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双指数先验下正态均值后验矩的一个注记AI 解读

SUMMARY General results on the behaviour of the posterior mean and variance of the mean of a normal distribution with known variance using a double-exponential prior are derived and complement the conjectures and particular examples given by Pericchi and Smith (1992) and Pericchi and Walley (1991).

《马氏距离与椭圆分布》的修订与勘误AI 解读

On page 518 the expressions for u2 and v2 should be U2= S2 _ (n3/N2), v2=t72-(m3/2N2). In view of the complexity of the formula (3d 1), it is worth noting that it gives the same numerical results, in a number of examples, as the subsequent formula of Mielke & Berry (1985). It also agrees numerically in these examples with the exact third central moment calculated using the enumeration algorithm of Saunders referred to in our paper.

马氏距离与椭圆分布AI 解读

The Mahalanobis distance is shown to be an appropriate measure of distance between two elliptic distributions having different locations but a common shape. This extends a result long familiar in multivariate analysis to a class of nonnormal distributions. It can also be used to show that the sample version of the Mahalanobis distance is appropriate under both estimative and predictive approaches to estimation for the family of multivariate normal distributions differing…

马氏距离与椭圆分布AI 解读

The Mahalanobis distance is shown to be an appropriate measure of distance between two elliptic distributions having different locations but a common shape. This extends a result long familiar in multivariate analysis to a class of nonnormal distributions. It can also be used to show that the sample version of the Mahalanobis distance is appropriate under both estimative and predictive approaches to estimation for the family of multivariate normal distributions differing…

似然比的保守置信区间AI 解读

A method is described for assigning an observation to one of two normal populations with differing, unknown means and differing, unknown variances. The classification procedure rests on the likelihood ratio, which, for a given observation, is a function of four unknown parameters. Sample information is used to obtain a confidence region for these parameters. From this confidence region, a conservative confidence interval for the likelihood ratio is derived. Interpreting the…

似然比的保守置信区间AI 解读

A method is described for assigning an observation to one of two normal populations with differing, unknown means and differing, unknown variances. The classification procedure rests on the likelihood ratio, which, for a given observation, is a function of four unknown parameters. Sample information is used to obtain a confidence region for these parameters. From this confidence region, a conservative confidence interval for the likelihood ratio is derived. Interpreting the…

相关观测下指数回归的进一步讨论AI 解读

Mitchell (1968) studied the properties of estimators of p in the exponential regression situation, E(yx)= α+βpx, when the observations are assumed correlated. In the notation of that paper it is now shown that the quadratic estimators r(O, c, d) have uniform minimum asymptotic variance among all linear and quadratic estimators of p and that estimators can be excluded from this class on grounds of possessing uniformly worse asymptotic biases.

相关观测下的指数回归AI 解读

Finney's(1958) model for correlated observations yx in the exponential regression situation, E(yx)=α= βpx, is studied in greater detail. It is shown that his maximum-likehood procedure for estimating p is valid in only certain special cases. Some of his results for linear and quadratic estimators of p have been extended and his conjecture on the constancy of the asymptotic variance of members of a class of quadratic estimators is shown to be true.

关于相关观测下指数回归的进一步讨论AI 解读

Mitchell (1968) studied the properties of estimators of p in the exponential regression situation, E(yx)= α+βpx, when the observations are assumed correlated. In the notation of that paper it is now shown that the quadratic estimators r(O, c, d) have uniform minimum asymptotic variance among all linear and quadratic estimators of p and that estimators can be excluded from this class on grounds of possessing uniformly worse asymptotic biases.

相关观测下的指数回归AI 解读

Finney's(1958) model for correlated observations yx in the exponential regression situation, E(yx)=α= βpx, is studied in greater detail. It is shown that his maximum-likehood procedure for estimating p is valid in only certain special cases. Some of his results for linear and quadratic estimators of p have been extended and his conjecture on the constancy of the asymptotic variance of members of a class of quadratic estimators is shown to be true.