Errors in discrimination with monotone missing data from multivariate normal populations
Errors in discrimination with monotone missing data from multivariate normal populations
复制标题
多元正态总体中单调缺失数据的辨别错误
DOI：
10.1016/j.csda.2005.04.008
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Loukas
中科院分区：
文献类型：
--
作者：
A. Batsidis;K. Zografos;S. Loukas
研究了线性判别函数用于将观测值X分类为两个独立的多元正态总体NPμ(ν)，Σ之一时的行为，其中两个独立的多元正态总体具有不同的均值向量μ(ν)，ν=1，2和一个共同的协方差矩阵Σ。以随机两步单调训练样本为基础，分三个复杂度递增阶段研究了参数估计的影响。给出了误分类概率分布函数的渐近表达式。此外，还给出了数值和仿真结果，以研究不同的估计方法和数据错失率对误分类概率分布的影响。文中还讨论了k步单调缺失训练样本情况和完全未知异方差正态总体情况下的两种推广。
The behavior of the linear discriminant function is studied, when it is used for the classification of an observation X into one of two independent multivariate normal populations Npμ(ν),Σ, with distinct mean vectors μ(ν), ν=1,2 and a common covariance matrix Σ. The effect of the estimation of the parameters, on the basis of random 2-step monotone training samples, is studied, in three stages of increasing complexity. Asymptotic expressions for the distribution functions of the probabilities of misclassification are derived. Moreover, numerical and simulation results are presented in order to study the effect to the distribution of the probabilities of misclassification using different estimation procedures and missingness rate in the data. Two extensions, related to the case of k-step monotone missing training samples and the case of completely unknown heteroscedastic normal populations are also discussed.