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.     

Monitoring prespecified changes in linear profiles using control charts with supplementary runs rules

In profile monitoring, some methods have been developed to detect the unspecified changes in the profiles. However, detecting changes away from the “normal” profile toward one of several prespecified “bad” profiles is one possible and challenging purpose. In this article, control charts with supplementary runs rules are developed to detect the prespecified changes in linear profiles. A control chart is first developed based on the Student's t-statistic in t test, and two runs rules are then supplemented to this chart, respectively. Simulation studies show that the proposed control schemes are effective and stable. Moreover, the control schemes are better than the existing alternative charts when the number of observations per sample profile is large. Finally, two illustrative examples indicate that our proposed schemes are effective and easy to be implemented.     

Robust estimation of complicated profiles using wavelets

Some quality characteristics are well defined when treated as the response variables and their relationships are identified to some independent variables. This relationship is called a profile. The parametric models, such as linear models, may be used to model the profiles. However, due to the complexity of many processes in practical applications, it is inappropriate to model the process using parametric models. In these cases non parametric methods are used to model the processes. One of the most applicable non parametric methods used to model complicated profiles is the wavelet. Many authors considered the use of the wavelet transformation only for monitoring the processes in phase II. The problem of estimating the in-control profile in phase I using wavelet transformation is not deeply addressed. Usually classical estimators are used in phase I to estimate the in-control profiles, even when the wavelet transformation is used. These estimators are suitable if the data do not contain outliers. However, when the outliers exist, these estimators cannot estimate the in-control profile properly. In this research, a robust method of estimating the in-control profiles is proposed, which is insensitive to the presence of outliers and could be applied when the wavelet transformation is used. The proposed estimator is the combination of the robust clustering and the S-estimator. This estimator is compared with the classical estimator of the in-control profile in the presence of outliers. The results from a large simulation study show that using the proposed method, one can estimate the in-control profile precisely when the data are contaminated either locally or globally.     

两个部分线性模型的比较

内容提要:对于两个部分线性模型参数部分中模型系数是否相等的检验问题,本文基于比较原假设与备择假设下模型拟合的残差平方和的思想构造了检验统计量,并给出了计算检验_^p* 值的F分布逼近法。     

Statistical inference in partially time-varying coefficient models

A partially time-varying coefficient time series model is introduced to characterize the nonlinearity and trending phenomenon. To estimate the regression parameter and the nonlinear coefficient function, the profile least squares approach is applied with the help of local linear approximation. The asymptotic distributions of the proposed estimators are established under mild conditions. Meanwhile, the generalized likelihood ratio test is studied and the test statistics are demonstrated to follow asymptotic χ²-distribution under the null hypothesis. Furthermore, some extensions of the proposed model are discussed and several numerical examples are provided to illustrate the finite sample behavior of the proposed methods.     

Likelihood Prediction for Generalized Linear Mixed Models under Covariate Uncertainty

This article presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction are explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. This article outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson errors-in-variable generalized linear model, it has been shown in certain cases that LP produces better results than already known methods.     

Semiparametric inference with a functional-form empirical likelihood

A functional-form empirical likelihood method is proposed as an alternative method to the empirical likelihood method. The proposed method has the same asymptotic properties as the empirical likelihood method but has more flexibility in choosing the weight construction. Because it enjoys the likelihood-based interpretation, the profile likelihood ratio test can easily be constructed with a chi-square limiting distribution. Some computational details are also discussed, and results from finite-sample simulation studies are presented.     

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.     

Nonparametric model checking for k-out-of-n systems

It is an important problem in reliability analysis to decide whether for a given k-out-of-n system the static or the sequential k-out-of-n model is appropriate. Often components are redundantly added to a system to protect against failure of the system. If the failure of any component of the system induces a higher rate of failure of the remaining components due to increased load, the sequential k-out-of-n model is appropriate. The increase of the failure rate of the remaining components after a failure of some component implies that the effects of the component redundancy are diminished. On the other hand, if all the components have the same failure distribution and whenever a failure occurs, the remaining components are not affected, the static k-out-of-n model is adequate. In this paper, we consider nonparametric hypothesis tests to make a decision between these two models. We analyze test statistics based on the profile score process as well as test statistics based on a multivariate intensity ratio and derive their asymptotic distribution. Finally, we compare the different test statistics.     

Allowing for non-ignorable non-response in the analysis of voting intention data

We apply some log-linear modelling methods, which have been proposed for treating non-ignorable non-response, to some data on voting intention from the British General Election Survey. We find that, although some non-ignorable non-response models fit the data very well, they may generate implausible point estimates and predictions. Some explanation is provided for the extreme behaviour of the maximum likelihood estimates for the most parsimonious model. We conclude that point estimates for such models must be treated with great caution. To allow for the uncertainty about the non-response mechanism we explore the use of profile likelihood inference and find the likelihood surfaces to be very flat and the interval estimates to be very wide. To reduce the width of these intervals we propose constraining confidence regions to values where the parameters governing the non-response mechanism are plausible and study the effect of such constraints on inference. We find that the widths of these intervals are reduced but remain wide.