Hellinger distance, Kullback-Leibler loss, and variance-stabilizing integrated square error are shown to be asymptotically equivalent up to a constant. Simulation confirmed the result. Implications of the result for dernel and histogram density estimation and the connection of the result with goodness of fit tests are discussed.

View full abstract

In a generalized linear regression model with autocorrelated error term, some shrinkage type regression predictors are examined in a situation where the prediction area is different from the sample area. The goodness of the shrinkage regression predictor is appraised on the basis of the expectations of prediction Mean Square Error(PMSE)with respect to the model condition parameter having a known prior distribution. A modified shrinkage type predictor is proposed. Moreover, simulation results are presented to exhibit the efficiency of the proposed predictor.

View full abstract

In a multiple linear regression model, the paper derives the exact distribution and density function of the modified generalized ridge(M-GR)regression estimators which includes the generalized ridge(GR)estimator. Based on the density function derived, the performance of the relative efficiency of the M-GR estimators to the ordinary least squares(OLS)estimator is also evaluated by numerical analysis.

View full abstract

The problem of estimating regression parameters in an exponential model with censoring is considered when it is a priori suspected that the parameters may be restricted to a subspace. James-Stein(JS)type of estimators is obtained which dominates the usual maximum likelihood(ml)estimators. The relative performance of the JS type estimators is compared to the ml estimators using quadratic distributional risk under local alternatives. It is demonstrated that the JS type estimators are asymptotically superior to the usual ml estimators. Further, it is shown that the JS type estimator is dominated by its truncated part.

View full abstract

For the analysis of square contingency tables, Tomizawa(1994), and Tomizawa, Seo and Yamamoto(1998)considered the measures to represent the degree of departure from symmetry. This paper proposes a measure to represent the degree of departure from conditional symmetry(being an extension of symmetry). The proposed measure is expressed by using Cressie and Read's(1984)power sivergence be useful for comparing the degree of departure from conditional symmetry in several tables.

View full abstract

Cressie and Read(1984)introduced the class of multinomial goodness-of-fit statistics, R^a, based on measures of the divergence between discrete distributions. All R^a have the same chi-squared limiting null distribution. The power of R^a is usually approximated by a noncentral chi-squared distribution that is also the same for all a. In this paper, we propose a new approximation of the power of R^a. The new power approximation, NT, is a normal approximation based on a normalizing transformation. The NT approximation is numerically compared with the other approximations. As a result of the comparison, we find that the NT approximation is superior to the other approximations when a=0(the loglikelihood ratio statistic)and is effective when a<0.

View full abstract

In the present paper we characterize mixture of geometric and Waring distributions by certain identities connecting the failure rate, mean residual life and second moment of residual life. The application of the characteristic property of the geometric mixture in identification and estimation of parameters of that model is also pointed out.

View full abstract

Lex X_U(1)<X_U(2)<…<X_U(n)<…be the sequence of the upper record values from a population with common distribution function F. In this paper, we first give a theorem to characterize the generalized mixtures of geometric distribution by the relation between E[X_U(n+1)|X_u(n)=x]and the function of the failure rate of the distribution, for any positive integer n. Secondly, we also use the same relation to characterize the generalized mixtures of exponential distribution. The characterizing relations were motivated by the work of Srivastava(1979), Ahsanullah and Holland(1984)and Nagaraja(1977).

View full abstract