized maximum likelihood estimator is not. [ABSTRACT FROM AUTHOR]

This paper aims to study the non parametric Negative Binomial Quasi-Maximum Likelihood Estimation (NBQMLE) for locally stationary integer valued processes. So, we have considered two locally stationary integer-valued models of negative binomial type, namely: INARCH (p) and INGARCH (p , q) models. Imposing some contraction arguments, we have extended the stationary negative-binomial QMLE to a localized one in our non-stationary environment. This estimation method is based on a kernel function that achieves the convergence rates of n h n order. Under some regularity assumptions, the consistency, as well as the asymptotic normality of the obtained estimator, are established. The performances of the established estimators are evaluated via a simulation study and an application to real data set. [ABSTRACT FROM AUTHOR]

Based on the expectile loss function and the adaptive LASSO penalty, the paper proposes and studies the estimation methods for the accelerated failure time (AFT) model. In this approach, we need to estimate the survival function of the censoring variable by the Kaplan–Meier estimator. The AFT model parameters are first estimated by the expectile method and afterwards, when the number of explanatory variables can be large, by the adaptive LASSO expectile method which directly carries out the automatic selection of variables. We also obtain the convergence rate and asymptotic normality for the two estimators, while showing the sparsity property for the censored adaptive LASSO expectile estimator. A numerical study using Monte Carlo simulations confirms the theoretical results and demonstrates the competitive performance of the two proposed estimators. The usefulness of these estimators is illustrated by applying them to three survival data sets. [ABSTRACT FROM AUTHOR]

For differential privacy under sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this article, we release the degree sequences of the binary networks under a general noisy mechanism, with the discrete Laplace mechanism as a special case. We establish the asymptotic result, including both consistency and asymptotically normality, of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real-data example are provided to illustrate the asymptotic results. [ABSTRACT FROM AUTHOR]

We investigate the parameter estimation and prediction of two forms of the stochastic SIR model driven by small Lévy noise with time-dependent periodic transmission. We present consistency and rate of convergence results for the least-squares estimators. We include simulation studies using the method of projected gradient descent. [ABSTRACT FROM AUTHOR]

The article concerns the problem of parameter estimation for Type-I censored data using general estimating equations. It proposes a new class of estimators that are analogs to the estimators obtained by the method of moments for complete samples. It is proved that the proposed estimators are exactly the maximum likelihood estimators in the class of distributions from the exponential family. The asymptotic properties of the presented estimators are compared to the maximum likelihood ones. The obtained results are presented jointly with a simulation study and computational examples. [ABSTRACT FROM AUTHOR]

Let $ \{X_{i},1\leq i\leq n\} $ { X i , 1 ≤ i ≤ n } be a sequence of linear process based on dependent random variables with random coefficients, which has a mean shift at an unknown location. The weighted sum of powers in mean (WSPM, for short) estimator of the change point is proposed. The weak consistency, the rate of weak consistency and strong consistency for the WSPM estimator are established under some mild conditions. Simulation studies and two real data exercises are also provided to show the superiority of this new method to some existing methods. [ABSTRACT FROM AUTHOR]

AbstractThe appearance of measurement errors and multicollinearity in data are two problematic issues that adversely affect the estimation of regression coefficients. In such circumstances, concerning regression coefficients, it can be practicable to utilize some prior information in the type of stochastic linear restrictions. The main purpose of this article is to overcome the problems of measurement errors and multicollinearity concurrently by utilizing stochastic prior information for the estimation of model coefficients in replicated ultrastructural measurement error (RUME) models. To this end, three classes of stochastic restricted estimators and their feasible forms are proposed. Large sample properties of newly introduced estimators are studied without making any distributional assumption. To evaluate the performance of newly defined estimators a numerical example is done by using real data, Cigar data set, and a Monte Carlo simulation study is also conducted. It is concluded that the newly proposed stochastic restricted estimators outperform the predefined estimators for the RUME models in the existence of multicollinearity. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we investigate the complete moment convergence and the Marcinkiewicz-Zygmund-type strong law of large numbers (SLLN, for short) for weighted sums of asymptotically negatively associated (ANA, for short) random variables. The results generalize and improve the corresponding one of Vu et al. (J. Theor. Probab. 34: 331-348, 2021) to the case of ANA random variables. With some properties of slowly varying function, three equivalent conditions of convergence properties for ANA sequences are established, as well as the SLLN for weighted sums of ANA random variables. As an application, the strong consistency of the least squared (LS, for short) estimators in an errors-in-variables (EV, for short) model based on ANA random errors is established. We also give a simulation to support the theoretical result based on finite samples. [ABSTRACT FROM AUTHOR]

In this article, we investigate a linear model that incorporates stationary causal processes, with a focus on utilizing Huber-Dutter methods to investigate the estimators of unknown parameters and a scale for the errors. Our results indicate that the Huber-Dutter methods can effectively be utilized for linear models that feature errors, which are short-range dependent linear processes, heavy-tailed linear processes, as well as some commonly used non linear time series. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of periodic integer-valued autoregressive BL-PINAR(1) models with Bell innovations distribution based on the binomial thinning operator. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed forms of these moments are, under the obtained conditions, derived. Furthermore, the periodic autocovariance structure is also considered while providing the closed form of the periodic autocorrelation function. The conditional least squares (CLS), Yule–Walker (YW), weighted conditional least squares (WCLS), and conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters. The asymptotic properties of the CLS and the YW estimators are obtained. The performances of these methods are compared through a simulation study. An application on a real data set is provided. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a first-order Periodic Generalized Poisson Integer-Valued Autoregressive model PGPINAR (1) which has been shown to be useful to describe overdispersion, equidispersion and underdispersion feature encountered in periodically correlated Integer-Valued time series. Some probabilistic and statistical properties are established, such as the periodically correlated stationarity conditions, in the first and the second moments are provided and the closed-forms of these moments are, under these conditions, derived. Moreover, the structure of the periodic autocovariance is obtained. The estimation problem is addressed through the Yule-Walker (YW) , the Two-Stage Conditional Least Squares (CLS) and the Conditional Maximum Likelihood (CML) methods. The performance of these methods is done through an intensive simulation study and an application on real data set is accomplished. Keywords and phrases: Periodic Generalized Poisson, Integer-Valued Autoregressive, Periodically correlated process, periodically stationary condition. [ABSTRACT FROM AUTHOR]

In the present paper, we are mainly concerned with the statistical inference for the functional of nonparametric copula models satisfying linear constraints. The asymptotic properties of the obtained estimates and test statistics are given. Finally, a general notion of bootstrap for the proposed estimates and test statistics, constructed by exchangeably weighting sample, is presented, which is of its own interest. These results are proved under some standard structural conditions on some classes of functions and some mild conditions on the model, without assuming anything about the marginal distribution functions, except continuity. Our theoretical results and numerical examples by simulations demonstrate the merits of the proposed techniques. [ABSTRACT FROM AUTHOR]

In real data analysis, the underlying model is frequently unknown. Hence, the modeling strategy plays a key role in the success of data analysis. Inspired by the idea of model averaging, we propose a novel semiparametric modeling strategy for the conditional quantile prediction, without assuming that the underlying model is any specific parametric or semiparametric model. Due to the optimality of the weights selected by leave-one-out cross-validation, the proposed modeling strategy provides a more precise prediction than those based on some commonly used semiparametric models such as the varying coefficient and additive models. Asymptotic properties are established in the proposed modeling strategy along with its estimation procedure. We conducted extensive simulations to compare our method with alternatives across various scenarios. The results show that our method provides more accurate predictions. Finally, we applied our approach to the Boston housing data, yielding more precise quantile predictions of house prices compared with commonly used methods, and thus offering a clearer picture of the Boston housing market. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an approximative maximum likelihood estimator (MLE) for the drift coefficient of a stochastic partial differential equation in the case where the corresponding Fourier coefficients u k (t) , k = 1 , ... , N over a finite interval of time [ 0 , T ] are observed on a uniform time grid: 0 = t 0 < t 1 < ⋯ < t M = T , with Δ : = t i − t i − 1 = T / M , i ˙ = 1 , ... , M . We provide an explicit Berry–Esseen bound in Kolmogorov distance for this approximative MLE when N , M , T → ∞ , assuming that T 3 N 7 / M 2 → 0 and N 2 / T → 0 . [ABSTRACT FROM AUTHOR]

In this article, we utilize the contrast function of the integrated diffusion process to derive parameter contrast estimators for the Cox-Ingersoll-Ross integrated diffusion process and discuss the asymptotic properties of the estimators using the mixing properties of the process. We first give the tail probability exponential inequality of the mixing long-span high-frequency data. Then, applying this inequality, we prove the strong consistency of the contrast estimators for the drift parameters and diffusion parameter of the CIR integrated diffusion process. In order to obtain these asymptotic properties, we require relatively low order r of the negative power moment E | X t − 1 | r of the diffusion process. In the existing literature, r > 9 is required in order to obtain weak consistency of the estimators. However, in our theorems, only r > 2 is required for the strong consistency of the diffusion parameter estimator, while r > 4 for the strong consistency of the drift parameter estimators. In the simulation analysis, we use the Euler discretization algorithm and the Milstein discretization algorithm, and the results show that the optimal sampling interval is around n − 1 / 3 . We use the daily log price data of the CSI 300 Index to estimate the CIR integrated diffusion model and construct a Bootstrap prediction model for the log price. The results show that the model has a good predictive performance. [ABSTRACT FROM AUTHOR]

This paper provides a least squares regression estimation of the tail index for long memory processes where the innovations are α -stable random sequences. The estimate is based on the property of the characteristic function of the process near the origin. The asymptotics of the estimator are obtained by choosing suitable regression samples with the help of the properties of the α -stable distribution. The numerical simulation and an empirical analysis of financial market data are conducted to assess the finite sample performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

Normal cluster-weighted models constitute a modern approach to linear regression which simultaneously perform model-based cluster analysis and multivariate linear regression analysis with random quantitative regressors. Robustified models have been recently developed, based on the use of the contaminated normal distribution, which can manage the presence of mildly atypical observations. A more flexible class of contaminated normal linear cluster-weighted models is specified here, in which the researcher is free to use a different vector of regressors for each response. The novel class also includes parsimonious models, where parsimony is attained by imposing suitable constraints on the component-covariance matrices of either the responses or the regressors. Identifiability conditions are illustrated and discussed. An expectation-conditional maximisation algorithm is provided for the maximum likelihood estimation of the model parameters. The effectiveness and usefulness of the proposed models are shown through the analysis of simulated and real datasets. [ABSTRACT FROM AUTHOR]

In practice, the failure type for some subjects may be missing or uncertain in competing risks data. Analysis of such uncertain failure type in current status data with two competing risks suffers from issues of model identifiability and requires some model assumptions to deal with that (Koley and Dewanji. Journal of Applied Statistics 49(7), (2022)). In this work, we attempt to alleviate this identifiability problem using some additional information and without any such model assumption. In particular, we consider additional information in the form of some prior knowledge on the missing probabilities. Next, we briefly discuss another type of additional information from a validation sample which ascertains failure type. We consider parametric estimation of the model parameters and non-parametric estimation of the sub-distribution functions. We investigate the associated large sample properties theoretically and the finite sample properties through simulation. We also consider analysis of a real data set for the purpose of illustration. [ABSTRACT FROM AUTHOR]

In this article, estimation for a new capability index S pmk ′ which is based on asymmetric loss function (linear-exponential) is discussed when the underlying process follows generalized exponential distribution. Various estimates of the model parameters are proposed including maximum likelihood method, bias-corrected maximum likelihood method and bootstrap bias-corrected maximum likelihood method, and subsequently the process capability index S pmk ′ are obtained. Through extensive simulation studies, we compare the performance of the aforementioned methods of estimation for the PCI S pmk ′ in terms of their absolute bias (AB) and mean squared errors (MSEs). Besides, four bootstrap methods are employed for constructing the confidence intervals for the index S pmk ′ by using the considered methods of estimation. Monte Carlo simulations are performed to compare the performances of the bootstrap confidence intervals (BCIs) with respect to average widths and coverage probabilities. Finally, to show the effectiveness of the proposed methods of estimation and BCIs, two published data sets related to electronic and food industries are analyzed. Simulation results showed that the bootstrap bias corrected maximum likelihood method of estimation gives the best results among other estimation methods in terms of AB and MSEs, while the two real data sets show that width of bias-corrected accelerated bootstrap interval is minimum among all other considered BCIs. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the following nearly nonsationary autoregressive model: y t = q n y t - 1 + u t , t = 1 , ... , n , where q n = 1 + c / k n with c a non-zero constant and { k n , n ⩾ 1 } a sequence of positive constants increasing to ∞ such that k n = o (n) as n → ∞ , and { u t , t ⩾ 1 } is a sequence of independent and identically distributed random variables which are in the domain of attraction of the normal law with zero mean and possibly infinity variance. The weighted composite quantile estimate of q n is examined, and the corresponding limiting distributions under the cases of c > 0 and c < 0 are established. Monte Carlo simulations are conducted to illustrate the theoretical results on finite-sample performance. The simulation results show that the weighted composite quantile estimate method is more robust and efficient than the composite quantile estimate method in terms of bias and accuracy, and we employ this estimator to analyze a real-world data set. [ABSTRACT FROM AUTHOR]

In the past two decades, model averaging has attracted more and more attention and is regarded as a much better tool to solve model uncertainty than model selection. Compared with the conditional mean regression, the quantile regression serves as a robust alternative and shows a lot more information about the conditional distribution of a response variable. In this paper, we propose a jackknife model averaging procedure that chooses the weights by minimizing a leave-one-out cross-validation criterion function for mixed-data kernel-weighted spline quantile regressions that contain both continuous and categorical regressors when all candidate models are potentially misspecified. We demonstrate the JMA estimator is asymptotically optimal in terms of minimizing the out-of-sample final prediction error. Simulation experiments are conducted to assess the relative finite-sample performance of the proposed JMA method with respect to other model selection and averaging methods. Our JMA method is applied to the wage and house datasets. [ABSTRACT FROM AUTHOR]

This paper deals with some probabilistic and statistical properties of periodic generalized Poisson integer-valued autoregressive processes of order p, PG P INAR (p). Necessary and sufficient conditions for the periodic stationarity, both in mean and second order, are established. The closed-forms of the mean and the second moment are, under these conditions, obtained. Moreover, the Wold–Cramér expression of the underlying second-order periodically stationary process is then established. The autocovariance structure is studied, while providing the closed-form of the periodic autocorrelation function. The Yule–Walker (YW), the two-stage conditional least squares (CLS) and the conditional maximum likelihood (CML) estimation methods of the underlying parameters are obtained. An intensive simulation study and an application on a real count data consisting of the daily number of daytime road accidents in Schiphol area, in Netherlands are provided. [ABSTRACT FROM AUTHOR]

The compound Poisson process (CPP) is a common mathematical model for describing many phenomena in medicine, reliability theory and risk theory. However, in the case of low-frequency phenomena, we are often unable to collect a sufficiently large database to conduct analysis. In this article, we focused on methods for determining confidence intervals for the rate of the CPP when the sample size is small. Based on the properties of process parameter estimators, we proposed a new method for constructing such intervals and compared it with other known approaches. In numerical simulations, we used synthetic data from several continuous and discrete distributions. The case of CPP, in which rewards came from exponential distribution, was discussed separately. The recommendation of how to use each method to have a more precise confidence interval is given. All simulations were performed in R version 4.2.1. [ABSTRACT FROM AUTHOR]

Analysis of binary matched pairs data is problematic due to infinite maximum likelihood estimates of the log odds ratio and potentially biased estimates, especially for small samples. We propose a penalised version of the log-likelihood function based on adjusted responses which always results in a finite estimator of the log odds ratio. The probability limit of the adjusted log-likelihood estimator is derived and it is shown that in certain settings the maximum likelihood, conditional and modified profile log-likelihood estimators drop out as special cases of the former estimator. We implement indirect inference to the adjusted log-likelihood estimator. It is shown, through a complete enumeration study, that the indirect inference estimator is competitive in terms of bias and variance in comparison to the maximum likelihood, conditional, modified profile log-likelihood and Firth's penalised log-likelihood estimators. [ABSTRACT FROM AUTHOR]

We consider a linear model with a change point according to the unknown random threshold of a covariate. We give the expectation-maximization (EM) estimation of the regression and change point parameters. The existence of the random change point is detected by the supremum (SUP) test of score statistics. Theoretically, we establish the convergence and asymptotic distribution of the estimation and show that the EM estimates converge in distribution to a normal distribution. In addition, the numerical performance of the proposed approach is demonstrated through simulation studies. Finally, applying our methodology to household financial decisions, we see that the average debt tolerance of Chinese households is estimated to be 1.1364 times the sum of total household income and financial assets. The effect of assets and income on consumption shows a rapid decline if the household exceeds the average debt tolerance. [ABSTRACT FROM AUTHOR]

We analyse a second-order SPDE model in multiple space dimensions and develop estimators for the parameters of this model based on discrete observations of a solution in time and space on a bounded domain. While parameter estimation for one and two spatial dimensions was established in recent literature, this is the first work which generalizes the theory to a general, multi-dimensional framework. Our approach builds upon realized volatilities, enabling the construction of an oracle estimator for volatility within the underlying model. Furthermore, we show that the realized volatilities have an asymptotic illustration as response of a log-linear model with spatial explanatory variable. This yields novel and efficient estimators based on realized volatilities with optimal rates of convergence and minimal variances. For proving central limit theorems, we use a high-frequency observation scheme. To showcase our results, we conduct a Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of the Hurst parameter, the diffusion parameter and the drift, which lies in a parametrised family of coercive drift coefficients. Our procedure is based on the assumption that the stationary distribution of the SDE and of its increments permits to identify the parameters of the model. Under this assumption, we prove consistency results and derive a rate of convergence for the estimator. Finally, we show that the identifiability assumption is satisfied in the case of a family of fractional Ornstein–Uhlenbeck processes and illustrate our results with some numerical experiments. [ABSTRACT FROM AUTHOR]

A useful strategy to examine serial correlation in panel regression models is to adopt serially correlated error terms. The random effect is also present to address the individual-specific heterogeneity. Familiar transformations can restructure the AR(1) process into a serially uncorrelated dynamic model. It may result in unfitting estimation results once the statistical inference is carried on the conditional likelihood. We discuss in the article the consequence of this action. In particular, in the case of large cross-section units and short time-sequences, we provide analytical expressions for the asymptotic bias of maximum likelihood estimates when the analyst naïvely neglects the initial conditions problem. Under several conditions, we compute the size of biases and measure the mean squared errors to illustrate this violation. We also construct a joint regression model of the initial and subsequent responses to handle the initial conditions. Then, we conduct simulation studies to determine the asymptotic behavior. [ABSTRACT FROM AUTHOR]

We consider model averaging estimation problem in the linear regression model with missing response data, that allows for model misspecification. Based on the 'complete' data set for the response variable after inverse propensity score weighted imputation, we construct a leave-one-out cross-validation criterion for allocating model weights, where the propensity score model is estimated by the covariate balancing propensity score method. We derive some theoretical results to justify the proposed strategy. Firstly, when all candidate outcome regression models are misspecified, our procedures are proved to achieve optimality in terms of asymptotically minimizing the squared loss. Secondly, when the true outcome regression model is among the set of candidate models, the resulting model averaging estimators of the regression parameters are shown to be root-n consistent. Simulation studies provide evidence of the superiority of our methods over other existing model averaging methods, even when the propensity score model is misspecified. As an illustration, the approach is further applied to study the CD4 data. [ABSTRACT FROM AUTHOR]

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators. [ABSTRACT FROM AUTHOR]

This paper proposes a novel estimator for support vector machines with matrix-valued covariates in a high-dimensional setting. We assume that the underlying parameter matrix lies in a low-dimensional subspace that is simultaneously low-rank and row (column) sparse. We formulate the problem as a regularized hinge loss minimization problem using the nuclear and group lasso norms as penalties to exploit the low-dimensional structure. Our primary focus is deriving the statistical convergence rate of the regularized estimator for the unknown parameter matrix. To validate our theoretical findings, we conducted numerical experiments on both simulated and real-world datasets, demonstrating the efficacy of the regularized support matrix machines framework. [ABSTRACT FROM AUTHOR]

We analyze issues related to estimation and inference for the constrained sum of squares estimator (CSS) of the k-factor Gegenbauer autoregressive moving average (GARMA) model. We present theoretical results for the estimator and show that the parameters that determine the cycle lengths are asymptotically independent, converging at rate T, the sample size, for finite cycles. The remaining parameters lack independence and converge at the standard rate. Analogous with existing literature, some challenges exist for testing the hypothesis of non-cyclical long memory, since the associated parameter lies on the boundary of the parameter space. We present simulation results to explore small sample properties of the estimator, which support most distributional results, while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume. [ABSTRACT FROM AUTHOR]

We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with Gaussian innovations having real characteristic roots with different absolute values. We use an appropriate random scaling such that the limit distribution is a two-dimensional normal distribution concentrated on a one-dimensional ray determined by the characteristic root having the larger absolute value. [ABSTRACT FROM AUTHOR]