日期精度：到日 5104 篇 · 到月 0 篇 · 到年 0 篇
模型维度的估计
The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.
形式 Edgeworth 展开的有效性
Let $\{Y_n\}_{n\geqq 1}$ be a sequence of i.i.d. $m$-dimensional random vectors, and let $f_1,\cdots, f_k$ be real-valued Borel measurable functions on $R^m$. Assume that $Z_n = (f_1(Y_n),\cdots, f_k(Y_n))$ has finite moments of order $s \geqq 3$. Rates of convergence to normality and asymptotic expansions of distributions of statistics of the form $W_n = n^{\frac{1}{2}}\lbrack H(\bar{Z}) - H(\mu)\rbrack$ are obtained for functions $H$ on $R^k$ having continuous derivatives…
Wishart 矩阵特征根的正相依性
It is shown that the characteristic roots of a Wishart matrix (identity covariance matrix) and the roots of $S_1 S_2^{-1}$ and $S_1(S_1 + S_2)^{-1}$ where $S_1, S_2$ are independent $p \times p$ Wishart matrices with the same covariance matrix, satisfy certain types of dependency relationships. That is, it is shown that these roots are (a) positive orthant dependent, (b) associated, (c) stochastically increasing in sequence, and (d) positively likelihood ratio dependent. An…
关于 Marshall 与 Olkin 的一个概率界
A counterexample is given to a proposition of Marshall and Olkin (1974, Ann. Statist.) describing a probability bound. A theorem which gives the conditions under which mixtures of associated random variables remain associated, is stated. This provides a method to obtain the required bound.
通过时域自回归模型拟合进行线性预测
Let $\{x_t\}$ be a purely nondeterministic stationary process satisfying all the assumptions made by Berk (1974), and $\{y_t\}$ be another purely nondeterministic stationary process. Assume that $y_t$ is independent of $x_t$ but has exactly the same statistical properties as that of $x_t$. Consider the linear prediction of future values of $y_t$ on the basis of past values, using prediction constants estimated from a realisation of $T$ observations of $x_t$ by least-squares…
时间序列分析中的一致性
A number of statistics that arise in time series analysis can be represented as the sum of a partial realization of a possibly serially dependent and nonstationary discrete-parameter stochastic process. The almost sure and $L_p, p > 1$, convergence of such statistics is investigated, under various moment conditions. The results are applied to the least squares estimates of multiple regressions.
一般多元方差分析问题
This paper treats a generalization of the classical MANOVA testing problem. The problem is reduced via invariance considerations and a new test statistic is proposed. This new test is shown to be a unique locally best invariant test and locally minimax.
不稳定过程边界参数估计量的渐近分布
The limit distribution of the least squares estimator $\hat{\alpha}$ of the parameter $\alpha$ of the first order stochastic difference equation, in the boundary case $|\alpha| = 1$, is presented. With this, the asymptotic distributional problem for any real $\alpha$ in the first order case is completely settled.
方向与取向数据均匀性的不变检验
The very general results of Beran and Gine on invariant tests of uniformity are applied to $S_p$, the surface of the unit hypersphere, and $H_p$, the surface of the unit hypersphere with antipodes identified, to give a class of invariant tests of uniformity for signed and unsigned directional data in $(p + 1)$-dimensions. The $(p + 1)$-dimensional analogues of the test statistics due to Rayleigh, Bingham, Ajne, and Gine are constructed as the simplest examples, and…
回归预检验后位置参数的非参数估计
For a simple regression model, the problem of estimating the intercept after a preliminary test on the regression coefficient is considered here. Some nonparametric procedures for this problem are formulated and their various asymptotic properties studied. Comparison with the conventional estimation procedures (for both the situations where the regression coefficient is treated as a nuisance parameter or not) has also been made.
Dirichlet 先验下的秩次估计
Suppose that a sample of size $n$ from a distribution function $F$ is obtained. However, only $r(< n)$ values from the sample are observed, say $X_1,\cdots, X_r$. Without loss of generality, we can consider $X_1,\cdots, X_r$ to be the first $r$ values in the (unordered) sample. The problem is to estimate the rank order $G$ of $X_1$ among $X_1,\cdots, X_n$. The situations of interest include $F$ nonrandom, either known or unknown, and $F$ random. The random case assumes that $F$…
给定均值与协方差的多元总体判别误差界
Let $\mathscr{F}_1, \mathscr{F}_2$ be two families of $p$-variate distribution functions with specified means $\mathbf{\mu}_i (i = 1,2)$ and nonsingular covariance matrices $\Sigma_i$, and let $\pi_i$ be the prior probability assigned to $\mathscr{F}_i$ for $i = 1, 2$. The objective is to discriminate whether an observation $\mathbf{x}$ is from a distribution $F_1 \in \mathscr{F}_1$ or $F_2 \in \mathscr{F}_2$. Given a pair $F = (F_1, F_2)$ the error probability for…
聚类准则的渐近分布
A set of observations is partitioned into $k$ clusters by optimizing a clustering criterion $W$. The asymptotic distribution of this clustering criterion may be determined simply in certain cases where the optimal sample partition differs negligibly from the optimal population partition. Detailed proofs are given in the one-dimensional case when the clustering criterion to be minimized is within cluster sum of squares. The asymptotic distributions are used to compute…
似然比统计量的大偏差及其在序贯检验中的应用
We study the tail of the null distribution of the $\log$ likelihood ratio statistic for testing sharp hypotheses about the parameters of an exponential family. We show that the classical chisquare approximation is of exactly the right order of magnitude, although it may be off by a constant factor. We then apply our results and techniques to find the error probabilities of a sequential version of the likelihood ratio test. The sequential version rejects if the likelihood…
特征根与矩阵随机变量：若干渐近结果综述
The exact noncentral distributions of matrix variates and latent roots derived from normal samples involve hypergeometric functions of matrix argument. These functions can be defined as power series, by integral representations, or as solutions of differential equations, and there is no doubt that these mathematical characterizations have been a unifying influence in multivariate noncentral distribution theory, at least from an analytic point of view. From a computational…
密度及其导数核估计的弱、强一致收敛
The estimation of a density and its derivatives by the kernel method is considered. Uniform consistency properties over the whole real line are studied. For suitable kernels and uniformly continuous densities it is shown that the conditions $h \rightarrow 0$ and $(nh)^{-1} \log n \rightarrow 0$ are sufficient for strong uniform consistency of the density estimate, where $n$ is the sample size and $h$ is the "window width." Under certain conditions on the kernel, conditions…
一个生物统计函数的估计
In the analysis of life tables one biometric function of interest is the life expectancy at age $x, e_x = E\lbrack X - x\mid X > x\rbrack$. Estimation of $e_x$ is considered, the standard estimator used in life tables is shown to be asymptotically unbiased, uniformly strong consistent, and converges in distribution to a Gaussian process. The connections of the estimator studied in this article and that used in reliability theory are illustrated.
绝对单调约束下剂量反应函数的最大似然估计
Statistical properties are derived for maximum likelihood estimates of dose-response functions in which the response probability is related to the dose by means of a polynomial of unknown degree with nonnegative coefficients. Dose-response functions of this form are predicted by the multistage model of carcinogenesis. We first establish necessary and sufficient conditions for strong consistency of the estimates. For these results no assumptions are made about the polynomial…
序贯实验的自适应偏币设计
In comparing two treatments, eligible subjects come to the experiment sequentially and must be treated at once. To reduce experimental bias and to increase the precision of inference about treatment effects, the adaptive biased coin design, which offers a compromise between perfect balance and complete randomization, is proposed and analyzed. This new design has the property that it forces a small-sized experiment to be balanced, but tends toward the complete randomization…
因果效应的贝叶斯推断：随机化的作用
Causal effects are comparisons among values that would have been observed under all possible assignments of treatments to experimental units. In an experiment, one assignment of treatments is chosen and only the values under that assignment can be observed. Bayesian inference for causal effects follows from finding the predictive distribution of the values under the other assignments of treatments. This perspective makes clear the role of mechanisms that sample experimental…
基于样本自相关的一阶移动平均模型估计
For the first order moving average we consider a proposal by Walker (Biometrika, 1961) to use $k$ sample autocorrelations $(1 < k < T, T$ sample size), to estimate the first autocorrelation of the model, and hence its basic parameter. When $k = k_T \rightarrow \infty$ as $T \rightarrow \infty$, the estimator is proved consistent and asymptotically normal and efficient, the latter provided $k_T$ dominates $\log T$ and is dominated by $T^\frac{1}{2}$. An alternative form of…
多元分布的最优Fisher信息
It is shown that within the class of all multivariate distributions depending on a location parameter (and satisfying certain smoothness conditions) and with a weighted norm constraint on the covariance matrix, the one with minimum Fisherian information is the Gaussian distribution. This result is then used in obtaining a tight upper bound on the error of estimating an unknown random vector observed in additive Gaussian noise under quadratic loss.
指数族分布贝叶斯估计量的收缩变换
Sufficient conditions are provided to ensure that the Bayes estimator with squared error loss for the natural parameter of an exponential family distribution is a linear function of the sample value, given that various contractions of the Bayes estimator are also Bayes estimators, generalizing a result of Meeden (1976).
多元正态概率不等式及其设计问题应用
Some results from the theory of total positivity and Schur convexity are applied in deriving inequalities for multivariate normal probabilities having a certain convariance matrix. The result is applied to determine an optimal experimental design in an analysis of covariance model when selection of the best treatment is desired.