日期精度：到日 1055 篇 · 到月 1123 篇 · 到年 161 篇 · 未提供 7 篇
参数由样本估计时经验分布函数的弱收敛
The weak convergence of the sample df is studied under a given sequence of alternative hypotheses when parameters are estimated from the data. For a general class of estimators it is shown that the sample df, when normalised, converges weakly to a specified normal process. The results are specialised to the case of efficient estimation.
若干非参数问题的贝叶斯分析
The Bayesian approach to statistical problems, though fruitful in many ways, has been rather unsuccessful in treating nonparametric problems. This is due primarily to the difficulty in finding workable prior distributions on the parameter space, which in nonparametric ploblems is taken to be a set of probability distributions on a given sample space. There are two desirable properties of a prior distribution for nonparametric problems. (I) The support of the prior…
使用样本分位数的拟合优度检验
Summary A goodness-of-fit test is constructed using sample quantiles for a p.d.f. F(x, θ) (where θ is to be estimated) which is continuous and strictly increasing at the quantiles of interest. It is shown to be asymptotically equivalent, under alternatives “close” to the null, to the usual goodness-of-fit test based on grouped observations, the advantage being that we may avoid the difficulties of choosing cell boundaries for grouping.
非独立同分布情形下约化经验与分位数过程的收敛及其顺序统计量应用
Any triangular array of row independent $\mathrm{rv}$'s having continuous $\mathrm{df}$'s can be transformed naturally so that the empirical and quantile processes of the resulting $\mathrm{rv}$'s are relatively compact. Moreover, convergence (to a necessarily normal process) takes place if and only if a simple covariance function converges pointwise. Using these results we derive the asymptotic normality of linear combinations of functions of order statistics of non-i.i.d. $\mathrm{rv}$…
备择假设下Kolmogorov–Smirnov型统计量的极限分布
Let $X_1, X_2, \cdots$ be a sequence of independent and identically distributed random variables with the common distribution being uniform on [0, 1]. Let $Y_1, Y_2, \cdots$ be a sequence of i.i.d. variables with continuous $\operatorname{cdf}F(t)$ and with [0, 1] support. Let $F_n(t, \omega)$ denote the empirical distribution function based on $Y_1(\omega), \cdots, Y_n(\omega)$ and let $G_m(t, \omega)$ the empirical $\operatorname{cdf}$ pertaining to $X_1(\omega), \cdots, X_m(\omega)$…
含两个内生解释变量时OLS与2SLS估计量分布函数的近似
Roberto S. Mariano, Approximations to the Distribution Functions of the Ordinary Least-Squares and Two-Stage Least-Squares Estimators in the Case of Two Included Endogenous Variables, Econometrica, Vol. 41, No. 1 (Jan., 1973), pp. 67-77
涉及次序统计量的两个恒等式
Two identities involving the distribution functions of order statistics are given, and are applied in proving some combinatorial results.
特征函数的数值反演
A method is described for finding a bound on the error when a version of the usual characteristic function inversion formula is evaluated by numerical integration. The method is applied to the calculation of the distribution function of a quadratic form in normal random variables.
用作拟合优度准则的次序统计量二次型
Consider a sample vector, z, whosen elements z(i)are the probability transforms z(i) θ P{x(i)} of the order statistics x(i) of a random sample of size n drawn from a cumulative distribution function P(x). Most nonparametric goodness-of-fit criteria concerned with testing whether the specified P(x) is the true one are computed from z. The criterion considered here is the x2-type criterion S2 θ (z – μ)′V–1(z – μ), where μ θ E(z) and V θ E{(z –;μ)(z – μ)′}. The extract…
不连续分布的 Kolmogorov 拟合优度检验
The Kolmogorov goodness-of-fit test is known to be conservative when the hypothesized distribution function is not continuous. A method for finding the exact critical level (approximate in the two-sided case) and the power in such cases is derived. Thus the Kolmogorov test may be used as an exact goodness-of-fit test for all completely specified distribution functions, whether continuous or not continuous. Several examples of the application of this extension of the…
一种连续经验贝叶斯平滑技术
Maritz (1966) and Lemon & Krutchkoff (1969) each describe discrete empirical Bayes smoothing techniques. These techniques essentially attempt to approximate the prior distribution function. Here a continuous smoothing technique which is based on a smooth and continuous approximation to the prior density function is presented. Results from a Monte Carlo study of the Poisson distribution are reported which show that the continuous smoothing technique has desirable small-sample…
双样本问题中渐近有效的线性有序秩检验
Summary In this paper the nonparametric two-sample problem is considered and tests are proposed for the hypothesis of identity of the two distribution functions. These tests are based on statistics which are linear combinations of ranks of the order statistics of one of the samples, in the two-sample rank order. It is seen that many existing statistics, proposed mainly on heuristic grounds, are members of this class. The asymptotic distribution of such statistics is…
截断参数分布中 MVU 与 ML 分布函数估计量的比较
The ratio of integrated mean square errors for minimum variance unbiased and maximum likelihood estimating distribution functions is computed for truncation parameter distributions as a relative efficiency measure. A “closeness” relative efficiency is also computed for these estimators for the same class of distributions. The MVU estimator is found to be more efficient than the ML estimator for all sample sizes exceeding two in both cases.
二元单非中心 t 分布的级数表示
This article presents a derivation of the probability density function and the cumulative distribution function of two correlated t statistics, for the central and singly noncentral case. The distribution of the ratios of means to standard deviations of a bivariate normal sample, is considered in particular.
多个分布中最大 α 分位数的无分布区间估计
A procedure based on order statistics is given for the interval estimation of the largest α-quantile of several continuous distributions. Results on infimum of coverage probability are obtained for one-sided and two-sided intervals. An optimality criterion is proposed and an algorithm is given for two-sided intervals. Large sample approximations are also considered.
市场需求曲线的极限函数形式
On the basic assumption that individual consumption of a good is a stochastic phenomenon, the first part of this article shows that under general conditions market quantity demanded is asymptotically (as n, the number of individuals in the market, increases) distributed as normal with and variance a function of own price given all other prices and individual incomes. Next, by the use of integral transforms, it is shown that the unknown market demand function can be…
Cramér–von Mises 统计量的分量：第一部分
Summary Let Fn(x) be the sample distribution function derived from a sample of independent uniform (0, 1) variables. The paper is mainly concerned with the orthogonal representation of the Cramér-von Mises statistic Wn2 in the form ∑j=1∞(jπ)−2znj2 where the znj are the principal components of n{Fn(x)−x}. It is shown that the znj are identically distributed for each n and their significance points are tabulated. Their use for testing goodness of fit is discussed and their…
作为拟合优度准则的次序统计量二次型
Consider a sample vector, z, whosen elements z(i)are the probability transforms z(i) θ P{x(i)} of the order statistics x(i) of a random sample of size n drawn from a cumulative distribution function P(x). Most nonparametric goodness-of-fit criteria concerned with testing whether the specified P(x) is the true one are computed from z. The criterion considered here is the x2-type criterion S2 θ (z – μ)′V–1(z – μ), where μ θ E(z) and V θ E{(z –;μ)(z – μ)′}. The extract…
累积分布函数参数置信带的一种构造方法
A method is developed for constructing a confidence band for a cumulative distribution function with known functional form. The band is derived using the maximum absolute difference between the true function and an estimator of it. The normal distribution with unknown mean and variance is treated in detail. The band derived in this case is found to be superior in certain instances to the one due to Kanofsky (1968a) with respect to the expected band width at selected points,…
一阶自回归序列参数的最大似然估计量分布
A method is given for obtaining values of the distribution function of the maximum likelihood estimator of the parameter in the first-order autoregressive series. Although exact results are obtainable in a special case, in general the distribution function involves the approximation of the distribution of a linear combination of chi-squared variates. Two such approximations are compared with simulated results. The method used is valid for any value of the parameter.
一种连续经验贝叶斯平滑技术
Maritz (1966) and Lemon & Krutchkoff (1969) each describe discrete empirical Bayes smoothing techniques. These techniques essentially attempt to approximate the prior distribution function. Here a continuous smoothing technique which is based on a smooth and continuous approximation to the prior density function is presented. Results from a Monte Carlo study of the Poisson distribution are reported which show that the continuous smoothing technique has desirable small-sample…