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多元模型协方差结构检验及其在家族疾病数据中的应用AI 解读

Recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit. Here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector θ. The idea is to extend this distribution, the “null” distribution, to a more general distribution that depends on θ, an additional scalar γ, and a specific quadratic function of the response vector chosen to capture features of an…

多元模型协方差结构的检验及家族疾病数据应用AI 解读

Recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit. Here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector θ. The idea is to extend this distribution, the “null” distribution, to a more general distribution that depends on θ, an additional scalar γ, and a specific quadratic function of the response vector chosen to capture features of an…

交叉验证、刀切法与自助法：前向逻辑回归的超额误差估计AI 解读

Given a prediction rule based on a set of patients, what is the probability of incorrectly predicting the outcome of a new patient? Call this probability the true error. An optimistic estimate is the apparent error, or the proportion of incorrect predictions on the original set of patients, and it is the goal of this article to study estimates of the excess error, or the difference between the true and apparent errors. I consider three estimates of the excess error:…

伪最大似然估计：理论与应用AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. random variables with probability distribution $F_{\theta, p}$ indexed by two real parameters. Let $\hat{p} = \hat{p}(X_1, \cdots, X_n)$ be an estimate of $p$ other than the maximum likelihood estimate, and let $\hat{\theta}$ be the solution of the likelihood equation $\partial/\partial \theta \ln L(\mathbf{x}, \theta, \hat{p}) = 0$ which maximizes the likelihood. We call $\hat{\theta}$ a pseudo maximum likelihood estimate of $\theta$, and…