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In this paper, the risk of the Stein-rule (SR) estimator is compared with that of the improved Stein-rule estimator using the Stein variance (SRSV) estimator under the balanced loss function. It is shown that the SRSV estimator dominates the SR estimator even if the loss function is extended to the BLF. Also, our numerical results show that the SRSV estimator dominates the OLS estimator when the weight of precision of estimation is larger than about half, and vice versa. Keywords: Balanced loss function; Inadmissibility; Stein-rule estimator; Stein variance estimator

In this paper, we derive the general formulae for the moments of a linear functional of the Stein-rule and positive-part Stein-rule estimators (i.e., h[prime][b.sub.SR] and h[prime][b.sub.PSR]) in a different way from Phillips (1984). The MSE dominance of h[prime][b.sub.PSR] over h[prime][b.sub.SR] and a sufficient condition for h[prime][b.sub.SR] to dominate a linear functional of the OLS estimator (h[prime]b) are shown. Using the formulae for the moments, we evaluate numerically the first four moments of [b.sub.SR] and [b.sub.PSR], and examine the bias, variance, MSE, skewness, and kurtosis. Key words: MSE dominance; Stein-rule estimator

In this paper we consider the power function of the classical F test for linear restrictions on the coefficients in a linear regression model with spherically symmetric disturbances when proxies are used in the place of unobservable regressors. To illustrate the results we numerically evaluate the power function for two families of variance-mixing distributions in a simple univariate regression model. Our results show the effects on the power function of the degree of nonnormality and of the correlation between the omitted and the proxy variable.

This paper, using the Imhof (1961) method, shows the method of evaluating numerically the exact distribution of a unit root test statistic when the error variance changes. Based on the method, the effect of the change in variance on the exact distribution is examined, and we tabulate numerically exact critical values when the sample size is small and moderate. [ABSTRACT FROM AUTHOR]

This paper, using the Imhof method, evaluates the numerically exact critical values of unit root tests based on the OLS estimator when there are drift and trend. The somewhat detailed tables of the exact critical values are presented. [ABSTRACT FROM AUTHOR]