Upper Bound for p-Value of the Test of Multivariate Normal Ordered Mean Vectors Against all Alternatives

Consider the problem of testing the isotonic of several p-variate normal mean vectors against all alternatives. It is difficult to compute the exact p-value for this problem of testing with the classical method when the covariance matrices are completely unknown. In the present paper, a test statistic is proposed for this problem of testing. A reformulation of the test statistic is given based on the orthogonal projections on the closed convex cones and then the upper bound for p-value of the test statistic is computed.     

Bridging the gap: A likelihood function approach for the analysis of ranking data

ABSTRACT

In the parametric setting, the notion of a likelihood function forms the basis for the development of tests of hypotheses and estimation of parameters. Tests in connection with the analysis of variance stem entirely from considerations of the likelihood function. On the other hand, non parametric procedures have generally been derived without any formal mechanism and are often the result of clever intuition. In the present article, we propose a more formal approach for deriving tests involving the use of ranks. Specifically, we define a likelihood function motivated by characteristics of the ranks of the data and demonstrate that this leads to well-known tests of hypotheses. We also point to various areas of further exploration such as how co-variates may be incorporated.     

A sinuous stratified unrelated question randomized response model

ABSTRACT

This paper considers the use of stratified random sampling with proportional as well as Neyman allocations to unrelated question randomized response strategy. It has been shown that, for the prior information given, our new model is more efficient in terms of variance (in the case of completely truthful reporting) and mean square error (in case of less than completely truthful reporting). Numerical illustrations are also given in support of the present study.     

An efficient new “Partial” randomized response model

ABSTRACT

In this article, a new “Partial” randomized response model has been proposed. Its properties are studied both theoretically and empirically. The proposed model is proved to be more efficient than the randomized response models studied by Eichhorn and Hayre (1983 Eichhorn, B.H., Hayre, L.S. (1983). Scrambled randomized response methods for obtaining sensitive quantitative dada. J. Stat. Plann. Inference. 7:307–316.[Crossref], [Web of Science ®] , [Google Scholar]) and the “Partial” randomized response model.     

A modified optimal orthogonal new additive model

ABSTRACT

In this article, a new randomized response model has been proposed. The proposed model is found to be more efficient than the randomized response models studied by Singh (2010 Singh, S. (2010). Proposed optimal orthogonal new additive model (POONAM). Statistica. Anno LXX(1):73–81. [Google Scholar]). The relative efficiency of the proposed model has been studied with respect to the Singh (2010 Singh, S. (2010). Proposed optimal orthogonal new additive model (POONAM). Statistica. Anno LXX(1):73–81. [Google Scholar]) model. Numerical illustrations are also given in support of the present study.     

Sequential order statistics from dependent random variables

Abstract

This paper provides an extension for “sequential order statistics” (SOS) introduced by Kamps. It is called “developed sequential order statistics” (DSOS) and is useful for describing lifetimes of engineering systems when component lifetimes are dependent. Explicit expressions for the joint density function, the marginal distributions and the means of DSOS are derived. Under the well known “conditional proportional hazard rate” (CPHR) model and the Gumbel families of copulas for dependency among component lifetimes, some findings are reported. For example, it is proved that the joint density functions of DSOS and SOS have the same structure. Various illustrative examples are also given.     

On Redundancy Allocation to Series and Parallel Systems of Two Components

Abstract

For two components and one standby redundancy, we develop a characterization on the hazard rate order and the reversed hazard rate order of the redundant system lifetime in the context of mutually independent components lifetimes. Also, the likelihood ratio order is derived on the lifetime of the series system with two components lifetimes and two matched active redundancies lifetimes both following the proportional hazard model.     

A note on stratification and gain in precision in estimating diversity from large samples

Several indices of entropy have been suggested in the literature as weighted diversity measures of a population with respect to a classification process. Among them, Shannon's entropy and Havrda -Charvát's non-additive entropies of order a, have been exhaustively used.

When the population is finite but too large to be censused, the diversity with respect to a given classification process must be estimated from a sample.

In this note, on the basis of an asymptotic study of the sample indices in the stratified random sampling, we are going to confirm that when we deal with large samples one can guarantee a gain in precision from stratified random over simple random sampling. This gain becomes considerable when the ‘inaccuracy" (as intended by Kerridge and Rathie and Kannapan) between the frequency vector in each stratum and that in the whole population, varies greatly from stratum to stratum.     

Local influence: a new approach

The concept of local influence was introduced by Cook(1986). Closer study of the idea of perturbations suggests that it is important to distinguish between those of the data and those of the model, and that in the latter case Cook's definition has a theoretical difficulty. Here a new measure is proposed, which has the incidental benefit of being simpler to compute.