Man-Lai Tang

To model count data with excess zeros, ones and twos, for the first time we introduce a so-called zero-one-two-inflated Poisson (ZOTIP) distribution, including the zero-inflated Poisson (ZIP) and the zero-and-one-inflated Poisson (ZOIP) distributions as two special cases. We establish three equivalent stochastic representations for the ZOTIP random variable to develop important distributional properties of the ZOTIP distribution. The Fisher scoring and expectation–maximization (EM) algorithms are derived to obtain the maximum likelihood estimates of parameters of interest. Bootstrap confidence intervals are also provided. Testing hypotheses are considered, simulation studies are conducted, and two real data sets are used to illustrate the proposed methods.

Recently, a so-called E-MS algorithm was developed for model selection in the presence of missing data. Specifically, it performs the Expectation step (E step) and Model Selection step (MS step) alternately to find the minimum point of the observed generalized information criteria (GIC). In practice, it could be numerically infeasible to perform the MS-step for high dimensional settings. In this paper, we propose a more simple and feasible generalized EMS (GEMS) algorithm which simply requires a decrease in the observed GIC in the MS-step and includes the original EMS algorithm as a special case. We obtain several numerical convergence results of the GEMS algorithm under mild conditions. We apply the proposed GEMS algorithm to Gaussian graphical model selection and variable selection in generalized linear models and compare it with existing competitors via numerical experiments. We illustrate its application with three real data sets.

Time lag effect exists widely in the course of economic operation. Some economic variables are affected not only by various factors in the current period but also by various factors in the past and even their own past values. As a class of dynamical models, autoregressive distributed lag (ARDL) models are frequently used to conduct dynamic regression analysis. In this paper, we are interested in the quantile regression (QR) modeling of the ARDL model in a dynamic framework. By combining the working likelihood of asymmetric Laplace distribution (ALD) with the expectation–maximization (EM) algorithm into the considered ARDL model, the iterative weighted least square estimators (IWLSE) are derived. Some Monte Carlo simulations are implemented to evaluate the performance of the proposed estimation method. A dataset of the consumption of electricity by residential customers is analyzed to illustrate the application.

Collecting representative data on sensitive issues has long been problematic and challenging in public health prevalence investigation (e.g. non-suicidal self-injury), medical research (e.g. drug habits), social issue studies (e.g. history of child abuse), and their interdisciplinary studies (e.g. premarital sexual intercourse). Alternative data collection techniques that can be adopted to study sensitive questions validly become more important and necessary. As an alternative to the famous Warner randomized response model, non-randomized response triangular model has recently been developed to encourage participants to provide truthful responses in surveys involving sensitive questions. Unfortunately, both randomized and non-randomized response models could underestimate the proportion of subjects with the sensitive characteristic as some respondents do not believe that these techniques can protect their anonymity. As a result, some authors hypothesized that lack of trust and noncompliance should be highest among those who have the most to lose and the least to use for the anonymity provided by using these techniques. Some researchers noticed the existence of noncompliance and proposed new models to measure noncompliance in order to get reliable information. However, all proposed methods were based on randomized response models which require randomizing devices, restrict the survey to only face-to-face interview and are lack of reproductivity. Taking the noncompliance into consideration, we introduce new non-randomized response techniques in which no covariate is required. Asymptotic properties of the proposed estimates for sensitive characteristic as well as noncompliance probabilities are developed. Our proposed techniques are empirically shown to yield accurate estimates for both sensitive and noncompliance probabilities. A real example about premarital sex among university students is used to demonstrate our methodologies.

In this paper, we propose robust randomized quantile regression estimators for the mean and (condition) variance functions of the popular heteroskedastic non parametric regression model. Unlike classical approaches which consider quantile as a fixed quantity, our method treats quantile as a uniformly distributed random variable. Our proposed method can be employed to estimate the error distribution, which could significantly improve prediction results. An automatic bandwidth selection scheme will be discussed. Asymptotic properties and relative efficiencies of the proposed estimators are investigated. Our empirical results show that the proposed estimators work well even for random errors with infinite variances. Various numerical simulations and two real data examples are used to demonstrate our methodologies.

The varying-coefficient single-index model (VCSIM) is a very general and flexible tool for exploring the relationship between a response variable and a set of predictors. Popular special cases include single-index models and varying-coefficient models. In order to estimate the index-coefficient and the non parametric varying-coefficients in the VCSIM, we propose a two-stage composite quantile regression estimation procedure, which integrates the local linear smoothing method and the information of quantile regressions at a number of conditional quantiles of the response variable. We establish the asymptotic properties of the proposed estimators for the index-coefficient and varying-coefficients when the error is heterogeneous. When compared with the existing mean-regression-based estimation method, our simulation results indicate that our proposed method has comparable performance for normal error and is more robust for error with outliers or heavy tail. We illustrate our methodologies with a real example.

In this article, we consider a generalized linear partially varying-coefficient model for longitudinal data analysis. A local quasi-likelihood method is proposed to estimate the constant-coefficient and varying-coefficient functions simultaneously based on the local polynomial kernel regression. The corresponding standard error estimates are derived. Large sample properties are investigated. The proposed methodologies are demonstrated by extensive simulation studies and a real example.

Mixture of linear regression models provide a popular treatment for modeling nonlinear regression relationship. The traditional estimation of mixture of regression models is based on Gaussian error assumption. It is well known that such assumption is sensitive to outliers and extreme values. To overcome this issue, a new class of finite mixture of quantile regressions (FMQR) is proposed in this article. Compared with the existing Gaussian mixture regression models, the proposed FMQR model can provide a complete specification on the conditional distribution of response variable for each component. From the likelihood point of view, the FMQR model is equivalent to the finite mixture of regression models based on errors following asymmetric Laplace distribution (ALD), which can be regarded as an extension to the traditional mixture of regression models with normal error terms. An EM algorithm is proposed to obtain the parameter estimates of the FMQR model by combining a hierarchical representation of the ALD. Finally, the iterated weighted least square estimation for each mixture component of the FMQR model is derived. Simulation studies are conducted to illustrate the finite sample performance of the estimation procedure. Analysis of an aphid data set is used to illustrate our methodologies.