Limited information bayesian analysis of a structural coefficient in a simultaneous equations system

An analytical expression is obtained for the marginal posterior density for a structural coefficient in a simultaneous equations system based on a limited information Bayesian analysis. A con- ditional posterior density is obtained given reduced form para- meters. This conditional posterior density is in univariate student t form. Numerical examples suggest that the conditional density hasa tighter distribution around the posterior mean than the unconditional density when the correlation between the endo- genous variables and the structural error term is high.     

Statistical analysis of a two-unit dependent repairable system

Maximum likelihood estimators are investigated a for lr-out-of 2:G repairable system when failures and repairs are statistically dependent. Under two censoring schemes Accelerated Life Testing Procedure (ALTP) is used to obtain the estimates. Information matrices are supplied and a special case when the failure and repair phenomenon are independent of each other is considered.     

Superiority comparisons between mixed regression estimators

This paper gives necessary and sufficient conditions for a mixed regression estimator to be superior to another mixed estimator. The comparisons are based on the mean square error matrices of the estimators. Both estimators are allowed to be biased.     

Some improved ratio type estimators of population mean and ratio in finite population sample surveys

In this paper we present a class of ratio type estimators of the population mean and ratio in a finite population sample surveys with without replacement simple random sampling design, where information on an auxiliary variate x positively correlated with the main variate y is available. Large sample approximations to mean square errors (MSE) of these estimatorsare evaluated and their MSE's are compared with the MSE of the usual ratio estimator [ybar]_R of [ybar] the population mean of y. It is shown that under certain conditions these estimators are more efficient than [ybar]_R. When a prior knowledge of the value of thecoefficient of variation, c_y, of y is at hand, ratio type estimator, say [ybar]₁ of [ybar] is proposed. It is shown, under certain conditions, that [ybar]₁ is more efficient than [ybar]_R. When values of c_y, c_x and the population correlation coefficient ρ is at hand, then we have proposed another estimator, say [ybar]₂ of [ybar], which is always better than [ybar]_R as far as the efficiency is concerned. In fact, is [ybar] ₂ is shown to be even better than [ybar]₁. Finally estimators better than the usual ratio estimator [ybar]/[xbar] of [Ybar] are given.     

Some tests for the power series distibutions in one parameter using the kullback-leibler information measure

The purpose of the article is, in case of one sample, to obtain tests concerning the parameter in the power series distribution in one parameter using Ku11back-Leibier information measure. The class of power series distibutions contains a host of discrete distributions. Ve illustrate the general results obtained in case of the geometric distibution.     

Estimation of gene/haplotype frequencies in genetic marker systems based on phenotype data

Two equivalent methods (gene counting and maximum likelihood) for estimating gene frequencies in a general genetic marker system based on observed phenotype data are derived. Under the maximum likelihood approach, an expression is given for the estimated covariance matrix from which estimated standard errors of the estimators can be found. In addition, consideration is given to the problem of estimating gene frequencies when there are available several independent population data sets.     

Bayesian analysis of a multiple-recapture model

In the Bayesian analysis of a multiple-recapture census, different diffuse prior distributions can lead to markedly different inferences about the population size N. Through consideration of the Fisher information matrix it is shown that the number of captures in each sample typically provides little information about N. This suggests that if there is no prior information about capture probabilities, then knowledge of just the sample sizes and not the number of recaptures should leave the distribution of Nunchanged. A prior model that has this property is identified and the posterior distribution is examined. In particular, asymptotic estimates of the posterior mean and variance are derived. Differences between Bayesian and classical point and interval estimators are illustrated through examples.     

Likelihood-based cross-validation score for selecting the smoothing parameter in maximum penalized likelihood estimation

Maximum penalized likelihood estimation is applied in non(semi)-para-metric regression problems, and enables us exploratory identification and diagnostics of nonlinear regression relationships. The smoothing parameter A controls trade-off between the smoothness and the goodness-of-fit of a function. The method of cross-validation is used for selecting A, but the generalized cross-validation, which is based on the squared error criterion, shows bad be¬havior in non-normal distribution and can not often select reasonable A. The purpose of this study is to propose a method which gives more suitable A and to evaluate the performance of it.

A method of simple calculation for the delete-one estimates in the likeli¬hood-based cross-validation (LCV) score is described. A score of similar form to the Akaike information criterion (AIC) is also derived. The proposed scores are compared with the ones of standard procedures by using data sets in liter¬atures. Simulations are performed to compare the patterns of selecting A and overall goodness-of-fit and to evaluate the effects of some factors. The LCV-scores by the simple calculation provide good approximation to the exact one if λ is not extremeiy smaii Furthermore the LCV scores by the simple size it possible to select X adaptively They have the effect, of reducing the bias of estimates and provide better performance in the sense of overall goodness-of fit. These scores are useful especially in the case of small sample size and in the case of binary logistic regression.