In many situations, inference for a scalar parameter in the presence of nuisance parameters requires integration of eithera joint density of pivotal quantities or a joint posterior density. For such inference, accurat...
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In many situations, inference for a scalar parameter in the presence of nuisance parameters requires integration of eithera joint density of pivotal quantities or a joint posterior density. For such inference, accurate approximations of marginaltail probabilities are useful to avoid high-dimensional integrals. Two tail probability approximations are developed in thispaper. Numerical results given for conditional inference in location-scale and linear regression models show the approximationsto be generally accurate even for small sample sizes.
The relationship between heart rate (HR) and PR interval (PR) has been investigated to determine inter-subject variability, within-subject variability and potential reference standards. Eight healthy male volunteers u...
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The relationship between heart rate (HR) and PR interval (PR) has been investigated to determine inter-subject variability, within-subject variability and potential reference standards. Eight healthy male volunteers underwent upright graded submaximal treadmill exercise during eight separate study sessions. All subjects exhibited statistically significant negative linear relationships between PR and HR. Although there was considerable inter-subject variability, there was little within-subject variability in the interpolated PR at HR between 80 and 120 beats min-1. The HR-PR regressionmodel has greatest validity within this HR range and for individual subjects rather than pooled or group data.
Newhouse and Oman (1971) identified the orientations with respect to the eigenvectors of X'X of the true coefficient vector of the linear regression model for which the ordinary ridge regression estimator performs...
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Newhouse and Oman (1971) identified the orientations with respect to the eigenvectors of X'X of the true coefficient vector of the linear regression model for which the ordinary ridge regression estimator performs best and performs worse when mean squared error is the measure of performance. In this paper the corresponding result is derived for generalized ridge regression for two risk functions: mean squared error and mean squared error of prediction.
It is shown that a necessary and sufficient condition derived by Farebrother (1984)for a generalized ridge estimator to dominate the ordinary least-squares estimator with respect to the mean-square-error-matrix criter...
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It is shown that a necessary and sufficient condition derived by Farebrother (1984)for a generalized ridge estimator to dominate the ordinary least-squares estimator with respect to the mean-square-error-matrix criterion in the linear regression model admits a similar interpretation as the well known criterion of Toro-Viz-carrondo and Wallace (1968)for the dominance of a restricted least-squares estimator over the ordinary least-squares estimator. Two other properties of the generalized ridge estimators, referring to the concept of admissibility, are also pointed out.
The power of the classical .F-test for testing the regression coefficient of a general linearmodel with elliptic t error variable depends on the degrees of freedom of the t- distribution. In this note it is shown tha...
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The power of the classical .F-test for testing the regression coefficient of a general linearmodel with elliptic t error variable depends on the degrees of freedom of the t- distribution. In this note it is shown that the power of the F-test based on t-distribution is greater than the normal based test at smaller level of significance.
It is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linearregression analysis by possibilistic linearmodels. linearregression by a possibilisti...
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It is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linearregression analysis by possibilistic linearmodels. linearregression by a possibilistic model is called possibilistic linearregression. This is a new interpretation of fuzzy linearregression and also includes a new method by which interval analysis can be done in fuzzy numbers.
Pliskin (1987) and Trenkler (1988) compared ridge-type estimators with good prior means. From a Bayesian viewpoint, these estimators are special cases of Bayesestimators and the mean square error matrix comparisons ca...
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Simple but flexible methods to detect deviations from the assumption of constant coefficients in linearregression are presented. Based on recursive residuals a runs test is developed as an alternative to CUSUM‐ and ...
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In the linear regression model without an intercept, it is known that the limiting power of the Durbin-Watson test (as correlation among errors increases) equals either one or zero, depending on the underlying regress...
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In the linear regression model without an intercept, it is known that the limiting power of the Durbin-Watson test (as correlation among errors increases) equals either one or zero, depending on the underlying regressor matrix. This paper considers the limiting power in the model with an intercept, and proves that it will never equal one or zero.
Stein-rule philosophy and mixed regression technique are combined to develop two families of improved estimators of regression coefficients in the linear regression model under incomplete prior information. The proper...
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Stein-rule philosophy and mixed regression technique are combined to develop two families of improved estimators of regression coefficients in the linear regression model under incomplete prior information. The properties of these estimators are studied when disturbances are small and non-normal. Conditions for their dominance over mixed regression estimator are derived taking risk as the criterion for performance.
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