Estimation of noncentrality parameters

We propose some estimators of noncentrality parameters which improve upon usual unbiased estimators under quadratic loss. The distributions we consider are the noncentral chi-square and the noncentral F. However, we give more general results for the family of elliptically contoured distributions and propose a robust dominating estimator.     

Estimates of fertility in Bangladesh

The attempt is made to estimate fertility levels in Bangladesh on the basis of data collected during the 1974 Census. In the 1st section attention is directed to providing an overall picture of the demographic situation in the country. Comparisons between the 1961 and 1974 data demonstrates that the 1974 Census data provide consistent results. Factors such as the degree of urbanization, literacy and economic participation rates--considered as indicators of development--all seem to show little progress during the intercensal period. The use of child/women ratios (CWRs) provides plausible evidence of the likelihood of a fertility decline. A decline in CWR values is small for "all areas" but a marked decline can be noted for "urban areas." The recorded mean number of children is less in 1974 than in 1961 for women under age 35 whereas for the older groups the 1974 Census shows higher mean numbers. The Bangladesh Fertility Survey (BFS) data result for the total fertility rate of 6.58 is very close to that estimated for the 1974 Census--6.59. The reverse survival method also indicates that birthrates have been lower during the 1969-1974 period.     

Statistical Analysis of Marginal Count Failure Data

Manufacturers want to assess the quality andreliability of their products. Specifically, they want to knowthe exact number of failures from the sales transacted duringa particular month. Information available today is sometimesincomplete as many companies analyze their failure data simplycomparing sales for a total month from a particular departmentwith the total number of claims registered for that given month.This information—called marginal count data—is, thus,incomplete as it does not give the exact number of failures ofthe specific products that were sold in a particular month. Inthis paper we discuss nonparametric estimation of the mean numbersof failures for repairable products and the failure probabilitiesfor nonrepairable products. We present a nonhomogeneous Poissonprocess model for repairable products and a multinomial modeland its Poisson approximation for nonrepairable products. A numericalexample is given and a simulation is carried out to evaluatethe proposed methods of estimating failure probabilities undera number of possible situations.     

Selecting a Good Stochastic System for the Large Number of Alternatives

In this article, we present the problem of selecting a good stochastic system with high probability and minimum total simulation cost when the number of alternatives is very large. We propose a sequential approach that starts with the Ordinal Optimization procedure to select a subset that overlaps with the set of the actual best m% systems with high probability. Then we use Optimal Computing Budget Allocation to allocate the available computing budget in a way that maximizes the Probability of Correct Selection. This is followed by a Subset Selection procedure to get a smaller subset that contains the best system among the subset that is selected before. Finally, the Indifference-Zone procedure is used to select the best system among the survivors in the previous stage. The numerical test involved with all these procedures shows the results for selecting a good stochastic system with high probability and a minimum number of simulation samples, when the number of alternatives is large. The results also show that the proposed approach is able to identify a good system in a very short simulation time.     

Income vulnerability of rural households in Bangladesh: a comparison between Bayesian and classical methods

The geographical location and the monsoon climate render Bangladesh highly vulnerable to natural hazards, deteriorating the country's socio-economic stability. This study is based on 500 randomly chosen rural households from the Household Income and Expenditure Survey [Bangladesh Bureau of Statistics, Planning Division, Ministry of Planning, Government of the People's Republic of Bangladesh, Dhaka, 2006]. The objectives are to estimate the income vulnerability of rural households and to check whether the Bayesian approaches (natural conjugate prior and non-informative prior estimates) have any superiority over the classical (feasible generalized least square (FGLS)) method. The poverty level, measured from the data, is 24%; whereas the vulnerability estimates, using FGLS, natural conjugate prior and non-informative prior are 31%, 69% and 82%, respectively. Vulnerability estimates by the Bayesian natural conjugate prior approach is found to have greater efficiency compared with FGLS and non-informative prior approaches.     

Optimum Critical Value for Pre-Test Estimator

In this paper, methods are proposed in finding the robust design in both Taguchi and Standard setups when a signal factor is present. The robust design is a set of level combinations of control factors so that the effect of controllable noise factors on response is minimum. Both univariate and multivariate methods are used in finding the influential noise factors for the determination of robust designs.     

New estimators of distribution functions

ABSTRACT

This article considers the estimation of a distribution function F_X(x) based on a random sample X₁, X₂, …, X_n when the sample is suspected to come from a close-by distribution F₀(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F₀(x). As a by-product similar estimators are proposed for population quantiles.     

Normal Deviation and Poisson Approximation of a Security Market by the Geometric Markov Renewal Processes

We consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. European call option pricing formulas for GMRP are presented.     

On shrinkage least squares estimation in a parallelism problem

In a multi-sample simple regression model, generally, homogeneity of the regression slopes leads to improved estimation of the intercepts. Analogous to the preliminary test estimators, (smooth) shrinkage least squares estimators of Intercepts based on the James-Stein rule on regression slopes are considered. Relative pictures on the (asymptotic) risk of the classical, preliminary test and the shrinkage least squares estimators are also presented. None of the preliminary test and shrinkage least squares estimators may dominate over the other, though each of them fares well relative to the other estimators.     

Optimum spacings for the joint estimation and tests of hypothesis of location and scale parameters of the cauchy distribution

A simultaneous test for the location and scale parameters of the Cauchy distribution is considered based on selected order statistics.. It is shown that optimum spacings that maximise the Pitman ARE of the test coincide with that of the optimum spacings for the estimation problem.