论文检索

多元校准中的置信区域AI 解读

The multivariate calibration problem is considered, in which a sample of $n$ observations on vectors $\xi_{(i)}$ (of "true values") and $Y_{(i)}$ (of less accurate but more easily obtained values) are to be used to estimate the unknown $\xi$ corresponding to a future $Y$. It is assumed that $Y = BX + \varepsilon$, where $\varepsilon$ is multivariate normal and $X = h(\xi)$ for known $h$. Current methods for obtaining a confidence region $C$ for $\xi$, which consist of…

结构化回归问题中的先验分布设定AI 解读

The problem of assessing the prior mean and covariance matrix of the vector of regression coefficients in the normal multiple linear regression model is considered. Arguments are advanced for using expectations regarding the form of the design matrix in specifying the prior for problems with a structure that can aid in specifying these expectations. This is illustrated with models having second-order terms. An example is given.

岭估计与 Stein 估计的另一种经验贝叶斯解释AI 解读

SUMMARY Ridge and Stein-like estimators have been motivated as being empirical Bayes estimates with respect to the prior β ~ N(0, τ2 V- 1) for the vector of regression coefficients β in the usual model y = Xβ + ϵ, where the hyperparameter τ2 is estimated from the data. V = I results in a ridge pattern of shrinkage while V = Xt X gives a Stein-like pattern. In this article an alternative formulation is considered, according to which the data represent a sample from a…

利用置信界选择岭回归的偏置参数AI 解读

Consider the multiple linear regression model Y = Xβ + ∈, ∈ ∼ Ň(0, σ2 I) where the matrix S = X' X is ill conditioned. A confidence bound approach is developed for choosing k in the ridge estimator β*(k) = (S + kI)–1 X' Y as follows: A parameter is defined that is essentially the largest (constant) k one could use and still have β*(k)'s mean squared error (MSE) be less than MSE (where is the usual estimate of β). A procedure is then developed to obtain a lower confidence…