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Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonp...

In this paper, we introduce a measurement error selection likelihood to select important variables and estimate additive components simultaneously in a high-dimensional additive model. Although the...

For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main effects, two-way interactions, etc. Such an approach has been pursued explicitly in smoothing spline ANOVA modeling and implicitly in various greedy methods such as MARS. We develop a new method for functional ANOVA modeling, based on doubly penalized estimation using total-variation and empirical-norm penalties, to achieve sparse selection of component functions and their knots. For this purpose, we formulate a new class of hierarchical total variations, which measures total variations at different levels including main effects and multi-way interactions, possibly after some order of differentiation. Furthermore, we derive suitable basis functions for multivariate splines such that the hierarchical total variation can be represented as a regular Lasso penalty, and hence we extend a previous backfitting algorithm to handle doubly penalized estimation for ANOVA modeling. We present extensive numerical experiments on simulations and real data to compare our method with existing methods including MARS, tree boosting, and random forest. The results are very encouraging and demonstrate considerable gains from our method in both prediction or classification accuracy and simplicity of the fitted functions.

Generalised additive models (GAMs) provide flexible models for a wide array of data sources. In the past, improvements of GAM estimation have focused on the smoothers used in the local scoring algo...

This paper is concerned with feature screening for the ultrahigh dimensional additive models with longitudinal data. The proposed method utilizes the quadratic inference functions to construct the ...

In this paper, a semiparametric mixture of regression models is proposed, where the regression functions are partially linear additive while the mixing proportions and variances are unknown constan...

Many non-linear models such as the additive models or varying models are often used to fit the complex data. However, how to select a simplified model in the prediction problem or data interpretati...

This paper considers the estimation for a partial index additive regression model, when the response variable and covariates in the index part are observed with additive distortion measurement erro...

The use of the 2-of-(H + 1) runs-rules and synthetic schemes to improve the performance of the currently available X¯ schemes in monitoring the process mean under the combined effect of measurement...

The models constituting a multiple model will correspond to d treatments of a base design. Using a classic result on cumulant generation function we show how to obtain least square estimators for cumulants and generalized least squares estimators for vectors \beta, l=1,...,d, in the individual models. Next we carry out ANOVA-like analysis for the action of the factors in the base design. This is possible since the estimators \tilde{\beta }(l) of \beta (l). l=1,...,d, have, approximately, the same covariance matrix. The eigenvectors of that matrix will give the principal estimable functions \epsilon_{i}^{\top} \beta (l) i=1,...,k, l=1,...,d, for the individual models. The ANOVA-like analysis will consider homologue components on principal estimable functions. To apply our results we assume the factors in the base design to have fixed effects. Moreover if w=1, and Z(1) has covariance matrix \sigma^{2} \m I_{n}, our treatment generalizes that previously given for multiple regression designs. In them we have a linear regression for each treatment of a base design. We then study the action of the factors on that design on the vectors \beta(l), l=1,...,d. An example of application of the proposed methodology is given.

This article is concerned with statistical inference of partially linear additive regression models where the covariates in parametric component are measured with errors. Using polynomial spline ap...

We propose and investigate additive density regression, a novel additive functional regression model for situations where the responses are random distributions that can be viewed as random densities and the predictors are vectors. Data in the form of samples of densities or distributions are increasingly encountered in statistical analysis and there is a need for flexible regression models that accommodate random densities as responses. Such models are of special interest for multivariate continuous predictors, where unrestricted nonparametric regression approaches are subject to the curse of dimensionality. Additive models can be expected to maintain one-dimensional rates of convergence while permitting a substantial degree of flexibility. This motivates the development of additive regression models for situations where multivariate continuous predictors are coupled with densities as responses. To overcome the problem that distributions do not form a vector space, we utilize a class of transformations that map densities to unrestricted square integrable functions and then deploy an additive functional regression model to fit the responses in the unrestricted space, finally transforming back to density space. We implement the proposed additive model with an extended version of smooth backfitting and establish the consistency of this approach, including rates of convergence. The proposed method is illustrated with an application to the distributions of baby names in the United States.

A semi-parametric spatial-temporal model is estimated using a hybrid of forward search algorithm and nonparametric regression in the context of backfitting an additive model. The model can account ...

Smooth backfitting has been shown to have better theoretical properties than classical backfitting for fitting additive models based on local linear regression. In this article, we show that the sm...

This article addresses the estimation procedures of population mean related to the quantitative sensitive variable with the help of a randomized device which makes the use of blank cards in the ran...

In this paper, we consider a new robust identification of linear parts in additive models. A one-step sparse algorithm based on local linear approximation is used for minimizing the proposed compos...

The additive model and the varying-coefficient model are both powerful regression tools, with wide practical applications. However, our empirical study on a financial data has shown that both of th...

We propose a new estimation method to estimate the nonparametric functions in additive models, where the response is subject to fixed censoring. Under some regularity conditions, we show that the p...

This article focuses on data integration problems where the predictor variables for some response variable partition into known subsets. This type of data is often referred to as multi-view data, a...

Data envelopment analysis (DEA) has been widely applied in measuring the efficiency of homogeneous decision-making units. Network DEA, as an important branch of DEA, was built to examine the internal structure of a system, whereas traditional DEA models regard a system as a ‘black box’. However, only a few previous studies on parallel systems have considered the interdependent relationship between system components. In recent years, parallel interdependent processes systems commonly exist in production systems because of serious competition among organisations. Thus, an approach to measure the efficiency of such systems should be proposed. This paper builds an additive DEA model to measure a parallel interdependent processes system with two components which have an interdependent relationship. Then, the model is applied to analyse the ‘985 Project’ universities in China, and certain policy implications are explained.

In practice, it is not uncommon to encounter the situation that a discrete response is related to both a functional random variable and multiple real-value random variables whose impact on the resp...

Double censoring often occurs in registry studies when left censoring is present in addition to right censoring. In this work, we examine estimation of Aalen's nonparametric regression coefficients...

Ultra-high-dimensional data are frequently seen in many contemporary statistical studies, which pose challenges both theoretically and methodologically. To address this issue under longitudinal dat...

Mathematical models for estimating the higher heating value of coals have constantly been developed and verified. Recently, models based on proximate analysis have gained much attention because of the relative ease in acquiring of such data. However, most models reported are focused solely in improving the accuracy of the estimates and oftentimes the realistic physical explanation and assumptions of the model are not looked into. Furthermore, most models found in literature are generated from coals of specific origin and thus limiting its applicability. In this work, a simple linear additive model with moisture, fixed carbon, volatile matter and ash as parameters was generated. In the generation of the model, proximate data sets (n > 8000) of coals form various origins was taken into consideration having higher heating values ranging from 0.09 to 36.26 MJ/kg. A plausible derivation of a model based on energy and material balance is also provided. The proposed improved model outperforms similar mod...

We introduce a new flexible distribution to deal with variables on the unit interval based on a transformation of the sinh–arcsinh distribution, which accommodates different degrees of skewness and kurtosis and becomes an interesting alternative to model this type of data. We also include this new distribution into the generalised additive models for location, scale and shape (GAMLSS) framework in order to develop and fit its regression model. For different parameter settings, some simulations are performed to investigate the behaviour of the estimators. The potentiality of the new regression model is illustrated by means of a real dataset related to the points rate of football teams at the end of a championship from the four most important leagues in the world: Barclays Premier League (England), Bundesliga (Germany), Serie A (Italy) and BBVA league (Spain) during three seasons (2011–2012, 2012–2013 and 2013–2014).

We investigate a class of partially linear functional additive models (PLFAM) that predicts a scalar response by both parametric effects of a multivariate predictor and nonparametric effects of a multivariate functional predictor. We jointly model multiple functional predictors that are cross-correlated using multivariate functional principal component analysis (mFPCA), and model the nonparametric effects of the principal component scores as additive components in the PLFAM. To address the high-dimensional nature of functional data, we let the number of mFPCA components diverge to infinity with the sample size, and adopt the component selection and smoothing operator (COSSO) penalty to select relevant components and regularize the fitting. A fundamental difference between our framework and the existing high-dimensional additive models is that the mFPCA scores are estimated with error, and the magnitude of measurement error increases with the order of mFPCA. We establish the asymptotic convergence ...

Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade,...

Lots of semi-parametric and nonparametric models are used to fit nonlinear time series data. They include partially linear time series models, nonparametric additive models, and semi-parametric sin...

Covariate-adaptive randomisation has a long history of applications in clinical trials. Shao, Yu, and Zhong [(2010). A theory for testing hypotheses under covariate-adaptive randomization. Biometri...

This paper studies the sparsity selection and estimation in nonparametric additive models. The sparsity refers to two types — across and within variables. Sparsity across variables corresponds to t...

M-estimation is a widely used method for robust statistical inference. In this article, using a B-spline series approximation with a double smoothly clipped absolute deviation penalization, we solv...

Many studies have dealt with the problem of fixed cost allocation by using data envelopment analysis. However, existing models allocate the fixed cost by treating the decision-making units (DMUs) as black-boxes and ignore the internal production structures of DMUs. To our knowledge, only a few work has considered the fixed cost allocation problem for an elementary two-stage production structure without external inputs and outputs. This paper deals with the fixed cost allocation problem for a general two-stage network production structure, in which both external inputs and outputs exist. Specifically, additive two-stage models are first presented to evaluate the performance for each DMU when allocating the fixed cost. Then, by introducing the concepts of satisfaction degree and fairness degree, we propose an approach to obtain an optimal allocation plan under the control of the centralized authority. Finally, an application to 27 banks is utilized to illustrate the proposed approach.

Error variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear models. We further propose an accurate estimate for error variance in ultrahigh-dimensional sparse additive model by effectively integrating sure independence screening and refitted cross-validation techniques. The root n consistency and the asymptotic normality of the resulting estimate are established. We conduct Monte Carlo simulation study to examine the finite sample performance of the newly proposed estimate. A real data example is used to illustrate the proposed methodology. Supplementary materials for this article are available online.

In this article, we propose a semiparametric mixture of additive regression models, in which the regression functions are additive and non parametric while the mixing proportions and variances are constant. Compared with the mixture of linear regression models, the proposed methodology is more flexible in modeling the non linear relationship between the response and covariate. A two-step procedure based on the spline-backfitted kernel method is derived for computation. Moreover, we establish the asymptotic normality of the resultant estimators and examine their good performance through a numerical example.

Existing models for coronary heart disease study use a set of common risk factors to predict the survival time of the disease, via the standard Cox regression model. For complex relationships betwe...

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

In this paper, semiparametric modelling for longitudinal data with an unstructured error process is considered. We propose a partially linear additive regression model for longitudinal data in which within-subject variances and covariances of the error process are described by unknown univariate and bivariate functions, respectively. We provide an estimating approach in which polynomial splines are used to approximate the additive nonparametric components and the within-subject variance and covariance functions are estimated nonparametrically. Both the asymptotic normality of the resulting parametric component estimators and optimal convergence rate of the resulting nonparametric component estimators are established. In addition, we develop a variable selection procedure to identify significant parametric and nonparametric components simultaneously. We show that the proposed SCAD penalty-based estimators of non-zero components have an oracle property. Some simulation studies are conducted to exami...

We postulate a spatiotemporal multilevel model and estimate using forward search algorithm and MLE imbedded into the backfitting algorithm. Forward search algorithm ensures robustness of the estimates by filtering the effect of temporary structural changes in the estimation of the group-level covariates, the individual-level covariates and spatial parameters. Backfitting algorithm provides computational efficiency of estimation procedure assuming an additive model. Simulation studies show that estimates are robust even in the presence of structural changes induced for example by epidemic outbreak. The model also produced robust estimates even for small sample and short time series common in epidemiological settings.

Biomass models for trees in Daxing’anling are imperative for carbon inventory, but available models are extremely scarce. The objective of this study was to formulate systems of additive equations to predict the aboveground biomass of two dominant deciduous species of Betula platyphylla and Populus davidiana in Daxing’anling using diameter at breast height (d) or both d and height (h) as independent variables. Best-fit models for individual fractions (stem wood, stem bark, branch, and foliage) were developed simultaneously on the basis of seemingly unrelated regression, forcing compatibility among different components. Model performance was validated by the jackknifing method. The results revealed that log-transformed models are favorable and that all models consistently fit well within R2 = 0.908 – 0.994, and = 0.898 – 0.994. Adding h into the additive models did not significantly improve the model fitting or performance, with branches and foliage yielding worse-fitting effects. Stem biomass cont...

While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been shown to admit desirable asymptotic properties when base learners are built with proper subsamples. In this work, we demonstrate that by defining an appropriate grid structure on the covariate space, we may carry out formal hypothesis tests for both variable importance and underlying additive model structure. To our knowledge, these tests represent the first statistical tools for investigating the underlying regression structure in a context such as random forests. We develop notions of total and partial additivity and further demonstrate that testing can be carried out at no additional computational cost by estimating the variance within the process of constructing the ensemble. Furthermore, we propose a novel extension of these testing procedures utilizing random projections in order to allow for computationally efficient testing procedures that retain high power even when the grid size is much larger than that of the training set.

Computer experiments with qualitative and quantitative factors occur frequently in various applications in science and engineering. Analysis of such experiments is not yet completely resolved. In this work, we propose an additive Gaussian process model for computer experiments with qualitative and quantitative factors. The proposed method considers an additive correlation structure for qualitative factors, and assumes that the correlation function for each qualitative factor and the correlation function of quantitative factors are multiplicative. It inherits the flexibility of unrestrictive correlation structure for qualitative factors by using the hypersphere decomposition, embracing more flexibility in modeling the complex systems of computer experiments. The merits of the proposed method are illustrated by several numerical examples and a real data application. Supplementary materials for this article are available online.

To investigate the adequacy of the widely used Cobb-Douglas and transcendental logarithmic (translog) models of the production functions of hospital inpatient services, the authors fitted these and additive models to data for the four most productive health services of 10 public hospitals in Galicia, Spain (the same four in each). Production, measured as admissions weighted in accordance with their diagnosis-related groups (DRGs), was treated as a function of physician full-time equivalents as surrogate labor factor and number of beds as surrogate capital factor. The results suggest that while the Cobb-Douglas and translog models suffice to represent the production functions of services with low average DRG weight, the greater flexibility of additive models is required for services with higher average DRG weight when only these two inputs are considered.

This paper deals with optimality aspects of block designs balanced for interference effects from neighboring units on both sides under a general non additive model along with random block effects. Here, a class of complete, circular block designs strongly balanced for interference effects has been shown to be universally optimal for the estimation of direct effects and interference effects (left and right) of treatments under a non additive mixed effects model.

In this thesis, we construct test statistic for association test and independence test in high dimension, respectively, and study the corresponding theoretical properties under some regularity cond...

The purpose of this study was to improve the dimensional accuracy of steel plate by updating the selection of combination parameters for slab design with statistical models. The generalised boosted regression model and the generalised additive models were used to predict the dimensional properties of the combination parameters with process factors. For real-life application, the modelling results were utilised to determine new combination parameter classes containing a larger number of process factors instead of only one. The research increased the knowledge of material sufficiency and the factors behind it. As a result, the new selection procedure is expected to increase yield and reduce the risk of rejection.

This paper considers variable selection in additive quantile regression based on group smoothly clipped absolute deviation (gSCAD) penalty. Although shrinkage variable selection in additive models with least-squares loss has been well studied, quantile regression is sufficiently different from mean regression to deserve a separate treatment. It is shown that the gSCAD estimator can correctly identify the significant components and at the same time maintain the usual convergence rates in estimation. Simulation studies are used to illustrate our method.

We propose a data-driven method to select significant variables in additive model via spline estimation. The additive structure of the regression model is imposed to overcome the ‘curse of dimensionality’, while the spline estimators provide a good approximation to the additive components of the model. The additive components are ordered according to their empirical strengths, and the significant variables are chosen at the first crossing of a predetermined threshold by the CUmulative Ratios of Empirical Strengths Total of the components. Consistency of the proposed method is established when the number of variables are allowed to diverge with sample size, while extensive Monte-Carlo study demonstrates superior performance of the proposed method and its advantages over the BIC method of Huang and Yang [(2004), ‘Identification of Nonlinear: Additive Autoregressive Models’, Journal of the Royal Statistical Society Series B, 66, 463–477] in terms of speed and accuracy.

The accurate prediction of long-term care insurance (LTCI) mortality, lapse, and claim rates is essential when making informed pricing and risk management decisions. Unfortunately, academic literature on the subject is sparse and industry practice is limited by software and time constraints. In this article, we review current LTCI industry modeling methodology, which is typically Poisson regression with covariate banding/modification and stepwise variable selection. We test the claim that covariate banding improves predictive accuracy, examine the potential downfalls of stepwise selection, and contend that the assumptions required for Poisson regression are not appropriate for LTCI data. We propose several alternative models specifically tailored toward count responses with an excess of zeros and overdispersion. Using data from a large LTCI provider, we evaluate the predictive capacity of random forests and generalized linear and additive models with zero-inflated Poisson, negative binomial, and Tweedie e...

Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares (PL) approach and Liu estimation method, we propose a PL Liu estimator for the parametric component. When some additional linear restrictions on the parametric component are available, the corresponding restricted Liu estimator for the parametric component is constructed. The properties of the proposed estimators are derived. Some simulations are conducted to assess the performance of the proposed procedures and the results are satisfactory. Finally, a real data example is analysed.