Coefficients In Linear Regression Model Research Articles

The mean squared errors of the maximum likelihood and natural-conjugate bayes regression estimators

This paper compares the natural-conjugate Bayes and the maximum likelihood estimators of the linear regression model coefficients in terms of matrix mean squared error. The principal result is an inequality involving the unknown parameters. Proposals are made for testing if this condition holds. The weakest involves estimation of the unknown parameters. Another suggestion exploits the relationship between the Bayes estimator and the constrained least squares estimator to derive weak classical hypothesis tests. The third approach uses the prior density for the parameters and Bayesian decision theory to determine the posterior probability that the mean squared error inequality is satisfied.

On some properties of a class of spearman rank statistics with applications

The object of the present investigation is to study some properties of a class of Spearman rank statistics and to apply these results in studying the properties of a sequential procedure proposed in Section 3. The problem is one of bounded length confidence intervals for simple regression coefficients in linear models where both variables are subject to error. It is shown that the proposed procedure is asymptotically ‘consistent’ and ‘efficient’ in the sense of Chow and Robbins [3].