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位置尺度族中次序统计量的最佳线性无偏预测AI 解读

In many life testing, reliability and replacement policy situations, it is desirable to predict the time of future failures from times of the early failures in the same sample. Interval prediction in this setting has been treated by several authors. In this article, the authors give best linear unbiased (blu) point predictors of future failures when the underlying distribution is known up to location and scale. Analogous large sample procedures based on sample quantile…

利用薪资数据估计百分位回归线AI 解读

In case of contamination, skewness or unequal variances, a nonparametric alternative to least squares regression is considered. In addition, investigators are often more interested in estimates of percentile lines than in the mean regression line. Thus, a modification of Brown-Mood regression is proposed to estimate the (100p) th percentile line α + βx of a random variable. This technique is applied to some data (artificial, but similar to real) relating the salary (y) of a…

若干 Rényi 型检验的功效界AI 解读

Let X 1, X 2, …, Xn be a random sample from a random variable with continuous distribution function H(x). Renyi-type statistics, such as are considered for testing the hypothesis H(x) = F(x) against the class of alternatives G (n)(x), satisfying sup z (F(x) — G (n)(x)) Δ n > 0. Sharp bounds on the power, both for finite sample size and asymptotic values, are obtained for each of the tests examined, and these tests are shown consistent with respect to the class of…

渐近最佳线性估计量最优分位点选择的统一方法AI 解读

Due to its computational simplicity and efficiency, asymptotically best linear estimates (ABLE) based on order statistics selected from a complete, or censored, sample are of particular importance. This article deals with a unified method for finding the optimum spacing (eventually the optimum rank of the order statistics) for the ABLE. Application of the method estimating one of the two (location and scale) parameters of various distributions is also discussed.

若干Rényi型检验的功效界AI 解读

Let X 1, X 2, …, Xn be a random sample from a random variable with continuous distribution function H(x). Renyi-type statistics, such as are considered for testing the hypothesis H(x) = F(x) against the class of alternatives G (n)(x), satisfying sup z (F(x) — G (n)(x)) Δ n > 0. Sharp bounds on the power, both for finite sample size and asymptotic values, are obtained for each of the tests examined, and these tests are shown consistent with respect to the class of…

Cramér–von Mises 统计量的分量（二）AI 解读

Summary Let θ^ be an asymptotically efficient estimator of parameter vector θ based on an ordered sample of n independent observations y 1, ..., y n from a distribution with distribution function F(y, θ) and let x^j=F(yj,θ^), j = 1, ..., n. Let Ŵn 2 be the Cramér–von Mises statistic calculated from ◯ 1, ..., ◯ n. This paper shows how to construct components ẑ n1, ẑ n2, ... such that Ŵ n 2 = ∑j=1 ∞ μj ẑ nj 2 where ẑ n1, ẑ n2, ... are asymptotically independent N(0, 1)…

检测均值变化的检验AI 解读

Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.

密度估计的插值样条方法（一）：等距节点AI 解读

Statistical properties of a variant of the histospline density estimate introduced by Boneva-Kendall-Stefanov are obtained. The estimate we study is formed for $x$ in a finite interval, $x\in\lbrack a, b\rbrack = \lbrack 0, 1\rbrack$ say, by letting $\hat{F}_n(x), x \epsilon\lbrack 0, 1\rbrack$ be the unique cubic spline of interpolation to the sample cumulative distribution function $F_n(x)$ at equi-spaced points $x = jh, j = 0, 1,\cdots, l + 1, (l + 1)h = 1$, which…

利用极端次序统计量进行统计推断AI 解读

A method is presented for making statistical inferences about the upper tail of a distribution function. It is useful for estimating the probabilities of future extremely large observations. The method is applicable if the underlying distribution function satisfies a condition which holds for all common continuous distribution functions.

对称分布的分布函数估计AI 解读

This paper considers the problem of estimating the distribution function of a symmetric distribution when the centre of symmetry is unknown. An estimator is proposed which is shown to be asymptotically better than the empirical distribution function for well-known distributions including the normal, double exponential and Cauchy.

通过随机化回答估计连续型随机变量的分布函数AI 解读

In 1965 Stanley Warner [8] illustrated a technique whereby one could estimate from a sample the proportion of persons in a population possessing some characteristic X, without pointedly asking the question, “Do you possess characteristic X?”. The present article uses a variation of these ideas suggested by Warner in a later paper [7] to estimate the distribution function of a continuous-type random variable. The technique is illustrated by estimating an income distribution…

摘要暂缺

收入分布的便捷描述模型：伽马密度AI 解读

The distribution of personal income is approximated by a two-parameter gamma density function (Pearson Type III). The two parameters may be considered as indicators of scale and of inequality, respectively. Maximum likelihood estimates of the parameters are derived from a random sample using graphical techniques, and a likelihood ratio test for the hypothesis that the inequality parameter is the same for different distributions is presented. The derivation of both the…

It is shown that among all cumulative distribution functions passing through $k \geqq 2$ given points there is a unique one with minimal Fisher information; it is obtained by a curious type of spline interpolation. This answers some questions raisd by D. G. Kendall and J. W. Tukey.

基于经验分布函数的拟合优度统计量及若干比较AI 解读

This article offers a practical guide to goodness-of-fit tests using statistics based on the empirical distribution function (EDF). Five of the leading statistics are examined—those often labelled D, W 2, V, U 2, A 2—and three important situations: where the hypothesized distribution F(x) is completely specified and where F(x) represents the normal or exponential distribution with one or more parameters to be estimated from the data. EDF statistics are easily calculated, and…

摘要暂缺

积分回归函数估计相关分布的收敛速率AI 解读

Brunk studied integral regression functions and has obtained strong laws and limiting distributions for estimators of these functions. In this note we will study additional conditions that ensure a rate of convergence of the distribution function of the maximum absolute difference of an integral regression function and its estimator, suitably normalized, to the distribution function of a normalized maximum absolute value of partial sums of random variables. These results are…

正则变化分布函数下的样本分位数AI 解读

A law of the iterated logarithm is proved for sample $p$-quantiles when the probability distribution function varies regularly at $\\xi$ with $F(\\xi) = p$.

贝叶斯分类的渐近结果AI 解读

We have a population composed of two subpopulations whose probability properties are described by known univariate distribution functions, $G(x)$ and $H(x)$, respectively. The probability of observing an individual from the first population is $\theta$, from the second is $1 - \theta$. We assume $\theta$ is a random variable with a prior distribution on (0, 1) and find the Bayes rule for classifying $n$ observations as from $G$ or from $H$ when the loss function is equal to…

含两个内生变量时三种 LIML 结构误差方差估计量精确矩的存在性AI 解读

This article derives the exact finite sample density functions of three alternative LIML estimators of the variance of the error term in a structural equation containing two endogenous (GΔ = 2) variables contained in a system of G(G ≥ 2) nondynamic structural equations. For the case considered, none of the density functions of the three LIML structural variance estimators define finite moments of positive integer order. It is also demonstrated that, corresponding to a fixed…

含两个内生变量时三种 LIML 结构方差估计量精确矩的存在性AI 解读

This article derives the exact finite sample density functions of three alternative LIML estimators of the variance of the error term in a structural equation containing two endogenous (GΔ = 2) variables contained in a system of G(G ≥ 2) nondynamic structural equations. For the case considered, none of the density functions of the three LIML structural variance estimators define finite moments of positive integer order. It is also demonstrated that, corresponding to a fixed…

随机序约束下随机变量的最大似然估计AI 解读

Brunk, Franck, Hanson and Hogg (1966) ("Maximum likelihood estimation of the distributions of two stochastically ordered random variables," J. Amer. Statist. Assoc. 61 1067-1080) found and studied maximum likelihood estimates of a pair of stochastically ordered distribution functions. In this paper we discuss a generalization of this problem in which we do not require the domain of these "distribution functions" to be the real line. We think of the order restriction we…

多个回归参数的秩得分比较AI 解读

For testing $\beta_i = \beta, i = 1,\cdots, k$, in the model $Y_{ij} = \alpha + \beta_iX_{ij} + Z_{ij} j = 1,\cdots, n_i$ a class of rank score tests is presented. The test statistic is based on the simultaneous ranking of all the observations in the different $k$ samples. Its asymptotic distribution is proved to be chi square under the hypothesis and noncentral chi square under an appropriate sequence of alternatives. The asymptotic efficiency of the given procedure…

经验概率测度的大偏差AI 解读

Sanov's statement of first-order asymptotic behaviour of probabilities of large deviations of an empirical distribution function is here established for empirical probability measures, with attendant simplification of conditions. For the case of distribution functions, our theorem is strictly more general than a specialisation of results of Hoadley.