Adjusted Hazard Rate Estimator Based on a Known Censoring Probability

In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson–Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol–Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques.     

A Generalized Time-Dependent Conditional Linear Model with Left-Truncated and Right-Censored Data

Consider the model φ(S(y | X)) = β(y) ^T X, where φ is a known link function, S(· | X) is the survival function of a response Y given a covariate X = (1, X, X ²,…, X ^p ), and β(y) is an unknown vector of time-dependent regression coefficients. The response Y is subject to left truncation and right censoring. We assume that given X, Y is independent of (C, T) where C and T are censoring and truncation variables with P(C ≥ T) = 1. In this article, with some modification of the assumptions in Lemmas 5 and 6 of Iglesias-Pérez and González-Manteiga (1999 Iglesias-Pérez , C. J. , González-Manteiga , W. G. ( 1999 ). Strong representation of a generalized product-limit estimator for truncated and censored data with some application . J. Nonparametric Statist. 10 : 213 – 244 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), we present an almost sure representation for the generalized product-limit estimator (GPL) of S(y | X). Based on the GPL and the approach of Teodorescu et al. (2010 Teodorescu , B. , Keilegom , I. V. , Cao , R. ( 2010 ). Generalized time-dependent conditional linear models under left truncation and right censoring . Ann. Instit. Statist. Math. 62 : 465 – 485 .[Crossref], [Web of Science ®] , [Google Scholar]), a least squares estimator of β(y) is obtained and a bootstrap procedure is proposed to choose the optimum bandwidth.     

Estimation on Varying-Coefficient Partially Linear Model With Different Smoothing Variables

The authors give the estimation on the varying-coefficient partially linear regression model with different smoothing variables. The efficient estimators of the intercept function and the coefficient functions are obtained by a one-step back-fitting technique based on their initial estimators given by local linear technique and the averaged method. Furthermore, their asymptotic normalities are given. Some simulation studies are used to illustrate the performances of the estimation.     

On the Use of Superpopulation Model in Estimation of Population Mean in Two-Occasion Rotation Patterns

The present work is an attempt to study the estimation of the population mean on the current occasion in two-occasion successive (rotation) sampling under a superpopulation model. Six different estimators are proposed for estimating the current population mean in two-occasion successive (rotation) sampling. Optimum replacement policies and performances of the proposed estimators have been discussed. Results are interpreted via empirical studies.     

Bayesian Analysis of Two-Regime Threshold Autoregressive Moving Average Model with Exogenous Inputs

We consider Bayesian analysis of threshold autoregressive moving average model with exogenous inputs (TARMAX). In order to obtain the desired marginal posterior distributions of all parameters including the threshold value of the two-regime TARMAX model, we use two different Markov chain Monte Carlo (MCMC) methods to apply Gibbs sampler with Metropolis-Hastings algorithm. The first one is used to obtain iterative least squares estimates of the parameters. The second one includes two MCMC stages for estimate the desired marginal posterior distributions and the parameters. Simulation experiments and a real data example show support to our approaches.     

Akaike Information Criterion for Selecting Variables in the Nested Error Regression Model

The Akaike Information Criterion (AIC) is developed for selecting the variables of the nested error regression model where an unobservable random effect is present. Using the idea of decomposing the likelihood into two parts of “within” and “between” analysis of variance, we derive the AIC when the number of groups is large and the ratio of the variances of the random effects and the random errors is an unknown parameter. The proposed AIC is compared, using simulation, with Mallows' C _p , Akaike's AIC, and Sugiura's exact AIC. Based on the rates of selecting the true model, it is shown that the proposed AIC performs better.     

Objective Priors for Parameters in a Normal Linear Regression with Measurement Error

We investigate certain objective priors for the parameters in a normal linear regression models with one of the explanatory variables subject to measurement error. We first show that the use of the standard non informative prior for normal linear regression without measurement error leads to an improper posterior in the measurement error model. We then derive the Jeffreys prior and reference priors, and show that they lead to proper posteriors. We use simulation study to compare the frequentist performance of the estimates derived using these priors, and the MLE.     

Inference Under Right Censoring in a Discrete Setup

In this article, we consider the right random censoring scheme in a discrete setup when the lifetime and censoring variables are independent and have geometric distributions with means 1/θ₁ and 1/θ₂, respectively. We first obtain the Maximum Likelihood and Method of Moment estimators of the unknown parameters. We also find the Bayes and Posterior Regret Gamma Minimax estimators of the parameters for the two cases when the prior distributions are dependent and independent, assuming a squared error loss function. We then discuss the Proportional Hazard model, and obtain Maximum Likelihood estimators of the unknown parameters and derive the Bayes estimators assuming squared error loss using Markov Chain Monte Carlo methods.     

Interval Estimation by Frequentist Model Averaging

An important contribution to the literature on frequentist model averaging (FMA) is the work of Hjort and Claeskens (2003 Hjort , N. L. , Claeskens , G. ( 2003 ). Frequestist model average estimators . J. Amer. Statist. Assoc. 98 : 879 – 899 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), who developed an asymptotic theory for frequentist model averaging in parametric models based on a local mis-specification framework. They also proposed a simple method for constructing confidence intervals of the unknown parameters. This article shows that the confidence intervals based on the FMA estimator suggested by Hjort and Claeskens (2003 Hjort , N. L. , Claeskens , G. ( 2003 ). Frequestist model average estimators . J. Amer. Statist. Assoc. 98 : 879 – 899 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) are asymptotically equivalent to that obtained from the full model under both parametric and the varying-coefficient partially linear models. Thus, as long as interval estimation rather than point estimation is concerned, the confidence interval based on the full model already fulfills the objective and model averaging provides no additional useful information.     

A Quality Control Approach of PVC Gloves Based on the Integration of SPC and EPC

Parameters in the production process of PVC gloves, such as production cycle, oven temperature, temperature, and viscosity of feed liquids are critical to the final quality of gloves. The dosing of feed liquids and plasticization of gloves are all controlled manually, and the viscosities of feed liquids and average oven temperature cannot be exactly regulated; those result in the degradation of final products and unreliability of the process. This article conducted studies on reliability enhancement of glove quality—an integrated control policy based on SPC and EPC was raised to minimize the process fluctuation, stabilize the output quality, and finally improve the process reliability. Using SPC method to eliminate the assignable factors in the process, when the process is under control, the EPC method was applied to make the process parameters closer to the target values which were decided through an inverse model of the process. The theory and methods were verified in the case study of PVC production control.