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分布刻画与拟合优度检验AI 解读

Summary In this article a systematic approach to providing goodness of fit tests is discussed, for the composite goodness of fit problem of testing that the distribution F of a random sample comes from a parametric family F o. Characterization procedures are emphasized, and it is shown that, at least for the exponential case, invariant characterizations appear to be better than those which are not invariant. A general technique is developed for producing invariant…

多元正态分布的条件概率积分变换与拟合优度检验AI 解读

Let $X_1, \cdots, X_n$ be a random sample from a full-rank multivariate normal distribution $N(\mu, \Sigma)$. The two cases (i) $\mu$ unknown and $\Sigma = \sigma^2\Sigma_0, \Sigma_0$ known, and (ii) $\mu$ and $\Sigma$ completely unknown are considered here. Transformations are given that transform the observation vectors to a (smaller) set of i.i.d. uniform rv's. These transformations can be used to construct goodness-of-fit tests for these multivariate normal…

非满秩正态回归中同时外推的一个判据AI 解读

In recent work by O'Reilly, a necessary and sufficient condition for the existence of an unbiased estimate of the distribution function of a "future" observation was given. The result was obtained under the condition that the model had full rank. Here, the result is generalized to any number of future observations and the full rank condition is relaxed. The corresponding uniformly minimum variance unbiased estimator is identified from the density estimates given by Ghurye…

正态回归中的一个外推判据AI 解读

In a full rank normal regression model, the existence of an unbiased estimate of the distribution associated to any "future" observation is studied. A necessary and sufficient condition in terms of the point at which the "future" observation will be taken is given for such an estimate to exist. This criterion is introduced to consider the validity of extrapolation.

条件概率积分变换及其复合假设卡方拟合优度检验应用AI 解读

It is shown that certain conditional distributions, obtained by conditioning on a sufficient statistic, can be used to transform a set of random variables into a smaller set of random variables that are identically and independently distributed with uniform distributions on the interval from zero to one. This result is then used to construct distribution-free tests of fit for composite goodness-of-fit problems. In particular, distribution-free chi-square goodness-of-fit…