LBI tests for the detection of compound normal distribution in control and treatment populations

Independent samples are drawn from control and treatment populations with normal and compound normal distributions respectively. We derive the locally best invariant (LBI) tests through Wijsman’s representation for the detection of mixture departures from the normal distribution. These tests may be viewed as tests for the equality of control and treatment populations. Further, they are optimally robust for the model considered by Durairajan and Raman (1994).     

Estimating functions in the Bayesian paradigm

Received: August 3, 1998; revised version: June 9, 1999     

Locally Maximin Test for the Mixture Proportion with Type-I Censoring

Mixtures of distributions arise frequently in the context of life testing experiments, where one also encounters the problem of censored data. In this article, we derive the locally most powerful (LMP) test for testing the mixing proportion in a general mixture model based on type-I censored data. We also prove the additional properties of unbiasedness and locally maximin using a novel approach. To this end, we prove an extension of a standard lemma in the testing literature (Lehmann, 1986 Lehmann , E. L. ( 1986 ). Testing Statistical Hypotheses . New York : Wiley .[Crossref] , [Google Scholar]) relating to families with monotone likelihood ratio.     

Optimal estimating function for estimation and prediction in semi-parametric models

In a seminal paper, Godambe [1985. The foundations of finite sample estimation in stochastic processes. Biometrika 72, 419–428.] introduced the ‘estimating function’ approach to estimation of parameters in semi-parametric models under a filtering associated with a martingale structure. Later, Godambe [1987. The foundations of finite sample estimation in stochastic processes II. Bernoulli, Vol. 2. V.N.V. Science Press, 49–54.] and Godambe and Thompson [1989. An extension of quasi-likelihood Estimation. J. Statist. Plann. Inference 22, 137–172.] replaced this filtering by a more flexible conditioning. Abraham et al. [1997. On the prediction for some nonlinear time-series models using estimating functions. In: Basawa, I.V., et al. (Eds.), IMS Selected Proceedings of the Symposium on Estimating Functions, Vol. 32. pp. 259–268.] and Thavaneswaran and Heyde [1999. Prediction via estimating functions. J. Statist. Plann. Inference 77, 89–101.] invoked the theory of estimating functions for one-step ahead prediction in time-series models. This paper addresses the problem of simultaneous estimation of parameters and multi-step ahead prediction of a vector of future random variables in semi-parametric models by extending the inimitable approach of 13 and 14. The proposed technique is in conformity with the paradigm of the modern theory of estimating functions leading to finite sample optimality within a chosen class of estimating functions, which in turn are used to get the predictors. Particular applications of the technique give predictors that enjoy optimality properties with respect to other well-known criteria.     

Quantitative models for optimal rest period scheduling

Mathematical and simulation models studying work-rest schedules in a production process are developed to arrive at an optimal rest policy to maximize work output per unit time. A CSMP simulation study is used to test the sensitivity of the results for different specific cases.     

Some observations in testing for nonstandard mixtures

We consider optimal testing procedures for specific models of early and instantaneous failures in reliability studies. These models are typically used to accommodate lifetime data that have a higher concentration of failures near time zero. We show that it is possible to derive uniformly most powerful tests, for testing the mixing parameter in the instantaneous failure model, for general lifetime distributions. A novel procedure to test for early failures, which uses an invariance property of the maximum likelihood estimate of the nuisance parameter, is also presented.     

Simultaneous equivariant estimation of the parameters of linear models

Consider a family of distributions which is invariant under a group of transformations. In this paper, we define an optimality criterion with respect to an arbitrary convex loss function and we prove a characterization theorem for an equivariant estimator to be optimal. Then we consider a linear model Y=Xβ+ε, in which ε has a multivariate distribution with mean vector zero and has a density belonging to a scale family with scale parameter σ. Also we assume that the underlying family of distributions is invariant with respect to a certain group of transformations. First, we find the class of all equivariant estimators of regression parameters and the powers of σ. By using the characterization theorem we discuss the simultaneous equivariant estimation of the parameters of the linear model.