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保序逻辑斯蒂判别AI 解读

We propose an isotonic logistic discrimination procedure which generalises linear logistic discrimination by allowing linear boundaries to be more flexibly shaped as monotone functions of the discriminant variables. Under each of three familiar sampling schemes for obtaining a training dataset, namely prospective, mixture and retrospective, we provide the corresponding likelihood-based inference. An application to a cancer study is given. In addition, we consider theoretical…

随机序约束下的多元分布估计AI 解读

Let F and G be the cdf's of two p-dimensional multivariate distributions, such that F is stochastically larger than G. A straightforward derivation is given of the generalized maximum likelihood estimators of F and G, based on random samples from each population. An algorithmic approach to computing these estimators is described and motivating numerical examples are discussed. The special case when F and G correspond to multivariate ordinal contingency tables is also…

已知方差的若干多元正态模型中相关系数的简易最优渐近正态估计AI 解读

It is well-known that in certain multivariate normal models with known variances, maximum likelihood estimation of correlations is arithmetically cumbersome. For certain of these models, a relatively simple estimation technique based on the sufficient statistics is given and shown to be best asymptotically normal. The procedure uses the fact that many of the likelihood equations for these models are essentially cubic equations. A consistent, explicit solution for the…

若干已知方差多元正态模型中相关系数的简便最优渐近正态估计AI 解读

It is well-known that in certain multivariate normal models with known variances, maximum likelihood estimation of correlations is arithmetically cumbersome. For certain of these models, a relatively simple estimation technique based on the sufficient statistics is given and shown to be best asymptotically normal. The procedure uses the fact that many of the likelihood equations for these models are essentially cubic equations. A consistent, explicit solution for the…

二元与三元绝对正态、t、卡方及 F 分布的正相依性AI 解读

It is shown that the bivariate density of the absolute normal distribution is totally positive of order 2. Necessary and sufficient conditions are given for the trivariate density of the absolute normal distribution to be totally positive of order 2 in pairs of arguments. These results are then used to show that certain generalized bivariate and trivariate $t, \chi^2$ and $F$ random variables are associated.

单调依赖AI 解读

Random variables $X$ and $Y$ are mutually completely dependent if there exists a one-to-one function $g$ for which $P\lbrack Y = g(X)\rbrack = 1.$ An example is presented of a pair of random variables which are mutually completely dependent, but "almost" independent. This example motivates considering a new concept of dependence, called monotone dependence, in which $g$ above is now required to be monotone. Finally, this monotone dependence concept leads to defining and…

用矩母函数刻画指数族分布AI 解读

It is shown that if $\mathbf{T}$ has an unknown exponential family distribution with natural parameter $\mathbf{\theta}$, then $\mathbf{G(\theta)} = \mathbf{ET}$ uniquely specifies the moment generating function. The converse is proved, namely, if $\{\mathbf{T_\theta}\}$ is a family of random variables with moment generating functions of a certain form, then it must be an exponential family. Moreover, several necessary and sufficient conditions are given so that a function…

两种回归模型的故事AI 解读

This expository article details the effects of the choice of underlying models in the statistical analysis of regression. The two models considered are when all the data are jointly normally distributed and when the independent variables are assumed to be constants. The standard results for both these models are conditionally related to each other in a unified manner, and an example is given where new results in one model can be obtained from old results in the other model.…