Characterization of an optimal matrix estimator under convex loss function

Characterization of an optimal vector estimator and an optimal matrix estimator are obtained. In each case appropriate convex loss functions are considered. The results are illustrated through the problems of simultaneous unbiased estimation, simultaneous equivariant estimation and simultaneous unbiased prediction. Further an optimality criterion is proposed for matrix unbiased estimation and it is shown that the matrix unbiased estimation of a matrix parametric function and the minimum variance unbiased estimation of its components are equivalent.     

Stress–strength models with more than two states under exponential distribution

In the stress–strength models, analysis is based on the reliability of the system where the system is either in operational state or in failure state. Ery?lmaz (2011 Ery?lmaz, S. (2011). A new perspective to stress–strength models. Ann. Inst. Stat. Math. 63(1):101–115.[Crossref], [Web of Science ®] , [Google Scholar]) introduced the stress–strength reliability in a different framework assigning more than two states to the system depending on the difference between strength and stress values. Unlike Ery?lmaz (2011 Ery?lmaz, S. (2011). A new perspective to stress–strength models. Ann. Inst. Stat. Math. 63(1):101–115.[Crossref], [Web of Science ®] , [Google Scholar]), the present article deals with the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. This article presents in detail the estimation aspect of the multistate stress–strength reliability function.     

Sequential estimation of a location parameter from delayed observations

The problem of sequentially estimating a location parameter is considered in the special case when the data arrive at random times. Certain classes of sequential estimation procedures are derived under a location invariant loss function and with the observation cost determined by a function of the moment of stopping and the number of observations up to this moment.     

Asymptotic distribution for the order statistics of a truncated one-parameter family of distributions

In this article we have presented some of the asymptotic theorems related to one-truncation parameter family of distributions ? Comparison of performance of different estimators and other inferential problems have been tackled - Also applications of the main results have been given and illustrated their uses with examples.     

On location and scale parameters of exponential distributions with censored observations

In this paper we first address the problem of estimating the common scale of several exponential distributions with unknown location parameters when censored samples are observed. The improved estimators are basically Stein type testimators. These testimators are then used to construct improved estimators of location parameters.     

Estimating quantiles of several normal populations with a common mean

Suppose we have k( ? 2) normal populations with a common mean and possibly different variances. The problem of estimation of quantile of the first population is considered with respect to a quadratic loss function. In this paper, we have generalized the inadmissibility results obtained by Kumar and Tripathy (2011 Kumar, S., Tripathy, M.R. (2011). Estimating quantiles of normal populations with a common mean. Commun. Stat. - Theory Methods 40:2719–2736.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for k = 2 to a general k( ? 2). Moreover, a massive simulation study has been done in order to numerically compare the risk values of various proposed estimators for the cases k = 3 and k = 4 and recommendations are made for the use of estimators under certain situations.     

Stable estimation of location parameter -nonasymptotic approach

Let X₁:, X₂:, …, X_n be iidrv's with cdf F?, F?(x)=F (x-θ), R. Let T be an equivariant median-unbiased estimator of θ. Let πε(F)={G = (1 -ε) F+εH, H any cdf} and let M(G, T) be a median of T if X₁ has cdf G. The oscillation of the bias of T, defined as

Bε(T)=sup (M(G₁ T) :G₁,G₂:∈π_σ:(F)} ,is considered and the estimator with the smallest B$epsi;(T) is explicitly constructed     

Estimating the common hazard rate of several exponential distributions

Abstract

In the present communication, we consider the estimation of the common hazard rate of several exponential distributions with unknown and unequal location parameters with a common scale parameter under a general class of bowl-shaped scale invariant loss functions. We have shown that the best affine equivariant estimator (BAEE) is inadmissible by deriving a non smooth improved estimator. Further, we have obtained a smooth estimator which improves upon the BAEE. As an application, we have obtained explicit expressions of improved estimators for special loss functions. Finally, a simulation study is carried out for numerically comparing the risk performance of various estimators.     

Equivariant estimation under the pitman closeness criterion

For the point estimation in models with group structures, an invariance approach to deriving superior estimators is discussed in the Pitman closeness (PC) criterion. When the maximal invariant statistic is parameter-free, that is, ancillary, the closest equivariant estimator to the true value in the PC criterion is presented. On the other hand, as an example where a distribution of the maximalinvariant statistic depends on unknown parameters, the paper treats the Stein problem in estimation of a variance and obtains an improved estimator in the PC criterion by Stein's invariance approach. Also the Stein problem in simultaneous estimation of a location vector of a spherical symmetric distribution is studied.