Testing for the parametric component of partially linear EV models under random censorship

This paper investigates the hypothesis test of the parametric component in partially linear errors-in-variables (EV) model with random censorship. We construct two test statistics based on the difference of the corrected residual sum of squares and empirical likelihood ratio under the null and alternative hypotheses. It is shown that the limiting distributions of the proposed test statistics are both weighted sum of independent standard chi-squared distribution with one degree of freedom under the null hypothesis. Based on the adjusted test statistics, we further develop two new types of test procedures. Finite sample performance of the proposed test procedures is evaluated by extensive simulation studies.     

On confidence intervals for the mean past lifetime function under random censorship

The mean past lifetime (MPL) function (also known as the expected inactivity time function) is of interest in many fields such as reliability theory and survival analysis, actuarial studies and forensic science. For estimation of the MPL function some procedures have been proposed in the literature. In this paper, we give a central limit theorem result for the estimator of MPL function based on a right-censored random sample from an unknown distribution. The limiting distribution is used to construct normal approximation-based confidence interval for MPL. Furthermore, we use the empirical likelihood ratio procedure to obtain confidence interval for the MPL function. These two intervals are compared with each other through simulation study in terms of coverage probability. Finally, a couple of numerical example illustrating the theory is also given.     

Approximate MLE for the scale parameter of the generalized exponential distribution under random censoring

In this paper, we consider the maximum likelihood estimator (MLE) of the scale parameter of the generalized exponential (GE) distribution based on a random censoring model. We assume the censoring distribution also follows a GE distribution. Since the estimator does not provide an explicit solution, we propose a simple method of deriving an explicit estimator by approximating the likelihood function. In order to compare the performance of the estimators, Monte Carlo simulation is conducted. The results show that the MLE and the approximate MLE are almost identical in terms of bias and variance.     

Maximum likelihood estimation in the proportional hazards model of random censorship

The maximum likelihood estimator (MLE) for the survival function S_Tunder the proportional hazards model of censorship is derived and shown to differ from the Abdushukurov-Cheng-Lin estimator when the class of allowable distributions includes all continuous and discrete distributions. The estimators are compared via an example. The MLE is calculated using a Newton-Raphson iterative procedure and implemented via a FORTRAN algorithm.     

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.     

Estimation of parameters under a random censorship model

The problem of estimation of parameters of a lifetime distribution is considered under the proportional hazards model of random censorship. Asymptotic variances of several estimators of survival function are compared in the eponential case.     

Quantile estimation in the proportional hazards model of random censorship

The asymptotic theory is given for quantile estimation in the proportional hazards model of random censorship. In this model, the tail of the censoring distribution function is some power of the tail of the survival distribution function. The quantile estimator is based on the maximum likelihood estimator for the survival time distribution, due to Abdushukurov, Cheng and Lin.     

Nonlinear semiparametric AR(1) model with skew-symmetric innovations

In this paper, we expand a first-order nonlinear autoregressive (AR) model with skew normal innovations. A semiparametric method is proposed to estimate a nonlinear part of model by using the conditional least squares method for parametric estimation and the nonparametric kernel approach for the AR adjustment estimation. Then computational techniques for parameter estimation are carried out by the maximum likelihood (ML) approach using Expectation-Maximization (EM) type optimization and the explicit iterative form for the ML estimators are obtained. Furthermore, in a simulation study and a real application, the accuracy of the proposed methods is verified.     

Umvu estimation for the cumulative hazard function in a pareto distribution of the first kind

The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator.     

Statistical diagnosis for non-parametric regression models with random right censorship based on the empirical likelihood method

In this paper, we consider statistical diagnostic for non-parametric regression models with right-censored data based on empirical likelihood. First, the primary model is transformed to the non-parametric regression model. Then, based on empirical likelihood methodology, we define some diagnostic statistics. At last, some simulation studies show that our proposed procedure can work fairly well.     

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.     

Estimating common parameters in heterogeneous random effects models

A question of fundamental importance for meta-analysis of heterogeneous multidimensional data studies is how to form a best consensus estimator of common parameters, and what uncertainty to attach to the estimate. This issue is addressed for a class of unbalanced linear designs which include classical growth curve models. The solution obtained is similar to the popular DerSimonian and Laird (1986) method for a simple meta-analysis model. By using almost unbiased variance estimators, an estimator of the covariance matrix of this procedure is derived. Combination of these methods is illustrated by two examples and are compared via simulation.     

Quantile regression for panel data models with fixed effects under random censoring

Abstract

The locally weighted censored quantile regression approach is proposed for panel data models with fixed effects, which allows for random censoring. The resulting estimators are obtained by employing the fixed effects quantile regression method. The weights are selected either parametrically, semi-parametrically or non-parametrically. The large panel data asymptotics are used in an attempt to cope with the incidental parameter problem. The consistency and limiting distribution of the proposed estimator are also derived. The finite sample performance of the proposed estimators are examined via Monte Carlo simulations.     

Inference on proportional hazard rate model parameter under Type-I progressively hybrid censoring scheme

ABSTRACT

In this paper, under Type-I progressive hybrid censoring sample, we obtain maximum likelihood estimator of unknown parameter when the parent distribution belongs to proportional hazard rate family. We derive the conditional probability density function of the maximum likelihood estimator using moment-generating function technique. The exact confidence interval is obtained and compared by conducting a Monte Carlo simulation study for burr Type XII distribution. Finally, we obtain the Bayes and posterior regret gamma minimax estimates of the parameter under a precautionary loss function with precautionary index k = 2 and compare their behavior via a Monte Carlo simulation study.     

Parameter estimation in semi-linear models using a maximal invariant likelihood function

In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King [2007. Maximal invariant likelihood based testing of semi-linear models. Statist. Papers 48, 357–383] derived the probability density function of the maximal invariant statistic for the non-linear component of these models. Using this density function as a likelihood function allows us to estimate these models in a two-step process. First the non-linear component parameters are estimated by maximising the maximal invariant likelihood function. Then the non-linear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood and maximum profile-marginal likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood.     

Familles of confidence bands for the survival function under the general random censorship model and the Koziol-Green model

Familles of asymptotic 100(1 – α)% level confidence bands for the survival function under the general random right-censorship (GRC) model and the proportional-hazards model of random right-censorship, also known as the Koziol-Green (KG) model, are developed. The family of bands under the GRC model is based on the well-known product-limit estimator (PLE), and this family is rich in that it contains as special cases the bands of Hall and Wellner (1980) and Gillespie and Fisher (1979), and more generally, the GF-type and HW-type bands of Csörg? and Horváth (1986), as well as new bands not previously studied. The familles of bands under the KG model are based on the maximum-likelihood estimator of F under this particular model. We compare the PLE-based bands and the MLE-based bands under the KG model. This enables us to study the loss in efficiency of the former bands when used in a setting where they are not optimal. The notion of asymptotic relative width efficiency (ARWE), defined to be the limiting ratio of the sample sizes needed by the bands to achieve the same asymptotic widths, is employed to compare two bands. Through this efficiency measure it is shown that if the censoring parameter β is known, then the PLE-based bands are highly inefficient relative to the MLE-based bands when β is large. When β is not known, the MLE-based bands are asymptotically conservative. Despite their conservatism, they still dominate the PLE-based bands when β is not too small or equivalently when the degree of censoring is not too light. We also compare the various PLE-based bands under the GRC model. The resulting information is valuable for evaluating competing PLE-based bands. We illustrate the confidence bands by utilizing the well-known Channing House data.     

Families of smooth confidence bands for the survival function under the general random censorship model

Randomly right censored data often arise in industrial life testing and clinical trials. Several authors have proposed asymptotic confidence bands for the survival function when data are randomly censored on the right. All of these bands are based on the empirical estimator of the survival function. In this paper, families of asymptotic (1-)100% level confidence bands are developed from the smoothed estimate of the survival function under the general random censorship model. The new bands are compared to empirical bands, and it is shown that for small sample sizes, the smooth bands have a higher coverage probability than the empirical counterparts.     

Adjusted empirical likelihood models with estimating equations for accelerated life tests

This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.     

A note on asymptotic distributions in directed exponential random graph models with bi-degree sequences

The asymptotic normality of a fixed number of the maximum likelihood estimators (MLEs) in the directed exponential random graph models with an increasing bi-degree sequence has been established recently. In this article, we further derive a central limit theorem for a linear combination of all the MLEs with an increasing dimension. Simulation studies are provided to illustrate the asymptotic results.     

Estimating the error distribution function in semiparametric additive regression models

We consider semiparametric additive regression models with a linear parametric part and a nonparametric part, both involving multivariate covariates. For the nonparametric part we assume two models. In the first, the regression function is unspecified and smooth; in the second, the regression function is additive with smooth components. Depending on the model, the regression curve is estimated by suitable least squares methods. The resulting residual-based empirical distribution function is shown to differ from the error-based empirical distribution function by an additive expression, up to a uniformly negligible remainder term. This result implies a functional central limit theorem for the residual-based empirical distribution function. It is used to test for normal errors.