Estimation of Allocation Rates in a Cluster Analysis Context
研究了在聚类分析中，利用混合似然法估计样本个体属于各总体的后验概率，并通过这些概率的最大值来估计正确分配率，同时用自助法减少估计偏差。
Abstract 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 maximum of these posterior probabilities. The estimates of the correct allocation rates provide a means of assessing the performance of the mixture approach to clustering. The bootstrap technique is investigated for its effectiveness in reducing the bias of the estimates so obtained. Results are reported for three real data sets and a simulation study. It is demonstrated that the proposed estimates generally provide useful information on the unobservable allocation rates of the mixture approach. Encouraging results are obtained for the bootstrap method of bias correction applied to the estimates of the individual and overall allocation rates.