Stein-rule Estimator Research Articles

The Distribution of the Stein-Rule Estimator in a Model with Non-Normal Disturbances

This paper derives the exact distribution and moments of the Stein-ruleestimator in a model where the disturbances follow a non-normal distribution of the Edgeworth or Gram-Charlier type. The results are achieved by combining the approach of Davis [4] for examining non-normality with the fractional calculus techniques of Phillips [11].

Stein-rule estimation of coefficients for 18 eastern hardwood cubic volume equations

A Stein-rule estimator, which shrinks least squares estimates of regression parameters toward their weighted average, was employed to estimate the coefficient in the constant form factor volume equation for 18 species simultaneously. The Stein-rule procedure was applied to ordinary least squares estimates and weighted least squares estimates. Simulation tests on independent validation data sets revealed that the Stein-rule estimates were biased, but predicted better than the corresponding least squares estimates. The Stein-rule procedures also yielded lower estimated mean square errors for the volume equation coefficient than the corresponding least squares procedure. Different methods of withdrawing sample data from the total sample available for each species revealed that the superiority of Stein-rule procedures over least squares decreased as the sample size increased and that the Stein-rule procedures were robust to unequal sample sizes, at least on the scale studied here.

A distribution function of the F-ratio when the Stein-rule estimator is used in place of the OLS estimator

In this paper, we derive a distribution function of the improved F-ratio obtained by using the Stein-rule estimator in place of the OLS estimator. It is shown that the test given by the improved F-ratio for the null hypothesis that all regression coefficients are zero can be conducted based on an F distribution, and the power of the test given by the improved F-ratio is lower than that of the test given by the usual F-ratio.

Restricted least squares, pre-test, ols and stein rule estimators: Risk comparisons under model misspecification

The predictive squared error risk behavior of a restricted least squares estimator (RLS), pre-test estimator (PT), and Stein rule (SR) estimator are each compared to the behavior of the OLS estimator when relevant variables are omitted. Risk superiority conditions dependent on prior constraint error and this model specification error in a two-dimensional parameter space are exhibited. Among the consequences of this model misspecification, it is found that (i) perfectly correct prior constraints do not ensure risk superiority of any of the alternatives to OLS, (ii) the risk difference between OLS and PT is no longer bounded, and (iii) the SR no longer dominates OLS. The usefulness of risk superiority hypothesis tests based on the doubly non-centralF distribution is examined.

The exact distribution of the Stein-rule estimator

This paper derives the exact density of the Stein-rule estimator in the setting of the general linear regression. The derivation is facilitated by the author's development of new algebraic methods that involve an extension of the Weyl calculus. General formulae for the moments of the estimator are also provided.

A Stein-rule method for pooling data

In this paper a Stein-rule estimator is discussed as an alternative to the traditional statistical approaches to pooling time-series and cross-section data. Ex post forecasts of the Stein-rule applied to a wilderness recreation demand model are compared to that of conventional estimators.

The approximate distribution function of the Stein-rule estimator

Abstract In this paper we provide Edgeworth expansion of the distribution function of the Stein-rule estimator of the regression coefficients. The condition of dominance of this estimator over the least squares estimator is also obtained under a new criterion.

Improved stein-rule estimator for regression problems

Stein-Rule estimator for regression problems has been studied by several authors including Sclove (1968) and others listed in Vinod's (1978) survey. Ullah and Ullah (1978) provide the expressions for the mean squared error ( MSE) of a double k-class ( KK) estimator with parameters k 1 and k 2. When k 2=1 the Stein-Rule estimator becomes a special case of KK and an optimal choice of k 1 is known. This paper explores optimal theoretical choice of k 1 and k 2. We note that negative choices of k 2 are permissible, and that thereis a large range of choices for K 1 and k 2 where the MSE of the Stein-Rule estimator can be reduced for regression problems based on multicollinear data. A simulation experiment is included.

The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics.

The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics.

A Monte Carlo comparison of traditional and Stein-rule estimators under squared error loss

This paper reports the results of using an orthonormal regression model, a squared error loss measure and Monte Carlo procedures, to compare the risk functions of traditional and Stein-rule pre-test estimators under a variety of conditions. The results of the sampling experiment indicate that the Stein-rule estimators not only dominate the sampling theory estimators used in applied econometric work but that in contrast to conventional wisdom thegains from using members of the Stein-rule family may be quite significant over a large range of the parameter space.

A Comparison of Traditional and Stein-Rule Estimators under Weighted Squared Error Loss

A Comparison of Traditional and Stein-Rule Estimators under Weighted Squared Error Loss