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单调潜变量模型中的条件关联与单维性AI 解读

Latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables, usually assuming the conditional independence of the observable variables given the latent variables. These models play an important role in educational measurement and psychometrics, in sociology and in population genetics, and are implicit in some work on systems reliability. We study a broad class of latent variable…

统计学与因果推断AI 解读

Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is addressed by using a particular model for causal inference (Holland and Rubin 1983; Rubin 1974) to critique the discussions of other writers on causation and causal inference. These…

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最小二乘回归的两种稳健替代方法AI 解读

We give Monte Carlo results on the performance of two robust alternatives to least-squares regression estimation—least-absolute residuals and the one-step sine estimator. We show how to scale the residuals for the sine estimator to achieve nearly constant efficiency for the normal distribution across various choices of the design matrix. We compare the two estimators to least squares for nine scale-contaminated normal distributions.

多项分布单元概率的同时估计AI 解读

A new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator, (the vector of observed proportions). The risk functions (expected squared-error loss) of these two estimators are examined in three ways using: (a) exact calculations, (b) standard asymptotic theory, and (c) a novel asymptotic framework in which the number of cells is large and the number of observations per cell is…

协方差稳定化变换AI 解读

After reviewing the asymptotic variance stabilizing transformations in one dimension, a generalization of these to multivariate cases is discussed. Results are given for the uniqueness of solutions when they exist, but unlike the one-dimensional case, covariance stabilizing transformations need not exist. In the two-dimensional case, a necessary and sufficient condition is given for the existence of solutions. It takes the form of a second-order partial differential equation…