Risk performance of a pre-test estimator for normal variance with the Stein-variance estimator under the LINEX loss function

In this paper, we derive the exact formula of the risk function of a pre-test estimator for normal variance with the Stein-variance (PTSV) estimator when the asymmetric LINEX loss function is used. Fixing the critical value of the pre-test to unity which is a suggested critical value in some sense, we examine numerically the risk performance of the PTSV estimator based on the risk function derived. Our numerical results show that although the PTSV estimator does not dominate the usual variance estimator when under-estimation is more severe than over-estimation, the PTSV estimator dominates the usual variance estimator when over-estimation is more severe. It is also shown that the dominance of the PTSV estimator over the original Stein-variance estimator is robust to the extension from the quadratic loss function to the LINEX loss function.     

A monte carlo study of the wald,lm, and lr tests in a heteroscedastic linear model

In this paper, we examine by Monte Carlo experiments the small sample properties of the W (Wald), LM (Lagrange Multiplier) and LR (Likelihood Ratio) tests for equality between sets of coefficients in two linear regressions under heteroscedasticity. The small sample properties of the size-corrected W, LM and LR tests proposed by Rothenberg (1984) are also examined and it is shown that the performances of the size-corrected W and LM tests are very good. Further, we examine the two-stage test which consists of a test for homoscedasticity followed by the Chow (1960) test if homoscedasticity is indicated or one of the W, LM or LR tests if heteroscedasticity should be assumed. It is shown that the pretest does not reduce much the bias in the size when the sizecorrected citical values are used in the W, LM and LR tests.     

On an adjustment of degrees of freedom in the minimim mean squared error ertimator

In this paper, we consider an adjustment of degrees of freedom in the minimum mean squared error (MMSE) estimator, We derive the exact MSE of the adjusted MMSE (AMMSE) estimator, and compare the MSE of the AMMSE estimator with those of the Stein-(SR), positive-part Stein-rule (PSR) and MMSE estimators by numerical evaluations. It is shown that the adjustment of degrees of freedom is effective when the noncentrality parameter is close to zero, and the MSE performance of the MMSE estimator can be improved in the wide region of the noncentrality parameter by the adjustment, ft is also shown that the AMMSE estimator can have the smaller MSE than the PSR estimator in the wide region of the noncentrality parameter     

OPTIMAL CRITICAL VALUES FOR A PRELIMINARY TEST IN POOLING MEANS

Given two random samples from normal populations with the same known variance, the experimenter wishes to estimate the mean of the fist population. Whether to pool the two samples or not is made to depend on the result of a preliminary normal test. The bias and mean square error of the pre-test estimator are presented. Based on two different criteria, a minimax regret and a minimum expected regret ones, the optimal critical values for the pre-test are given. The minimax regret value is unique (about 1.37), while the alternative values vary depending on the mean and precision included in the prior distribution.     

Frugality-based advantage

We analyze frugality-based advantage and explain its types and implications. Frugality-based advantage is an advantage that a firm achieves over competitors in its ability to develop and use frugal innovations, that is, innovations that overcome external resource constraints. We differentiate among three types of frugality-based advantages based on the external constraints they solve: (1) Input frugality-based advantage, which is the result of addressing restrictions in the provision of inputs needed for the production process; (2) Income frugality-based advantage, which is driven by solving limitations in the income of consumers; and (3) Infrastructure frugality-based advantage, which is the outcome of resolving constraints in the hard and soft infrastructure of the country. We explain how these three types of frugality-based advantages differ in their transferability across locations and their sustainability across time. Frugality-based advantage complements the resource-based view by explaining how the scarcity of external resources, rather than their abundance, can support the advantage of some firms.     

Yoga stretching for improving salivary immune function and mental stress in middle-aged and older adults

Protection against age-related immune suppression is important in elderly individuals. This study determined the effect of yoga on mucosal immune function and mental stress. Saliva samples were collected from 23 adult women (age: 60.4 ± 10.4 years) before and after 90 minutes of yoga stretching or rest to measure secretory immunoglobulin A (SIgA), cortisol, and testosterone. The SIgA concentration and secretion rate were significantly higher after yoga than before (p < .05). The cortisol concentration and secretion rate were lower and testosterone secretion rate higher after yoga (p < .05). Yoga stretching can reduce stress and enhance mucosal immune function in elderly women.     

On the Sampling Performance of an Improved Stein Inequality Restricted Estimator

Using the Stein (1964) variance estimator, this paper defines a modified Stein inequality constrained estimator and derives its exact risk under quadratic loss. Numerical evaluations show that over a wide range of the parameter space, the modified Stein inequality constrained estimator has lower risk than the traditional Stein inequality constrained estimator introduced by Judge et al . (1984).     

Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness criterion when variables are omitted

This paper compares the Stein and the usual estimators of the error variance under the Pitman nearness (PN) criterion in a regression model which is mis-specified due to missing relevant explanatory variables. The exact expression of the PN-probability is derived and numerically evaluated. Contrary to the well-known result under mean squared errors (MSE), with the PN criterion the Stein variance estimator is uniformly dominated by the usual estimator when no relevant variables are excluded from the model. With an increased degree of model mis-specification, neither estimator strictly dominates the other. The authors are grateful to two anonymous referees for their valuable comments. Also, the first author is grateful to the Japan Society for the Promotion of Science for partial financial support.     

On small sample properties of the almost unbiased generalized ridge estimator

The purpose of this paper is to examine small sample properties of the operational almost unbiased generalized ridge estimator (E) . The exact first two moments of theAUGRE are derived. It is shown that although the reduction of the bias of the AUGRE is substantial, the AUGRE is rather inefficient than the generalized ridge estimator without the bias correction in a wide range of a noncen-trality parameter in terms of the mean square error.     

On estimating the common mean in two normal distributions after a preliminary test for equality of variances

Given two random samples of equal size from two normal distributions with common mean but possibly different variances, we examine the sampling performance of the pre-test estimator for the common mean after a preliminary test for equality of variances. It is shown that when the alternative in the pretest is one-sided, the Graybill-Deal estimator is dominated by the pre-test estimator if the critical value is chosen appropriately. It is also shown that all estimators, the grand mean, the Graybill-Deal estimator and the pre-test estimator, are admissible when the alternative in the pre-test is two-sided. The optimal critical values in the two-sided pre-test are sought based on the minimax regret and the minimum average risk criteria, and it is shown that the Graybill-Deal estimator is most preferable under the minimum average risk criterion when the alternative in the pre-test is two-sided.