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稀疏包络模型：多元线性回归的高效估计与响应变量选择AI 解读

The envelope model allows efficient estimation in multivariate linear regression. In this paper, we propose the sparse envelope model, which is motivated by applications where some response variables are invariant with respect to changes of the predictors and have zero regression coefficients. The envelope estimator is consistent but not sparse, and in many situations it is important to identify the response variables for which the regression coefficients are zero. The…

缩放包络：多元线性回归中的尺度不变与高效估计AI 解读

Efficient estimation of the regression coefficients is a fundamental problem in multivariate linear regression. The envelope model proposed by Cook et al. (2010) was shown to have the potential to achieve substantial efficiency gains by accounting for linear combinations of the response vector that are essentially immaterial to coefficient estimation. This requires in part that the distribution of those linear combinations be invariant to changes in the nonstochastic…

包络与偏最小二乘回归AI 解读

Summary We build connections between envelopes, a recently proposed context for efficient estimation in multivariate statistics, and multivariate partial least squares (PLS) regression. In particular, we establish an envelope as the nucleus of both univariate and multivariate PLS, which opens the door to pursuing the same goals as PLS but using different envelope estimators. It is argued that a likelihood-based envelope estimator is less sensitive to the number of PLS…

内包络：多元线性回归的高效估计AI 解读

In this article we propose a new model, called the inner envelope model, which leads to efficient estimation in the context of multivariate normal linear regression. The asymptotic distribution and the consistency of its maximum likelihood estimators are established. Theoretical results, simulation studies and examples all show that the efficiency gains can be substantial relative to standard methods and to the maximum likelihood estimators from the envelope model introduced…

多元线性回归中用于高效估计的部分包络模型AI 解读

We introduce the partial envelope model, which leads to a parsimonious method for multivariate linear regression when some of the predictors are of special interest. It has the potential to achieve massive efficiency gains compared with the standard model in the estimation of the coefficients for the selected predictors. The partial envelope model is a variation on the envelope model proposed by Cook et al. (2010) but, as it focuses on part of the predictors, it has looser…

序贯临床试验中次要终点的检验与置信区间AI 解读

In a sequential clinical trial whose stopping rule depends on the primary endpoint, inference on secondary endpoints is an important long-standing problem. Ignoring the possibility of early stopping based on the primary endpoint may result in substantial bias. To address this problem, a commonly used approach is to develop bias correction by estimating the bias in the case of bivariate normal outcomes and appealing to joint asymptotic normality of the statistics associated…