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s 值：回归系数稳健程度的低情境依赖度量AI 解读

This paper proposes a context-minimal range of alternative regression models that is used to generate a range of alternative estimates. A prior distribution is assumed with a zero mean but an ambiguous covariance matrix. The choice of the prior covariance matrix is facilitated by transformation to standardized variables which makes the prior expected R2 equal to the sum of the prior variances. Three different ranges of the prior expected R2 are used to define three different…

贝叶斯先验征询的诊断方法AI 解读

One elicitation diagnostic identifies a family of prior distributions that are so diffuse that they are practically equivalent to the "completely" diffuse prior. Another elicitation diagnostic identifies a family of prior distributions that concentrate enough mass in the neighborhood of zero that they are practically equivalent to the dogmatic prior that sets a parameter exactly equal to zero. If either question thus posed can be answered in the affirmative then there is no…

规划、批评与修订AI 解读

This paper presents a more complete theory of data analysis which allows for changes in the state of mind of the observer and also for approximations that limit planning costs. Discussion is included on the form that criticism should take, and the extent to which planned responses to the data can legitimately be revised after the data are reviewed. The proper role of diagnostics is discussed. Some diagnostic statistics are genuinely criticisms, but many are pre-test…

线性方程组中的变量测量误差AI 解读

This paper extends the simple errors-in-variable bound to the setting of systems of equations. Both diagonal and nondiagonal measurement error covariance matrices are considered. In the nondiagonal case, the analogue of the simple errors-in-variable interval of estimates is an ellipsoid with diagonal equal to the line segment connecting t he direct least squares with a two-stage least-squares estimate. For the diagonal case, the set of estimates under some conditions must li…

广义最小二乘估计的全局敏感性结果AI 解读

The covariance matrix for the residuals of a regression process is written as the identity matrix plus a matrix V. The matrix V is bounded from above, and the corresponding set of generalized least squares estimates is identified. The extreme estimates in this set are functions of the usual t statistics; in particular the number ((T - k)/8)1/2/|t| measures the influence of reweighting extreme observations, where T - k gives the degrees of freedom, t is the t statistic, and…

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加权回归估计值的集合AI 解读

We present in this article several results that characterize the set of all weighted regressions. The set of weighted regression estimates is the set of all generalized least squares estimates for covariance matrices that have positive weights on the diagonal and have zeroes elsewhere. The study of sets of estimates is a method for dealing with distributional uncertainty, which does not require the strong assumption of a particular distribution. We show that the set of…

加权回归估计的集合AI 解读

We present in this article several results that characterize the set of all weighted regressions. The set of weighted regression estimates is the set of all generalized least squares estimates for covariance matrices that have positive weights on the diagonal and have zeroes elsewhere. The study of sets of estimates is a method for dealing with distributional uncertainty, which does not require the strong assumption of a particular distribution. We show that the set of…

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不依赖坐标的岭回归界AI 解读

The dependence of ridge-regression estimates on the choice of parameterization is defined with reference to the hull of all possible ridge estimates for all possible parameterizations. A reanalysis of Hoerl and Kennard's (1970) 10-factor example and Marquardt and Snee's (1975) acetylene data reveals that most conclusions depend on the parameterization.

不依赖坐标表示的岭回归界AI 解读

The dependence of ridge-regression estimates on the choice of parameterization is defined with reference to the hull of all possible ridge estimates for all possible parameterizations. A reanalysis of Hoerl and Kennard's (1970) 10-factor example and Marquardt and Snee's (1975) acetylene data reveals that most conclusions depend on the parameterization.

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回归选择策略与显露的先验AI 解读

The computation and selection of constrained regressions may be motivated by prior information and, if so, a regression selection strategy reveals the implicit prior. The selection strategies of principal component regression, stepwise regression, and imposing equality constraints are connected with prior densities which are uniform on spheres, hyperbolas, and cones, respectively. Omitting variables in a predetermined order reveals lexicographic priors.

回归选择策略与揭示的先验AI 解读

The computation and selection of constrained regressions may be motivated by prior information and, if so, a regression selection strategy reveals the implicit prior. The selection strategies of principal component regression, stepwise regression, and imposing equality constraints are connected with prior densities which are uniform on spheres, hyperbolas, and cones, respectively. Omitting variables in a predetermined order reveals lexicographic priors.

简单变量测量误差模型中最小二乘与工具变量估计的比较AI 解读

IF ONE OF THE EXPLANATORY VARIABLES in a linear regression model is measured with error, the ordinary least squares estimator is known to be biased and inconsistent. Given suitable assumptions, an instrumental variables estimator is known to be consistent. In a large sample, the instrumental variables estimator is thus unambiguously preferred, but the choice of an estimator in a small sample remains a puzzle. The method of maximum likelihood sheds light on this puzzle. It…

矩阵加权平均与后验界AI 解读

Summary Bounds for matrix weighted averages of pairs of vectors are presented. The weight matrices are constrained to certain classes suggested by the Bayesian analysis of the linear regression model and the multivariate normal model. The bounds identify the region within which the posterior location vector must lie if the prior comes from a certain class of priors.

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作为访问偏向记忆的“解释结果”AI 解读

This article presents an inference-cum-memory model with uncertain parameter p and binomial data. The model is intended to represent the phenomenon especially common in the social sciences of explaining the results of a statistical calculation. The principal assumptions of the model are that experiments, not sufficient statistics, are stored in memory, and that the experiments are categorized by and accessed according to their implications for inference. The nonsample…

错误模型与数据分析后的模型构建AI 解读

This article proposes a method of discounting evidence when linear regression models are constructed after the data have been partially analyzed. The solution parallels a formal decision theoretic analysis of a presimplification problem in which models or model spaces are simplified before observation in order to avoid observation or processing costs. Post-data model construction is interpreted as the data-dependent decision that this pre-simplification is undesirable. The…

错误模型与数据分析后的模型构建AI 解读

This article proposes a method of discounting evidence when linear regression models are constructed after the data have been partially analyzed. The solution parallels a formal decision theoretic analysis of a presimplification problem in which models or model spaces are simplified before observation in order to avoid observation or processing costs. Post-data model construction is interpreted as the data-dependent decision that this pre-simplification is undesirable. The…