Sequential estimation problems for negative exponential populations

The literature on sequential estimation problems for negative exponential populations has been reviewed here, We attempt to bring in all the published and unpublished materials known to us in a fairly coherent fashion. Both the concepts and theoretical findings are discussed.     

Bayesian autoregressive spectral analysis

The article describes an operational Bayesian approach to making inferences for the spectral density function for univariate autoregressive processes and for the AR operator of multivariate autoregressive processes. The derivation of the approach is described. Numerical examples, including the Wolfer Sunspot numbers, are used to demonstrate the practical usefulness of the approach.     

Order statistics from the linear-exponential distribution,part I: increasing hazard rate case

For the linear-exponential distribution with increasing hazard rate, exact and explicit expressions for means, product moments and percentage points of order statistics are obtained. Some recurrence relations for both single and product moments of order statistics are also derived. These recurrence relations would enable one to obtain all the higher order moments of order statistics for all sample sizes from those of the lower order     

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

ABSTRACT

This article considers the problem of testing equality of parameters of two exponential distributions having common known coefficient of variation, both under unconditional and conditional setup. Unconditional tests based on BLUE'S and LRT are considered. Using the Conditionality Principle of Fisher, an UMP conditional test for one-sided alternative is derived by conditioning on an ancillary. This test is seen to be uniformly more powerful than unconditional tests in certain given ranges of ancillary. Simulation studies on the power functions of the tests are done for this purpose.     

POWER FUNCTION FOR INVERSE GAUSSIAN REGRESSION MODELS

Inverse Gaussian regression models are useful for data where both the independent and dependent variable are nonnegative and the variance of the dependent variable depends on the independent variable. Zero intercept inverse Gaussian regression models are presented with nonconstant variance, constant ratio of variance to the mean and constant coefficient of variation. The power function for testing hypotheses about the slope is given for all of these models.     

Robust Estimators for the Parameters of Multivariate Lognormal Distribution

Abstract

In this paper, we introduce a class of location and scale estimators for the p-variate lognormal distribution. These estimators are obtained by applying a log transform to the data, computing robust Fisher consistent estimators for the obtained Gaussian data and transforming those estimators for the lognormal using the relationship between the parameters of both distributions. We prove some of the properties of these estimators, such as Fisher consistency, robustness and asymptotic normality.     

Estimation of a Gamma Scale Parameter Under Asymmetric Squared Log Error Loss

Abstract

Estimation of scale parameter under the squared log error loss function is considered with restriction to the principle of invariance and risk unbiasedness. An explicit form of minimum risk scale-equivariant estimator under this loss is obtained. The admissibility and inadmissibility of a class of linear estimators of the form (cT + d) are considered, where T follows a gamma distribution with an unknown scale parameter η and a known shape parameter ν. This includes the admissibility of the minimum risk equivariant estimator on η (MRE).     

Ridge regression estimators in the linear regression models with non-spherical errors

The present paper considers a family of ordinary ridge regression estimators in the linear regression model when the disturbances covariance matrix depends upon a few unknown parameters. An asymptotic expansion for the distribution of the ridge regression estimator is developed and under the quadratic loss function its asymptotic risk is compared with that of the feasible GLS estimator.