Semiparametric Smooth Coefficient Stochastic Frontier Model With Panel Data

ABSTRACT

We investigate the semiparametric smooth coefficient stochastic frontier model for panel data in which the distribution of the composite error term is assumed to be of known form but depends on some environmental variables. We propose multi-step estimators for the smooth coefficient functions as well as the parameters of the distribution of the composite error term and obtain their asymptotic properties. The Monte Carlo study demonstrates that the proposed estimators perform well in finite samples. We also consider an application and perform model specification test, construct confidence intervals, and estimate efficiency scores that depend on some environmental variables. The application uses a panel data on 451 large U.S. firms to explore the effects of computerization on productivity. Results show that two popular parametric models used in the stochastic frontier literature are likely to be misspecified. Compared with the parametric estimates, our semiparametric model shows a positive and larger overall effect of computer capital on the productivity. The efficiency levels, however, were not much different among the models. Supplementary materials for this article are available online.     

Semiparametric estimation of the cumulative incidence function under competing risks and left-truncated sampling

In this article, we propose semiparametric methods to estimate the cumulative incidence function of two dependent competing risks for left-truncated and right-censored data. The proposed method is based on work by Huang and Wang (1995). We extend previous model by allowing for a general parametric truncation distribution and a third competing risk before recruitment. Based on work by Vardi (1989), several iterative algorithms are proposed to obtain the semiparametric estimates of cumulative incidence functions. The asymptotic properties of the semiparametric estimators are derived. Simulation results show that a semiparametric approach assuming the parametric truncation distribution is correctly specified produces estimates with smaller mean squared error than those obtained in a fully nonparametric model.     

Local GMM Estimation of Semiparametric Panel Data with Smooth Coefficient Models

In this article, we consider the estimation of semiparametric panel data smooth coefficient models. We propose a class of local generalized method of moments (LGMM) estimators that are simple and easy to implement in practice. We show that the proposed LGMM estimators are consistent and asymptotically normal. Monte Carlo simulations suggest that our proposed estimator performs quite well in finite samples. An empirical application using a large panel of U.K. firms is also presented.     

A Semiparametric Approach for Accelerated Failure Time Models with Covariates Subject to Measurement Error

There are relatively few discussions about measurement error in the accelerated failure time (AFT) model, particularly for the semiparametric AFT model. In this article, we propose an adjusted estimation procedure for the semiparametric AFT model with covariates subject to measurement error, based on the profile likelihood approach and simulation and exploration (SIMEX) method. The simulation studies show that the proposed semiparametric SIMEX approach performs well. The proposed approach is applied to a coronary heart disease dataset from the Busselton Health study for illustration.     

Estimation for semiparametric varying coefficient models with different smoothing variables under random right censoring

In this paper we study a semiparametric varying coefficient model when the response is subject to random right censoring. The model gives an easy interpretation due to its direct connectivity to the classical linear model and is very flexible since nonparametric functions which accommodates various nonlinear interaction effects between covariates are admitted in the model. We propose estimators for this model using mean-preserving transformation and establish their asymptotic properties. The estimation procedure is based on the profiling and the smooth backfitting techniques. A simulation study is presented to show the reliability of the proposed estimators and an automatic bandwidth selector is given in a data-driven way.     

Testing generalized linear and semiparametric models against smooth alternatives

We propose goodness-of-fit tests for testing generalized linear models and semiparametric regression models against smooth alternatives. The focus is on models having both continous and factorial covariates. As a smooth extension of a parametric or semiparametric model we use generalized varying-coefficient models as proposed by Hastie and Tibshirani. A likelihood ratio statistic is used for testing. Asymptotic expansions allow us to write the estimates as linear smoothers which in turn guarantees simple and fast bootstrapping of the test statistic. The test is shown to have √ n -power, but in contrast with parametric tests it is powerful against smooth alternatives in general.     

A test for lack-of-fit of zero-inflated negative binomial models

When a count data set has excessive zero counts, nonzero counts are overdispersed, and the effect of a continuous covariate might be nonlinear, for analysis a semiparametric zero-inflated negative binomial (ZINB) regression model is proposed. The unspecified smooth functional form for the continuous covariate effect is approximated by a cubic spline. The semiparametric ZINB regression model is fitted by maximizing the likelihood function. The likelihood ratio procedure is used to evaluate the adequacy of a postulated parametric functional form for the continuous covariate effect. An extensive simulation study is conducted to assess the finite-sample performance of the proposed test. The practicality of the proposed methodology is demonstrated with data of a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.     

Generalized partially linear varying coefficient models with multiple smoothing variables

This paper is concerned with semiparametric efficient estimation of a generalized partially linear varying coefficient model. The model studied in this paper is very flexible, accommodating various nonlinear relations between the response variable and a set of predictor variables. It is a structured regression model and is particularly useful in dealing with a discrete response variable. We apply the smooth backfitting technique to estimate the nonparametric part of the model and employ the profiling approach to obtain a semiparametric efficient estimator of the parametric part.     

Semiparametric Estimation of Stochastic Production Frontier Models

This article extends the linear stochastic frontier model proposed by Aigner, Lovell, and Schmidt to a semiparametric frontier model in which the functional form of the production frontier is unspecified and the distributions of the composite error terms are of known form. Pseudolikelihood estimators of the parameters characterizing the two error terms of the model are constructed based on kernel estimation of the conditional mean function. The Monte Carlo results show that the proposed estimators perform well in finite samples. An empirical application is presented. Extensions to a partially linear frontier function and to more flexible one-sided error distributions than the half-normal are discussed     

Nonlinear semiparametric autoregressive model with finite mixtures of scale mixtures of skew normal innovations

We propose data generating structures which can be represented as the nonlinear autoregressive models with single and finite mixtures of scale mixtures of skew normal innovations. This class of models covers symmetric/asymmetric and light/heavy-tailed distributions, so provide a useful generalization of the symmetrical nonlinear autoregressive models. As semiparametric and nonparametric curve estimation are the approaches for exploring the structure of a nonlinear time series data set, in this article the semiparametric estimator for estimating the nonlinear function of the model is investigated based on the conditional least square method and nonparametric kernel approach. Also, an Expectation–Maximization-type algorithm to perform the maximum likelihood (ML) inference of unknown parameters of the model is proposed. Furthermore, some strong and weak consistency of the semiparametric estimator in this class of models are presented. Finally, to illustrate the usefulness of the proposed model, some simulation studies and an application to real data set are considered.     

A Bayesian semiparametric model for non negative semicontinuous data

When the target variable exhibits a semicontinuous behavior (a point mass in a single value and a continuous distribution elsewhere), parametric “two-part models” have been extensively used and investigated. The applications have mainly been related to non negative variables with a point mass in zero (zero-inflated data). In this article, a semiparametric Bayesian two-part model for dealing with such variables is proposed. The model allows a semiparametric expression for the two parts of the model by using Dirichlet processes. A motivating example, based on grape wine production in Tuscany (an Italian region), is used to show the capabilities of the model. Finally, two simulation experiments evaluate the model. Results show a satisfactory performance of the suggested approach for modeling and predicting semicontinuous data when parametric assumptions are not reasonable.     

Inverse censoring weighted median regression

We implement semiparametric random censorship model aided inference for censored median regression models. This is based on the idea that, when the censoring is specified by a common distribution, a semiparametric survival function estimator acts as an improved weight in the so-called inverse censoring weighted estimating function. We show that the proposed method will always produce estimates of the model parameters that are as good as or better than an existing estimator based on the traditional Kaplan–Meier weights. We also provide an illustration of the method through an analysis of a lung cancer data set.     

Checking the linear transformation model for clustered failure time observations

The linear transformation model is a semiparametric model which contains the Cox proportional hazards model and the proportional odds model as special cases. Cai et al. (Biometrika 87:867-878, 2000) have proposed an inference procedure for the linear transformation model with correlated censored observations. In this article, we develop formal and graphical model checking techniques for the linear transformation models based on cumulative sums of martingale-type residuals. The proposed method is illustrated with a clinical trial data.     

A class of semiparametric transformation models for survival data with a cured proportion

We propose a new class of semiparametric regression models based on a multiplicative frailty assumption with a discrete frailty, which may account for cured subgroup in population. The cure model framework is then recast as a problem with a transformation model. The proposed models can explain a broad range of nonproportional hazards structures along with a cured proportion. An efficient and simple algorithm based on the martingale process is developed to locate the nonparametric maximum likelihood estimator. Unlike existing expectation-maximization based methods, our approach directly maximizes a nonparametric likelihood function, and the calculation of consistent variance estimates is immediate. The proposed method is useful for resolving identifiability features embedded in semiparametric cure models. Simulation studies are presented to demonstrate the finite sample properties of the proposed method. A case study of stage III soft-tissue sarcoma is given as an illustration.     

Semiparametric Regression Analysis of Longitudinal Skewed Data

In this paper, we develop a semiparametric regression model for longitudinal skewed data. In the new model, we allow the transformation function and the baseline function to be unknown. The proposed model can provide a much broader class of models than the existing additive and multiplicative models. Our estimators for regression parameters, transformation function and baseline function are asymptotically normal. Particularly, the estimator for the transformation function converges to its true value at the rate n ^{? 1 ∕ 2}, the convergence rate that one could expect for a parametric model. In simulation studies, we demonstrate that the proposed semiparametric method is robust with little loss of efficiency. Finally, we apply the new method to a study on longitudinal health care costs.     

A semiparametric approach for modelling multivariate nonlinear time series

In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada     

Variable selection for semiparametric varying coefficient partially linear model based on modal regression with missing data

Abstract

In this article, we focus on the variable selection for semiparametric varying coefficient partially linear model with response missing at random. Variable selection is proposed based on modal regression, where the non parametric functions are approximated by B-spline basis. The proposed procedure uses SCAD penalty to realize variable selection of parametric and nonparametric components simultaneously. Furthermore, we establish the consistency, the sparse property and asymptotic normality of the resulting estimators. The penalty estimation parameters value of the proposed method is calculated by EM algorithm. Simulation studies are carried out to assess the finite sample performance of the proposed variable selection procedure.     

Semiparametric Spatial Autoregressive Models With Endogenous Regressors: With an Application to Crime Data

This study considers semiparametric spatial autoregressive models that allow for endogenous regressors, as well as the heterogenous effects of these regressors across spatial units. For the model estimation, we propose a semiparametric series generalized method of moments estimator. We establish that the proposed estimator is both consistent and asymptotically normal. As an empirical illustration, we apply the proposed model and method to Tokyo crime data to estimate how the existence of a neighborhood police substation (NPS) affects the household burglary rate. The results indicate that the presence of an NPS helps reduce household burglaries, and that the effects of some variables are heterogenous with respect to residential distribution patterns. Furthermore, we show that using a model that does not adjust for the endogeneity of NPS does not allow us to observe the significant relationship between NPS and the household burglary rate. Supplementary materials for this article are available online.     

Efficient Estimation in Heteroscedastic Partially Linear Varying Coefficient Models

This article considers statistical inference for the heteroscedastic partially linear varying coefficient models. We construct an efficient estimator for the parametric component by applying the weighted profile least-squares approach, and show that it is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator reaches the semiparametric efficiency bound. Simulation studies are conducted to illustrate the performance of the proposed method.     

Classification using semiparametric mixtures

A new density-based classification method that uses semiparametric mixtures is proposed. Like other density-based classifiers, it first estimates the probability density function for the observations in each class, with a semiparametric mixture, and then classifies a new observation by the highest posterior probability. By making a proper use of a multivariate nonparametric density estimator that has been developed recently, it is able to produce adaptively smooth and complicated decision boundaries in a high-dimensional space and can thus work well in such cases. Issues specific to classification are studied and discussed. Numerical studies using simulated and real-world data show that the new classifier performs very well as compared with other commonly used classification methods.