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处理模型选择变异的加权包络估计AI 解读

Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical…

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…

连续统回归的若干认识及其渐近性质AI 解读

Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter γ. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter γ. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum…

协方差约简模型：协方差矩阵谱建模的替代方法AI 解读

We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices.

偏逆回归AI 解读

In regression with a vector of quantitative predictors, sufficient dimension reduction methods can effectively reduce the predictor dimension, while preserving full regression information and assuming no parametric model. However, all current reduction methods require the sample size n to be greater than the number of predictors p. It is well known that partial least squares can deal with problems with n < p. We first establish a link between partial least squares and…

无需矩阵求逆的回归降维AI 解读

Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to d < n linear combinations of the original p predictors. However, standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix. We propose a method for estimating the…

基于切片平均方差估计的边际检验AI 解读

We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared…

多元回归条件均值的最优充分降维AI 解读

The aim of this article is to develop optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression. The context is roughly the same as that of a related method by Cook & Setodji (2003), but the new method has several advantages. It is asymptotically optimal in the sense described herein and its test statistic for dimension always has a chi-squared distribution asymptotically under the null hypothesis. Additionally, the optimal method…

异方差线性模型的 D 最优设计AI 解读

The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the…

摘要暂缺

最小平方与最小中位平方拟合残差的模型误设诊断比较AI 解读

This article explores model misspecification diagnostics based on least squares and least median of squares fits. It shows that in some circumstances, least median of squares methods (or any other estimator with the exact fit property) fail to reveal an incorrectly specified mean function, but least squares methods succeed.

非线性回归中的偏差AI 解读

We investigate the biases of the residuals and maximum likelihood parameter estimates from normal nonlinear regression models. Emphasis is placed on a class of partially nonlinear models, on the role of individual cases in determining bias, on how bias affects standard diagnostic methods, and on the relationship between bias and curvature.

非线性回归中的偏差AI 解读

We investigate the biases of the residuals and maximum likelihood parameter estimates from normal nonlinear regression models. Emphasis is placed on a class of partially nonlinear models, on the role of individual cases in determining bias, on how bias affects standard diagnostic methods, and on the relationship between bias and curvature.

摘要暂缺

非线性回归中的残差AI 解读

We employ a quadratic expansion to investigate the behaviour of the ordinary residuals in nonlinear regression. These residuals can produce misleading results when used in diagnostic methods analogous to those for linear regression. We suggest a new type of residual that overcomes many of the potential shortcomings of the ordinary residuals.