D. V. Gokhale

On maximum product of spagings (mps) estimation for burr xii distributions

In recent years, the family of Burr XII distributions has been successfully and frequently used inmany applied areas. The object of this paper is to compere the maximum likelihood (ML) and the maximum product of spacing?; (MPS) estimation for this family. Since analytical approach is intractable, recourse is taken to extensive computer usage, in both Monte Carlo and bootstrap simulations. For sample sizes, it is shown that the MPS method of estimation is superior, in the senseof smaller mean squared errors (MSE), to the ML method for many parametric configurations. For large sample sizes (n≤30) MPS and ML methods give nearly identical results, as is to be expeded.

The minimum discrimination information approach in analyzing categorical data

A brief review of the minimum discrimination information (MDI) approach in analyzing categorical data is presented in a question -answer format, An example is given to bring out situations in which the MDI approach is more useful. No new results are proved.

Distributions most nearly compatible with given families of conditional distributions

Consider a discrete bivariate random variable (X, Y) with possible values 1, 2, ...,I forX and 1, 2, ...J forY. Suppose that putative families of conditional distributions, forX given values ofY and ofY given values ofX, are available. After reviewing conditions for compatibiity of such conditional specifications of the distribution of (X, Y), attention is focussed on the incompatible case. The Kullback-Leibler information function is shown to provide a convenient measure of inconsistency. Using it, algorithms are provided for computing the joint distribution for (X, Y) that is least discrepant from the given inconsistent conditional specifications. Other discrepancy measures are briefly discussed.

Minimum discrimination information estimator of the mean with known coefficient of variation

Abstract Estimation of a mean when the coefficient of variation is known is treated as a constrained optimization of the Kullback-Leibler distrimination information function. The procedure is semi-parametric in that it uses a normal distribution as the maximum entropy model to develop an estimator for the mean of all distributions in the location-scale family with finite entropy. The performance of the proposed procedure is compared with some existing methods in a bootstrap study of data from a laboratory experiment. Monte Carlo simulations are also used to compare the mean squared error of several estimators under various distribution assumptions and over a wide range of values for the coefficient of variation and sample size. The new estimator shows smaller mean squared error than its nonprametric counterpart and it competes well with its parametric counterparts.

A note on combining parametric and non-parametric regression

A combination of a parametric estimate and a nonparametric estimate of a model for a regression function is considered. The optimal linear combination is estimated from the data by the least squares estimate of the combining coefficient. The estimate so obtained is compared with the one proposed by Wooldridge (1992) and Burman and Chaud-huri,the latter being based on Stein (1956). A test procedure for deciding about the parametric specification is also studied.

On estimation of parameters of the exponential power family of distributions

Consider the three-parameter exponential power distribution with location parameter μ, scale parameter σ2 and shape (power) parameter β. This is a general symmetric family of distributions with normal, double exponential and rectangular as special cases. Such distributions are used in Bayesian statistics as a wider choice of symmetric parent distribution and in classical statistics in determination of lack of normality. This note obtains simultaneous estimates of μ, σ2 and β by method of moments and method of maximum likelihood. It also studies the behavior of estimates of β through Monte Carlo simulation when values of μ and σ2 are set equal to zero and unity respectively.

A note on shrinkage factors in two stage testimation

We obtain a simple and natural testimator which has locally, at the parametric point corresponding to the prior knowledge, a smaller mean squared error than any other two stage testimator of a location or a scale parameter of an arbitrary distribution.

An extension of bayesian measure of information to regression

This paper extends Lindleys measure of average information to the linear model, E(Y∣s) = Xs. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters s will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested.

Statistical Inference for Damaged Poisson Distribution

Abstract For non-negative integer-valued random variables, the concept of “damaged” observations was introduced, for the first time, by Rao and Rubin [Rao, C. R., Rubin, H. (1964). On a characterization of the Poisson distribution. Sankhya 26:295–298] in 1964 on a paper concerning the characterization of Poisson distribution. In 1965, Rao [Rao, C. R. (1965). On discrete distribution arising out of methods of ascertainment. Sankhya Ser. A. 27:311–324] discusses some results related with inferences for parameters of a Poisson Model when it has occurred partial destruction of observations. A random variable is said to be damaged if it is unobservable, due to a damage mechanism which randomly reduces its magnitude. In subsequent years, considerable attention has been given to characterizations of distributions of such random variables that satisfy the “Rao–Rubin” condition. This article presents some inference aspects of a damaged Poisson distribution, under reasonable assumption that, when an observation on the random variable is made, it is also possible to determine whether or not some damage has occurred. In other words, we do not know how many items are damaged, but we can identify the existence of damage. Particularly it is illustrated the situation in which it is possible to identify the occurrence of some damage although it is not possible to determine the amount of items damaged. Maximum likelihood estimators of the underlying parameters and their asymptotic covariance matrix are obtained. Convergence of the estimates of parameters to the asymptotic values are studied through Monte Carlo simulations.

An information criterion for normal regression estimation

A discrimination information approach for evaluating the performance of a special class of linear transforms of the least squares (LS) estimates is proposed. An information criterion is defined which is shown to be a well-behaved function of the transformation matrix. The proposed criterion is related to the predictive mean squared error (PMSE) of the linear transform estimates. The relation between the information criterion and the PMSE leads to a weak necessary condition for the uniform PMSE dominance of the linear transform estimates over the LS estimates. Application of the proposed information criterion as a diagnostic for ridge regression is discussed. An illustrative example is also analyzed.