Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

On Optimal Estimating Functions in the Presence of Nuisance Parameters

When there is only one interesting parameter θ₁ and one nuisance parameter θ₂, Godambe and Thompson (1974 Godambe , V. P. , Thompson , M. E. ( 1974 ). Estimating equations in the presence of a nuisance parameter . Ann. Statist. 2 : 568 – 571 .[Crossref], [Web of Science ®] , [Google Scholar]) showed that the optimal estimating function for θ₁ essentially is a linear function of the θ₁-score, the square of the θ₂-score, and the derivative of θ₂-score with respect to θ₂. Mukhopadhyay (2000b) generalized this result to m nuisance parameters. Mukhopadhyay (2000 Mukhopadhyay , P. ( 2000 ). On some lower bounds for the variance of an estimating function . Int. J. Math. Statist. Sci. 9 ( 2 ). [Google Scholar] 2002a Mukhopadhyay , P. ( 2002a ). On estimating functions in the presence of a nuisance parameter . Commun. Statist. Theor. Mem. 31 ( 1 ): 31 – 36 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] b Mukhopadhyay , P. ( 2002b ): Some lower bounds on variance of estimating functions . J. Statist. Res. 36 ( 2 ): 189 – 197 . [Google Scholar]) obtained lower bounds to the variance of regular estimating functions in the presence of nuisance parameters. Taking cues from these results we propose a method of finding optimal estimating function for θ₁ by taking the multiple regression equation on θ₁ score and Bhattacharyya's (1946 Bhattacharyya , A. ( 1946 ). On some analogues of the amount of information and their use in statistical estimation . Sankhya A 8 : 1 – 14 . [Google Scholar]) scores with respect to θ₂. The result is extended to the case of m nuisance parameters.     

Factors Influencing Family Business Continuity in Indian Small and Medium Enterprises (SMEs)

Most of the research on family business continuity is based in the western world. Continuity of family business is affected by social and cultural factors on one hand and on the stage of growth of the economy on the other. This paper focuses on the continuity concerns with reference to (1) the Eastern context and (2) the developing economy’s context, by studying Indian family businesses, with (3) specific focus on Small and Medium Enterprises (SMEs). Data were collected from SME business families using a questionnaire. The impact of various factors was examined on the family, the business and the inductee. This empirical study validates some of the drivers of effective succession identified so far in the literature. It sharply identifies the variables that can be more relevant and can directly affect the outcome in terms of positive impact on the business, family and the inductee. The findings of the study will be of great help in successful succession planning for the growth and development of SMEs that contribute significantly to economic growth.     

Note on umvsu-estimation under randomized response model

Considering a class ofs randomized response trials for eliciting sensitive information from a sample survey and a class of ordered sampling designs, a uniformly minimum variance unbiased estimator of population variance (of the sensitive character) has been obtained. This note indicates that a theorem (theorem 3.9) of Cassel, Sarndal and Wretman (1977) and the results in the present note can be extended to estimation of any symmetric function of population values in the field of direct response surveys and randomized response surveys respectively.     

SAVE: Robust or not?

Abstract

Sliced average variance estimation (SAVE) is one of the best methods for estimating central dimension-reduction subspace in semi parametric regression models when covariates are normal. In recent days SAVE is being used to analyze DNA microarray data especially in tumor classification but most important drawback is normality of covariates. In this article, the asymptotic behavior of estimates of CDR space under varying slice size is studied through simulation studies when covariates are non normal but follows linearity condition as well as when covariates slightly perturbed from normal distribution and we observed that serious error may occur under violation normality assumption.     

Committee Decisions with Partisans and Side-Transfers

A dichotomous decision-making context in committees is considered where potential partisan members with predetermined votes can generate inefficient decisions and buy neutral votes. The optimal voting rule minimizing the expected costs of inefficient decisions for the case of a three-member committee is analyzed. It is shown that the optimal voting rule can be non-monotonic with respect to side-transfers: in the symmetric case, majority voting is optimal under either zero, mild or full side-transfer possibilities, whereas unanimity voting may be optimal under an intermediate side-transfer possibility. The side-transfer possibilities depend on the power of partisans (their ability or willingness to pay for neutral votes) relative to the corruptibility of neutral members (personal cost of deliberately casting a `wrong' vote).