Seemingly unrelated systems of econometric equations

A generalization of Zellner's SUR model is derived for sets of seemingly unrelated systems of econometric equations. The resulting structural form – worked out for a set of Cowles Commission-type simultaneous equations systems – is general enough to include any SUR-type or panel-type specification of systems of econometric equations with contemporaneously correlated errors. Maximum estimation efficiency is obtained by treating all the individual subsystems at once rather than in a subsystem-by-subsystem fashion.     

Quantile regression for robust estimation and variable selection in partially linear varying-coefficient models

In this paper, we develop a new estimation procedure based on quantile regression for semiparametric partially linear varying-coefficient models. The proposed estimation approach is empirically shown to be much more efficient than the popular least squares estimation method for non-normal error distributions, and almost not lose any efficiency for normal errors. Asymptotic normalities of the proposed estimators for both the parametric and nonparametric parts are established. To achieve sparsity when there exist irrelevant variables in the model, two variable selection procedures based on adaptive penalty are developed to select important parametric covariates as well as significant nonparametric functions. Moreover, both these two variable selection procedures are demonstrated to enjoy the oracle property under some regularity conditions. Some Monte Carlo simulations are conducted to assess the finite sample performance of the proposed estimators, and a real-data example is used to illustrate the application of the proposed methods.     

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT

The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].     

Joint GEEs for multivariate correlated data with incomplete binary outcomes

This study considers a fully-parametric but uncongenial multiple imputation (MI) inference to jointly analyze incomplete binary response variables observed in a correlated data settings. Multiple imputation model is specified as a fully-parametric model based on a multivariate extension of mixed-effects models. Dichotomized imputed datasets are then analyzed using joint GEE models where covariates are associated with the marginal mean of responses with response-specific regression coefficients and a Kronecker product is accommodated for cluster-specific correlation structure for a given response variable and correlation structure between multiple response variables. The validity of the proposed MI-based JGEE (MI-JGEE) approach is assessed through a Monte Carlo simulation study under different scenarios. The simulation results, which are evaluated in terms of bias, mean-squared error, and coverage rate, show that MI-JGEE has promising inferential properties even when the underlying multiple imputation is misspecified. Finally, Adolescent Alcohol Prevention Trial data are used for illustration.     

Difference-based matrix perturbation method for semi-parametric regression with multicollinearity

This paper addresses the collinearity problems in semi-parametric linear models. Under the difference-based settings, we introduce a new diagnostic, the difference-based variance inflation factor (DVIF), for detecting the presence of multicollinearity in semi-parametric models. The DVIF is then used to device a difference-based matrix perturbation method for solving the problem. The electricities distribution data set is analyzed, and numerical evidences validate the effectiveness of the proposed method.     

Estimation and diagnostic for skew-normal partially linear models

Partially linear models (PLMs) are an important tool in modelling economic and biometric data and are considered as a flexible generalization of the linear model by including a nonparametric component of some covariate into the linear predictor. Usually, the error component is assumed to follow a normal distribution. However, the theory and application (through simulation or experimentation) often generate a great amount of data sets that are skewed. The objective of this paper is to extend the PLMs allowing the errors to follow a skew-normal distribution [A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178], increasing the flexibility of the model. In particular, we develop the expectation-maximization (EM) algorithm for linear regression models and diagnostic analysis via local influence as well as generalized leverage, following [H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111–126]. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration in order to fit PLMs under asymmetric distributions. An illustrative comparison is performed between normal and skew-normal errors.     

Unified Inference for Sparse and Dense Longitudinal Data in Time‐varying Coefficient Models

Time‐varying coefficient models are widely used in longitudinal data analysis. These models allow the effects of predictors on response to vary over time. In this article, we consider a mixed‐effects time‐varying coefficient model to account for the within subject correlation for longitudinal data. We show that when kernel smoothing is used to estimate the smooth functions in time‐varying coefficient models for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases might lead to erroneous conclusions for statistical inference. In order to solve this problem, we establish a unified self‐normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and an analysis of Baltimore MACS data.     

Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear‐Index

More flexible semiparametric linear‐index regression models are proposed to describe the conditional distribution. Such a model formulation captures varying effects of covariates over the support of a response variable in distribution, offers an alternative perspective on dimension reduction and covers a lot of widely used parametric and semiparameteric regression models. A feasible pseudo likelihood approach, accompanied with a simple and easily implemented algorithm, is further developed for the mixed case with both varying and invariant coefficients. By justifying some theoretical properties on Banach spaces, the uniform consistency and asymptotic Gaussian process of the proposed estimator are also established in this article. In addition, under the monotonicity of distribution in linear‐index, we develop an alternative approach based on maximizing a varying accuracy measure. By virtue of the asymptotic recursion relation for the estimators, some of the achievements in this direction include showing the convergence of the iterative computation procedure and establishing the large sample properties of the resulting estimator. It is noticeable that our theoretical framework is very helpful in constructing confidence bands for the parameters of interest and tests for the hypotheses of various qualitative structures in distribution. Generally, the developed estimation and inference procedures perform quite satisfactorily in the conducted simulations and are demonstrated to be useful in reanalysing data from the Boston house price study and the World Values Survey.     

Robust Poisson likelihood estimation for frailty Cox models: A simulation study

Frailty models can be fit as mixed-effects Poisson models after transforming time-to-event data to the Poisson model framework. We assess, through simulations, the robustness of Poisson likelihood estimation for Cox proportional hazards models with log-normal frailties under misspecified frailty distribution. The log-gamma and Laplace distributions were used as true distributions for frailties on a natural log scale. Factors such as the magnitude of heterogeneity, censoring rate, number and sizes of groups were explored. In the simulations, the Poisson modeling approach that assumes log-normally distributed frailties provided accurate estimates of within- and between-group fixed effects even under a misspecified frailty distribution. Non-robust estimation of variance components was observed in the situations of substantial heterogeneity, large event rates, or high data dimensions.