Optimal Tests for No Contamination in Reliability Models

Inferences on mixtures of probability distributions, in general,and of life distributions, in particular, are receiving considerableimportance in recent years. The likelihood ratio procedure oftesting for the null hypothesis of no contamination is oftenvery cumbersome and lacks its usual asymptotic properties. Recently,SenGupta (1991) has introduced the notion of an `L-optimal' testfor such testing problems. The idea is to recast the originalseveral parametric hypotheses representation of the null hypothesisin terms of only a single hypothesis involving an appropriatelychosen parametric function. This approach is shown to be bothmathematically elegant and operationally simple for a quite generalclass of mixture distributions which contains, in particular,all mixtures of the one-parameter exponential family and alsoa very rich subclass of mixtures useful in life-testing and reliabilityanalysis. It is also illustrated through two examples—onebased on real-life data and the other on a simulated sample.     

A-optimal designs for optimum mixture in an additive quadratic mixture model

In the analysis of experiments with mixtures, quadratic models have been widely used. The optimum designs for the estimation of optimum mixing proportions in a quadratic mixture model have been studied by Pal and Mandal [Optimum designs for optimum mixtures. Statist Probab Lett. 2006;76:1369–1379] and Mandal et al. [Optimum mixture designs: a pseudo-Bayesian approach. J Ind Soc Agric Stat. 2008;62(2):174–182; Optimum mixture designs under constraints on mixing components. Statist Appl. 2008;6(1&2) (New Series): 189–205], using a pseudo-Bayesian approach. In this paper, a similar approach has been employed to obtain the A-optimal designs for the estimation of optimum proportions in an additive quadratic mixture model, proposed by Darroch and Waller [Additivity and interaction in three-component experiments with mixture. Biometrika. 1985;72:153–163], when the number of components is 3, 4 and 5. It has been shown that the vertices of the simplex are necessarily the support points of the optimum design, and the other support points include barycentres of depth at most 2.     

A new class of estimators of finite population mean in sample surveys

This article suggests the class of estimators of population mean of study variable using various parameters related to an auxiliary variable with its properties in simple random sampling. It has been identified that the some existing estimator/classes of estimators are members of suggested class. It has been found theoretically as well as empirically that the suggested class is better than the existing methods.     

Optimum mixture designs in some constrained experimental regions

In a mixture experiment, the response depends on the mixing proportions of the components present in the mixture. Optimum designs are available for the estimation of parameters of the models proposed in such situations. However, these designs are found to include the vertex points of the simplex Ξ defining the experimental region, which are not mixtures in the true sense. Recently, Mandal et al. (2015 Mandal, N.K., Pal, M., Sinha, B.K., and Das, P. (2015). Optimum mixture designs in a restricted region. Stat. Pap. 56(1):105–119.[Crossref], [Web of Science ®] , [Google Scholar]) derived optimum designs when the experiment is confined to an ellipsoidal region within Ξ, which does not include the vertices of Ξ. In this paper, an attempt has been made to find optimum designs when the experimental region is a simplex or is cuboidal inside Ξ and does not contain the extreme points.     

Cross‐Cultural Measurement Invariance of Adolescent Self‐Report on the Pediatric Quality of Life Inventory™ 4.0

This study evaluated the cross‐cultural measurement invariance of the Pediatric Quality of Life Inventory version 4.0 (PedsQL^?) among adolescents sampled from Bulgaria, Croatia, India, Indonesia, Nigeria, Serbia, and Turkey. The multiple‐indicator multiple‐cause (MIMIC) model was used, which allowed controlling of demographic variables (i.e., age, gender, and socioeconomic status). Significant effects of country on scores within the PedsQL^? domains were observed, with up to 17 items showing differential item functioning (DIF) across the countries. We did not find support for cross‐cultural measurement invariance hypotheses for scores on the PedsQL^? adolescent self‐report in this study. Researchers should use caution in making cross‐cultural quality of life comparisons while using the PedsQL.     

Optimum designs for estimation of optimum point under cost constraint

In this paper, we consider the estimation of the optimum factor combination in a response surface model. Assuming that the response function is quadratic concave and there is a linear cost constraint on the factor combination, we attempt to find the optimum design using the trace optimality criterion. As the criterion function involves the unknown parameters, we adopt a pseudo-Bayesian approach to resolve the problem.