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关于混合模型假设检验中 Aitkin–Rubin 方法的札记AI 解读

SUMMARY In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.

聚类分析中正确分配率的估计AI 解读

A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the…

聚类分析中正确分配率的估计AI 解读

A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the…

基于未分类初始样本的线性判别函数效率AI 解读

Estimation of the optimal linear discriminant function is considered on the basis of a sample of observations known only to belong to a mixture of two univariate normal populations with a common variance. The asymptotic efficiency of the procedure so obtained is evaluated relative to that of Anderson's classification statistic.

基于未分类初始样本的线性判别函数效率AI 解读

Estimation of the optimal linear discriminant function is considered on the basis of a sample of observations known only to belong to a mixture of two univariate normal populations with a common variance. The asymptotic efficiency of the procedure so obtained is evaluated relative to that of Anderson's classification statistic.

判别分析中表观误判率的偏差AI 解读

The apparent error rate is a commonly used estimator of the actual error rate in discriminant analysis. In this study the asymptotic bias of the apparent error rate is derived in the context of two multivariate normal populations with unknown different means and unknown common covariance matrix. From the derived expansion a correction term ia available for reducing the bias of the apparent error rate from the first to the second order with respect to the reciprocals of the…

判别分析中表观错误率的偏差AI 解读

The apparent error rate is a commonly used estimator of the actual error rate in discriminant analysis. In this study the asymptotic bias of the apparent error rate is derived in the context of two multivariate normal populations with unknown different means and unknown common covariance matrix. From the derived expansion a correction term ia available for reducing the bias of the apparent error rate from the first to the second order with respect to the reciprocals of the…

判别分析中构造渐近最优分配规则的迭代重分类程序AI 解读

The construction of a suitable rule of allocation in the two-population discrimination problem is considered in the case where there are initially available from the populations II1, II2, n 1, n 2 observations and M unclassified observations. An iterative reclassification procedure based on the n 1 + n 3 + M observations is proposed and found asymptotically optimal when M → ∞ and n 1 and n 2 are moderately large. The case of finite M is evaluated by a Monte Carlo experiment…

判别分析中构造渐近最优分类规则的迭代重分类程序AI 解读

The construction of a suitable rule of allocation in the two-population discrimination problem is considered in the case where there are initially available from the populations II1, II2, n 1, n 2 observations and M unclassified observations. An iterative reclassification procedure based on the n 1 + n 3 + M observations is proposed and found asymptotically optimal when M → ∞ and n 1 and n 2 are moderately large. The case of finite M is evaluated by a Monte Carlo experiment…

判别分析中条件错误率与风险的渐近分布AI 解读

The distributions of the conditional error rate and risk associated with Anderson's classification statistic in the context of the two-population discrimination problem with different means and common covariance matrix are studied. For the most general case where all three population parameters are unknown, the distributions are able to be approximated in the form of asymptotic expansions of degrees higher than previously available.

判别分析中条件误判率与风险的渐近分布AI 解读

The distributions of the conditional error rate and risk associated with Anderson's classification statistic in the context of the two-population discrimination problem with different means and common covariance matrix are studied. For the most general case where all three population parameters are unknown, the distributions are able to be approximated in the form of asymptotic expansions of degrees higher than previously available.