Unbiased estimation in type II censored samples prom two-truncation parameter family

We consider a type II censored sample data from a two-truncation parameter density and obtain the UMVU estimator for an U-estimable parametric function. An explicit expression for the estimator is derived and some interesting special cases are developed. The shortest length confidence interval for the density is also obtained.     

Admissible estimation in an one parameter nonregular family of absolutely continuous distributions

Consider the problem of estimating under squared error loss an arbitrarily positive, strictly increasing or decreasing parametric function based on a sample of size n in an one parameter nonregular family of absolutly continuous distributions with both endpoints of the support depending on a single parameter. We first provide sufficient conditions for the admissibility of generalized Bayes estimators with respect to some specific priors and then treat several examples which illustrate the admissibility of best invariant estimators in some location or scale parameter problems.     

Bayesian robustness of credible regions in the presence of nuisance parameters

The problem of finding the most robust γ-level credible region for the parameter of interest in the presence of a nuisance parameter, with respect to a class of ε-contaminated priors, is studied. The case of arbitrary con-taminations is first analyzed; it is proved that the most robust region for the parameter of interest is theγ-level highest marginal likelihood region (forγ ≥ 0.5). Then, the result is extended to any measurable (not necessarily one-to-one) function of the parameter. Finally, the case of contaminations assigning fixed probabilities to the sets of a partition of the parameter space is analyzed and a partial result is given.     

A REPARAMETERISATION METHOD FOR EMBEDDED MODELS

ABSTRACT

A reparameterisation procedure is investigated for embedded model problems. The procedure is given by solving differential equations determined by indeterminate forms of limit. Some properties are provided for the existence of an embedded model. Note that an embedded model may include another embedded model. We introduce the concept of embedded model of kth generation and discuss the use of one-by-one elimination procedure to construct graphs of embedded models. As examples, we derive embedded models for some distributions, to which existing method cannot be applied. Our method includes the method given by Cheng et al. [1] Cheng, R.C.H., Evans, B.E. and Iles, T.C. 1992. Embedded Models in Non-Linear Regression. J. R. Statist. Soc. B, 54: 877–888.  [Google Scholar] as a special case.     

SECOND-ORDER ASYMPTOTICS FOR SCORE TESTS IN HETEROSKEDASTIC t REGRESSION MODELS

ABSTRACT

This paper develops corrected score tests for heteroskedastic t regression models, thus generalizing results by Cordeiro, Ferrari and Paula[1] Cordeiro, G.M., Ferrari, S.L.P. and Paula, G.A. 1993. Improved Score Tests for Generalized Linear Models. Journal of the Royal Statistical Society B, 55: 661–674.  [Google Scholar] and Cribari-Neto and Ferrari[2] Cribari-Neto, F. and Ferrari, S.L.P. 1995. Second-order Asymptotics for Score Tests in Generalised Linear Models. Biometrika, 82: 426–432. [Crossref], [Web of Science ®] , [Google Scholar] for normal regression models and by Ferrari and Arellano-Valle[3] Ferrari, S.L.P. and Arellano-Valle, R. 1996. Modified Likelihood Ratio and Score Tests in Linear Regression Models Using the t Distribution. Brazilian Journal of Probability and Statistics, 10: 15–33.  [Google Scholar] for homoskedastic t regression models. We present, in matrix notation, Bartlett-type correction formulae to improve score tests in this class of models. The corrected score statistics have a chi-squared distribution to order n ^?1, where n is the sample size. We apply our main result to a few special models and present simulation results comparing the performance of the usual score tests and their corrected versions.     

Some moment properties and limit theorems of the reversed generalized logistic distribution with applications

In this paper we discuss an extended form of the logistic distribution and refer to it as the reversed generalized logistic distribution. We study some moment properties, and derive exact and explicit formulas for the mean, median, mode, variance, coefficients of skewness and kurtosis, and percentage points of this distribution. In addition, we study its limiting distributions as the shape parameter tends to zero or infinity. We also discuss some possible applications in bioassays through logistic regression approach.     

On exact computation of minimum sample size for restricted estimation of a binomial parameter

The problem of determining minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level is considered. It is assumed that available auxiliary information allows to restrict the parameter space to some interval whose left boundary is above zero. A range-preserving estimator resulting from the conditional maximization of the likelihood function is considered. A method for exact computation of minimum sample size controlling for the relative error is proposed. Several tables of minimum sample sizes for typical situations are also presented. The range-preserving estimator achieves the same precision and confidence level as the unrestricted maximum likelihood estimator but with a smaller sample.     

Use of the Bootstrap and Cross-Validation in Ridge Regression

Several existing methods for the choice of the ridge parameter are reviewed, and a bootstrap method is proposed. The bootstrap provides independent measures of prediction errors based on multiple predictions along with an estimate of the standard error of prediction. The bootstrap and selected competitors are compared through Monte Carlo simulations for various degrees of design matrix collinearity and varying levels of signal-to-noise ratio. The procedure is also illustrated by application to two published data sets. In one case, the bootstrap choice of the ridge parameter leads to a smaller mean squared error of prediction than the ridge trace method. In the second case, an optimal choice of no perturbation is confirmed. Benefits of the bootstrap choice include its less subjective nature, ease of implementation, and robustness.     

On the Characteristic Function for Asymmetric Exponential Power Distributions

The econometric literature has seen a surge of developments in the theory and applications of asymmetric exponential power distributions (AEPDs). Here, for the first time, we derive explicit closed form expressions for the characteristic function of AEPDs. The expressions involve the complex parameter Wright generalized hypergeometric function.