Inference for the Birnbaum–Saunders Lifetime Regression Model with Applications

The Birnbaum–Saunders distribution is a positively skewed distribution that is frequently used for analyzing lifetime data. Regression analysis is widely used in this context when some covariates are involved in the life-test. In this article, we discuss the maximum likelihood estimation of the model parameters and associated inference. We discuss the likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. A Monte Carlo simulation study is then carried out to examine the performance of the proposed estimators and the interval estimation methods. Finally, some numerical data analyses are done for illustrating all the inferential methods developed here.     

Parameter Estimation of Type-II Hybrid Censored Weighted Exponential Distribution

A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. We study the estimation of parameters of weighted exponential distribution based on Type-II hybrid censored data. By applying the EM algorithm, maximum likelihood estimators are evaluated. Using Fisher information matrix, asymptotic confidence intervals are provided. By applying Markov chain Monte Carlo techniques, Bayes estimators, and corresponding highest posterior density confidence intervals of parameters are obtained. Monte Carlo simulations are performed to compare the performances of the different methods, and one dataset is analyzed for illustrative purposes.     

Estimates based on preliminary data from a specific subsample and from respondents not included in the subsample

Various approaches to obtaining estimates based on preliminary data are outlined. A case is then considered which frequently arises when selecting a subsample of units, the information for which is collected within a deadline that allows preliminary estimates to be produced. At the moment when these estimates have to be produced it often occurs that, although the collection of data on subsample units is still not complete, information is available on a set of units which does not belong to the sample selected for the production of the preliminary estimates. An estimation method is proposed which allows all the data available on a given date to be used to the full-and the expression of the expectation and variance are derived. The proposal is based on two-phase sampling theory and on the hypothesis that the response mechanism is the result of random processes whose parameters can be suitably estimated. An empirical analysis of the performance of the estimator on the Italian Survey on building permits concludes the work. The Sects. 1,2,3,4 and the technical appendixes have been developed by Giorgio Alleva and Piero Demetrio Falorsi; Sect. 5 has been done by Fabio Bacchini and Roberto Iannaccone. Piero Demetrio Falorsi is chief statisticians at Italian National Institute of Statistics (ISTAT); Giorgio Alleva is Professor of Statistics at University “La Sapienza” of Rome, Fabio Bacchini and Roberto Iannaccone are researchers at ISTAT.     

Structural changes during a century of the world’s most popular sport

The analysis in this paper employs a methodology for dating structural breaks in tests with non-standard asymptotic distributions. The application examines whether changes in the rules of a game and major social and political events during the past century had significant effects upon various outcomes of this game. The statistical methodology first applied here proves successful as most breaks can be traced to specific events and rule changes. Dating these breaks allows us to obtain useful insights into production and competition processes in this industry. As such, using empirical tests we illustrate the utility of a valuable statistical technique not applied previously.Ignacio Palacios-Huerta: I am grateful to Gary S. Becker, Tony Lancaster, Robin Lumsdaine, Kevin M. Murphy, Gabriel Perez-Quiros, Ana I. Saracho, Amy Serrano, an associate editor and a referee for useful suggestions. I am also indebted to Barry Blake, Vicki Bogan, Salwa Hammami and Karen Wong for able research assistance, Tony Brown at the Association of Football Statisticians for the data the Hoover Institution for its hospitality, and the Spanish Ministerio de Ciencia y Tecnologia for financial support (grant BEC 2003-08182). The Gauss programs used in this paper were kindly provided by Bruce E. Hansen. Any errors are mine alone.     

Imputation by power transformation

In this paper, a new power transformation estimator of population mean in the presence of non-response has been suggested. The estimator of mean obtained from proposed technique remains better than the estimators obtained from ratio or mean methods of imputation. The mean squared error of the resultant estimator is less than that of the estimator obtained on the basis of ratio method of imputation for the optinum choice of parameters. An estimator for estimating a parameter involved in the process of new method of imputation has been discussed. The MSE expressions for the proposed estimators have been derived analytically and compared empirically. Product method of imputation for negatively correlated variables has also been introduced. The work has been extended to the case of multi-auxiliary information to be used for imputation.     

Parametrically Guided Non-parametric Regression

We present a new approach to regression function estimation in which a non-parametric regression estimator is guided by a parametric pilot estimate with the aim of reducing the bias. New classes of parametrically guided kernel weighted local polynomial estimators are introduced and formulae for asymptotic expectation and variance, hence approximated mean squared error and mean integrated squared error, are derived. It is shown that the new classes of estimators have the very same large sample variance as the estimators in the standard non-parametric setting, while there is substantial room for reducing the bias if the chosen parametric pilot function belongs to a wide neighbourhood around the true regression line. Bias reduction is discussed in light of examples and simulations.     

Likelihood inference for lognormal data with left truncation and right censoring with an illustration

The lognormal distribution is quite commonly used as a lifetime distribution. Data arising from life-testing and reliability studies are often left truncated and right censored. Here, the EM algorithm is used to estimate the parameters of the lognormal model based on left truncated and right censored data. The maximization step of the algorithm is carried out by two alternative methods, with one involving approximation using Taylor series expansion (leading to approximate maximum likelihood estimate) and the other based on the EM gradient algorithm (Lange, 1995). These two methods are compared based on Monte Carlo simulations. The Fisher scoring method for obtaining the maximum likelihood estimates shows a problem of convergence under this setup, except when the truncation percentage is small. The asymptotic variance-covariance matrix of the MLEs is derived by using the missing information principle (Louis, 1982), and then the asymptotic confidence intervals for scale and shape parameters are obtained and compared with corresponding bootstrap confidence intervals. Finally, some numerical examples are given to illustrate all the methods of inference developed here.     

Interval shrinkage estimators

This paper considers estimation of an unknown distribution parameter in situations where we believe that the parameter belongs to a finite interval. We propose for such situations an interval shrinkage approach which combines in a coherent way an unbiased conventional estimator and non-sample information about the range of plausible parameter values. The approach is based on an infeasible interval shrinkage estimator which uniformly dominates the underlying conventional estimator with respect to the mean square error criterion. This infeasible estimator allows us to obtain useful feasible counterparts. The properties of these feasible interval shrinkage estimators are illustrated both in a simulation study and in empirical examples.     

Simultaneous confidence regions for the parameters of a Poisson INAR(1) model

The INAR(1) model (integer-valued autoregressive) is commonly used to model serially dependent processes of Poisson counts. We propose several asymptotic simultaneous confidence regions for the two parameters of a Poisson INAR(1) model, and investigate their performance and robustness for finite-length time series in a simulation study. Practical recommendations are derived, and the application of the confidence regions is illustrated by a real-data example.