A Review and Comparison of Bandwidth Selection Methods for Kernel Regression

Over the last decades, several methods for selecting the bandwidth have been introduced in kernel regression. They differ quite a bit, and although there already exist more selection methods than for any other regression smoother, one can still observe coming up new ones. Given the need of automatic data‐driven bandwidth selectors for applied statistics, this review is intended to explain and, above all, compare these methods. About 20 different selection methods have been revised, implemented and compared in an extensive simulation study.     

Estimating the Kullback–Liebler risk based on multifold cross‐validation

This paper concerns a class of model selection criteria based on cross‐validation techniques and estimative predictive densities. Both the simple or leave‐one‐out and the multifold or leave‐m‐out cross‐validation procedures are considered. These cross‐validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.     

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Functional data analysis is a field of growing importance in Statistics. In particular, the functional linear model with scalar response is surely the model that has attracted more attention in both theoretical and applied research. Two of the most important methodologies used to estimate the parameters of the functional linear model with scalar response are functional principal component regression and functional partial least‐squares regression. We provide an overview of estimation methods based on these methodologies and discuss their advantages and disadvantages. We emphasise that the role played by the functional principal components and by the functional partial least‐squares components that are used in estimation appears to be very important to estimate the functional slope of the model. A functional version of the best subset selection strategy usual in multiple linear regression is also analysed. Finally, we present an extensive comparative simulation study to compare the performance of all the considered methodologies that may help practitioners in the use of the functional linear model with scalar response.     

Varying Coefficient Regression Models: A Review and New Developments

Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.     

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.     

Recent Developments in Dealing with Item Non‐response in Surveys: A Critical Review

The most common way for treating item non‐response in surveys is to construct one or more replacement values to fill in for a missing value. This process is known as imputation. We distinguish single from multiple imputation. Single imputation consists of replacing a missing value by a single replacement value, whereas multiple imputation uses two or more replacement values. This article reviews various imputation procedures used in National Statistical Offices as well as the properties of point and variance estimators in the presence of imputed survey data. It also provides the reader with newer developments in the field.