Approximate Tests of Independence and Goodness of Fit Based on Stratified Multistage Samples
研究了复杂抽样设计下非线性统计量的方差估计问题，并针对拟合优度和独立性检验开发了替代的卡方检验方法，通过模拟实验验证其性质。
Abstract The impact on linear statistics of the sample design used in obtaining survey data is the subject of much of sampling literature. Recently, more attention has been paid to the design's impact on nonlinear statistics; the major factor inhibiting these investigations has been the problem of estimating at least the first two moments of such statistics. The present article examines the problem of estimating the variances of nonlinear statistics from complex samples, in the light of existing literature. The behavior of the chi-squared statistic computed from a complex sample to test hypotheses of goodness of fit or independence is studied. Alternative tests are developed and their properties studied in simulation experiments.