Communications in Statistics: Theory and Methods

Pewsey, Arthur

doi: 10.1081/STA-120028370pmid: N/A

Abstract In this paper, bias-corrected estimation for the parameters of the general half-normal distribution is explored. Bias-corrected, maximum likelihood based, point estimates are identified and a bias-corrected confidence interval construction given for the estimation of the distribution's location parameter. The results from a Monte Carlo experiment designed to compare the performance of the bias-corrected inferential tools with their non-bias-corrected counterparts are presented and the inferential improvements accruing from bias-correction are identified. The application and advantages of the developed methodology are illustrated in the analysis of data on the percentage body fat of elite male athletes.

Girard, Stéphane

doi: 10.1081/STA-120028371pmid: N/A

Abstract We present a new estimator of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse cumulative hazard function. Our estimator is based on the log-spacings of the upper order statistics. Therefore, it is very similar to the Hill estimator for the extreme value index. We prove the weak consistency and the asymptotic normality of our estimator. Its asymptotic as well as its finite sample performances are compared to classical ones.

Gruber, Dr. Marvin H. J.

doi: 10.1081/STA-120028372pmid: N/A

Abstract A setup with r uncorrelated linear models is considered. A generalization of Zellner's balanced loss function is proposed. Zellner's balanced loss function takes both error of estimation and goodness of fit into account. The classical loss function only considers error of estimation. Empirical Bayes and approximate minimum mean square error estimators are derived. The efficiency of these estimators is evaluated averaging over Zellner's balanced loss function. Comparisons are then made with the least square estimator and the analogous estimators for the classical loss function. Three kinds of James–Stein type estimators are considered that are similar to empirical Bayes estimators originally formulated by Rao, Wind and Dempster.

Lin, Jin-Guan; Wei, Bo-Cheng

doi: 10.1081/STA-120028373pmid: N/A

Abstract This paper discusses the tests of heteroscedasticity and/or correlation in the framework of pth antedependence errors, in which the variances of the random errors are determined by their correlation and those of white noises. We first discuss the test for heteroscedasticity of random errors, which is equivalent to the simultaneous test of correlation of random errors and homoscedasticity of white noises. When random errors' correlation or heteroscedasticity of white noises occurs, we then consider individual tests for heteroscedasticity of white noises and correlation respectively, in which there are some nuisance parameters involved. The likelihood ratio statistics, score statistics and their adjustments are derived and illustrated with chloride data [Bates, D. M., Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications. New York: John Wiley & Sons] and the relaxation data of the current [Glasbey, C. A. (1980). Nonlinear regression with autoregressive time series errors. Biometrics 36:135–140; Seber, G. A. F., Wild, C. J. (1989). Nonlinear Regression. New York: John Wiley & Sons].

González-Manteiga, W.; Pérez-González, A.

doi: 10.1081/STA-120028374pmid: N/A

Abstract Missing data occur in most applied statistical analysis. The need to estimate the conditional or unconditional mean of a variable when some of its observations are missing is very frequent. In this article we study the effect of missing observations on the response variable in the estimation of a multivariate regression function. This effect is also considered in the estimation of the marginal mean. Following the research of Chu and Cheng [Chu, C. K., Cheng, P. E. (1995). Nonparametric regression estimation with missing data. J. Statist. Planning Inference 48:85–99] for the univariate case, we propose three non-parametric estimators of the regression function based on the Multivariate Local Linear Smoother [see Ruppert, D., Wand, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22(3):1346–1370]. The first consists of using only complete observations; the other two use simple or multiple imputation techniques respectively to complete the sample. The behavior in function of the Asymptotic Mean Squared Error (AMSE) is studied for the estimators. A method for obtaining optimal estimated bandwidth matrices based on the Bootstrap resampling mechanism is proposed.

Franzén, Stefan

doi: 10.1081/STA-120028375pmid: N/A

Abstract In this paper we will present a method for constructing fixed length confidence intervals using Sequential Probability Ratio Tests (SPRT). We will see that under the conditions of monotone likelihood ratio and that the log likelihood function is concave as a function of the parameter, the set of parameters corresponding to null hypotheses that has not been rejected is an interval. We apply the SPRT fixed length confidence interval to a sequence of observations on a Bernoulli distributed random variable where we get a SPRT fixed length interval for the parameter p.

Lin, Fei

doi: 10.1081/STA-120028376pmid: N/A

Abstract In an experiment of treatment selections, random samples are drawn from k populations with different means. The probability that, among the samples, the sample mean from the population with the highest underlying expected value turns out to be the highest is called the probability of correct selection (PCS). In this article, a probability inequality motivated by the PCS problem, is obtained with respect to change in variances. As an application of the inequality in normal mean selection, it is shown that in a multiple treatment experiment setting, by increasing sample sizes, and thus obtaining a higher precision in the estimation of means, in general (but not always), one will have a higher PCS. However, there are special case exceptions.

Iyer, Srikanth K.; Manjunath, D.

doi: 10.1081/STA-120028377pmid: N/A

Abstract We derive bivariate exponential, gamma, Coxian or hyperexponential distributions. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX + Z where a is a positive constant and Z is independent of X. By fixing the marginal distributions of X and Y, we characterize the distribution of Z. To obtain negative correlations, we define X = aP + V and Y = bQ + W where P and Q are exponential antithetic random variables. Our bivariate models are useful in introducing dependence between the interarrivals and service times in a queueing model and in the failure process in multicomponent systems. The primary advantage of our model in the context of queueing analysis is that it remains mathematically tractable because the Laplace Transform of the joint distribution is a rational function, that is a ratio of polynomials. Further, the variates can be very easily generated for computer simulation. These models can also be used for the study of transmission controlled queueing networks.

Sun, Jianguo; Sun, Liuquan; Flournoy, Nancy

doi: 10.1081/STA-120028378pmid: N/A

Abstract Competing risks analysis of the case-cohort design is often required in epidemiological studies and for this, some methods have been proposed under the proportional hazards model. It is known that the proportional hazards model may not fit survival data well sometimes. This paper considers the analysis under the additive hazards model. Methods are proposed for estimating regression parameters and cumulative baseline hazard functions as well as cumulative incidence functions. The proposed estimators are shown to be consistent and asymptotically normal using the martingale central limit theory. Simulation studies are conducted and suggest that the proposed methods perform well.

Lagos, Bernardo M.

doi: 10.1081/STA-120028379pmid: N/A

Abstract In this paper we extend heuristically a simple formula for the local power of second order for the likelihood ratio, the Wald and score statistics, when a Gaussian autoregressive and moving average model of first order is considered and the interest and nuisance parameter vectors are multi-dimensional. The second order local power for the three criteria mentioned here are compared using particular models and hypotheses.