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随机系数回归模型中的最小距离估计AI 解读

Random coefficient regression models are important in modeling heteroscedastic multivariate linear regression in econometrics. The analysis of panel data is one example. In statistics, the random and mixed effects models of ANOVA, deconvolution models and affine mixture models are all special cases of random coefficient regression. Some inferential problems, such as constructing prediction regions for the modeled response, require a good nonparametric estimator of the…

多元参数模型的随机最小距离检验AI 解读

Stochastic procedures are randomized statistical procedures which are functions of the observed sample and of one or more artificially constructed auxiliary samples. As the size of the auxiliary samples increases, a stochastic procedure becomes nearly nonrandomized. The stochastic test of this paper arises as a numerically feasible approximation to a natural minimum distance goodness-of-fit test for multivariate parametric models. The distance being minimized here is the…

随机化估计与检验AI 解读

Stochastic procedures are randomized tests, estimates and confidence sets with two properties: (i) They are functions of an original sample and one or more artificially constructed auxiliary samples. (ii) They become nearly nonrandomized when the auxiliary samples increase in size. The stochastic procedures of this paper, which arise as approximations to numerically intractable procedures, involve iterated bootstrap techniques and random sampling schemes over abstract…

多元分布的置信集合AI 解读

The confidence sets for a $q$-dimensional distribution studied in this paper have several attractive features: affine invariance, correct asymptotic level whatever the actual distribution may be, numerical feasibility, and a local asymptotic minimax optimality property. When dimension $q$ equals one, the confidence sets reduce to the usual Kolmogorov-Smirnov confidence bands, except that critical values are determined by bootstrapping.

一般回归函数的最优估计AI 解读

Let $\Theta$ be a convex subset of $R^d$, and for each $\theta \in \Theta$ let $F(\theta; dt)$ be a probability on the line. For any vector $a_n = (a_{n1}, a_{n2}, \cdots, a_{nn})$ where $a_{ni} \in \Theta$, let $X_{n1}, \cdots, X_{nn}$ be independent observations, the distribution of $X_{ni}$ being $F(a_{ni}; dt)$. The main results give a method of estimating the unknown regression function $a_n$ based on a minimum distance recipe. Under regularity assumptions, the proposed…