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加权最小二乘估计的最优极小极大随机设计AI 解读

Summary This work studies an experimental design problem where the values of a predictor variable, denoted by $x$, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to $m(x)$, but it is not assumed that the model is correctly specified. It follows that the quantity of interest is the best linear approximation of $m(x)$, which is denoted by $\ell(x)$. It is shown that in this framework the ordinary least…

大幅改善协变量平衡的近随机实验设计AI 解读

Summary We present a procedure that divides a set of experimental units into two groups that are similar on a prespecified set of covariates and are almost as random as with a complete randomization. Under complete randomization, the difference in the standardized average between treatment and control is $O_{\rm p}(n^{-1/2})$, which may be material in small samples. We present an algorithm that reduces imbalance to $O_{\rm p}(n^{-3})$ for one covariate and $O_{\rm p}\{n^{-(1 + 2/p)}\}$…

高维回归中的条件性原则AI 解读

Summary Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A conditional and an unconditional framework are considered, where conditioning is with respect to the covariates, which are ancillary to the parameter of interest. In recent papers, a consistent estimator was developed in the…