The exact distribution and density functions of the stein-type estimator for normal variance

In this paper, we derive the exact distribution and density functions of the Stein-type estimator for the normal variance. It is shown by numerical evaluation that the density function of the Stein-type estimator is unimodal and concentrates around the mode more than that of the usual estimator.     

Unbiasedness of fourier integral estimator under weaker assumptions

The Fourier integral estimator (FIE) of the hazard rate function have been introduced by Singpurwalla and Wong (1983) in order to improve the rate of convergence of mean square error. However, the asymptotic properties are derived under several assumptions. These assumptions are too strong to be satisfied in most applications. The situation becomes worse when some of these assumptions appear contradictory to each other. This greatly limits the usage of FIE. This paper endeavors to release or weaken some of these assumptions and therefore expand the applicable coverage of FIE.     

The general expressions for the moments of lawless and wang's ordinary ridge regression estimator

In this paper, we derive the exact general expressions for the moments of an ordinary ridge regression (ORR) estimator for individual regression coefficients in a different way from Firinguetti (1987). Using the derived expressions, we evaluate numerically the first four moments of the ORR estimator, and examine its bias, mean square error, skewness and kurtosis. Further, Monte Carlo experiments are carried out in order to examine the shape of the density function of the ORR estimator.     

A functional approach to estimating finite population distribution functions

Existing estimators of a finite population distribution function that utilize auxiliary information are often constructed by a point wise argument. As a result, these estimators are not always monotone. We adopt a functional approach to the problem and propose two estimators based on compositions of functions. Asymptotic variance formulae are derived for the proposed es-timators. Comparisons are made with existing estimators in a simulation study using three natural populations.     

Estimation of non-occurrence probability in periodic model

Dimitrov and Khalil (1992) introduced a class of new probability distributions for modeling environmental evolution with periodic behavior. One of the key parameters in these distributions is α, the probability that the event being studied does not occur. In that article the authors derive an estimator for this parameter assuming a series of conditions. In this article it is shown that the estimator is valid under more general conditions, i.e. same of the assumptions are not necessary. It is shown that under the assumption that the elapsed time measured from the starting point of a period until the first occurrence time of the event given that the event occurred in this cycle is related to α, an approximate maximum likelihood estimator of a is proposed. The large sample properties of the estimator are discussed. Monte Carlo study is done for supporting the theoretical results.     

Estimation of reliability under ordered restriction on the parameters

This paper deals with the estimation of reliability for a strength-stress model under ordered restriction on the parameters. It is assumed that components have exponential distributions and are arranged in a parallel system and the failure of one component, results in increasing the failure rate of the remaining components. Results are derived when (i) the ordering of the means is taken into account and when (ii) the ordering of the means is ignored. Simulation studies are carried out to compare the results. It is noticed that, in almost all cases, in case (i) the estimates are closer to the true value with smaller mean squared error (MSE) and smaller’ standard deviation than in case (ii). Thus when the ordering of the means is present in the model, such information should be incorporated in the estimation of reliability.     

Parameter estimation for ihe birnbaum-saunders distribution based on symmetrically censored samples

Ihe Bimbaum-Saunders distribution was derived to model fatigue life. Frequently, it becomes necessary to stop a life testing process before all the test items have failed. Therefore, estimation procedures need to be developed for use when censoring occurs. In this article, we have derived estimators for the parameters of this distribution which may be used for complete samples or Type II symmetrically censored samples A simulation study was also conducted to examine the performance of these estimators.     

Two-stage james-stein estimators of the mean based on prior knowledge

We suggest five types of two-stage James-Stein type estimators of the mean vector μ based on prior knowledge about μ and two-stage sampling scheme proposed by Waikar and Katti(1971) Their risks are evaluated and calculated to compare with two-stage estimator suggested by Waikar and Katti(1971) when the prior form of an initial estimate of μ is 0. We find that the five estimators suggested here all have high efficiencies in large dimensions and/or in large value of ratio of two sample sizes at each stage.     

Estimating multivariate random effects without replication

This paper considers the estimation of multivariate random effects that are measured with error, but for which there are no replications. Using structural simplification of the correlation of the data, separate estimates are generated for the covariance of the random effects and the covariance of the error. An estimator of the random effects based on a truncated eigen structure is defined, and matrix mean squared error and its trace (risk) are analyzed, with comparison to the maximum likelihood estimator (m.l.e) and also to the Stein-like estimator of Efron and Morris (1972). It is shown that the estimator has risk which is smaller than the risk of the maximum likelihood estimator and the Efron-Morris estimator in most cases.     

A note on partially adaptive estimation via a normal mixture

This note shows that the partially adaptive estimator proposed in Phillips (1994) is a consistent estimator of regression parameters in a degenerate but important case.