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逆分布函数尾部的同时置信界AI 解读

Confidence bounds are derived for the upper 100$p$ percentile of an inverse distribution function. These bounds are considerably less conservative than similar bounds which apply to the entire function.

光滑权重下次序统计量线性组合的 Edgeworth 展开AI 解读

Edgeworth expansions for linear combinations of order statistics are established. The theorems require smooth weight functions and the underlying distribution function must possess a finite fourth moment. In addition a local smoothness condition is imposed on the underlying distribution function.

Summary This paper presents a method, based on the empirical distribution function, for testing goodness of fit (gf) under composite null hypotheses. After the unknown parameters are estimated from the entire data set, the procedure calls for the transformed sample to be randomly partitioned into a large number of groups, and a gf statistic calculated for each group. These statistics are used to construct a test which can attain, asymptotically, any desired level α, and…

参数估计下基于克拉美–冯·米塞斯统计量正交分量线性组合的检验AI 解读

In a previous work, the author showed how linear combinations of the orthogonal components of the Cramer-von Mises statistic could be used to test fit to a fully specified distribution function. In this paper, the results are extended to the case where $r$ parameters are estimated from the data. It is shown that if the coefficient vector of the linear combination is orthogonal to a specified $r$ dimensional subspace, then the asymptotic distribution of that combination is…

右删失观测下递增失效率分布函数的最大似然估计AI 解读

The maximum likelihood estimator of a distribution function with increasing failure rate is derived based on a set of observations subject to arbitrary right censorship. This estimator is defined everywhere on the positive real line while the Kaplan-Meier estimator may not be. The small sample properties of this estimator are indicated by results of a Monte Carlo study for the Weibull distribution.

多样本置换检验的渐近展开AI 解读

Let $V_n$ be the standardized sum of squares of the means of $r + 1$ random samples of sizes $s_0, s_1, \cdots, s_r$, where $n = s_0 + s_1 + \cdots + s_r$, taken without replacement from $n$ numbers. Then using an approximation to the characteristic function of the means, an asymptotic expansion is obtained for the distribution of $V_n$ with first term being the distribution function of $\chi^2_r$ and with error of approximation generally of smaller order than $1/n$. When…

分组收入频数数据下稳定分布的统计推断AI 解读

This paper discusses inferential procedures for the family of stable distributions, when the data are tabulated in the form of interval frequencies. The estimation criteria used are minimum chi-square and multinomial maximum likelihood. In evaluating the theoretical probabilities corresponding to the intervals, use is made of the inversion theorem for characteristic functions. Chi-square tail probabilities for independent samples are pooled by means of theKolmogorov…

指数与威布尔失效模式下最小值模型的最大似然估计AI 解读

The existence and some properties of maximum likelihood estimators (MLE's) are studied for a minimum-type distribution function corresponding to a minimum of two independent random variables having exponential and Weibull distributions. It is shown that if all three parameters are unknown, then there is a path in the parameter space along which the likelihood function (LF) tends to infinity. It is also proved that if the Weibull shape parameter is known, then the LF is…

若干单侧多样本Smirnov型统计量的分布AI 解读

Consider the problem of testing the equality of k populations in cases in which the populations can be ordered a priori from low to high on the basis of some underlying variable. This article proposes a new statistic based on the sums of the Smirnov-type statistic and provides evidence that the test based on this statistic has high power for a wide range of alternatives suggested by this problem. To construct the statistic, let Fj (x) be the empirical distribution for the…

II 型删失数据的卡方拟合优度检验AI 解读

The theory of general chi-square statistics for testing fit to parametric families of distributions is extended to samples censored at sample quantiles. Data-dependent cells with sample quantiles as cell boundaries are employed. Asymptotic distribution theory is given for statistics in which unknown parameters are estimated by estimators asymptotically equivalent to linear combinations of functions of order statistics. Emphasis is placed on obtaining statistics having a…

密度估计偏差的 L₂ 范数渐近分布AI 解读

Let $(\phi_\nu)^\infty_{\nu=0}$ be a complete orthonormal system of functions on a interval $\lbrack a, b\rbrack$ and let $w$ be a function defined on $\mathbb{R}$ with support $\lbrack a, b\rbrack$ and strictly positive on $(a, b)$. Let $(x_j)^\infty_{j=1}$ be i.i.d.rv's absolutely continuous with density function $f$ with respect to Lebesgue measure $\mu$ on $\mathbb{R}$. Let $f_n$ be the estimate of $f$ defined for $x\in (a, b)$ by $f_n(x) = \Sigma^m_{\nu=0}a_\nu(m)\hat{d}_\nu\phi_\nu(x)/w(x)$…

广义回归残差的经验分布函数AI 解读

Generalised residuals, as defined by Cox and Snell, may be thought of as residuals from generalised regression. Under regularity conditions on the regression and on the estimator of the unknown parameters, the asymptotic behaviour of the empirical distribution of these residuals is determined. The addition of a random adjustment to the maximum likelihood estimator leads to the familiar Brownian bridge as the limit.

用于对称性检验的 Cramér–von Mises 型统计量AI 解读

A Cramér-von Mises-type statistic for testing symmetry, proposed independently by Orlov (1972) and Rothman and Woodroofe (1972), is decomposed into components in the manner of Durbin and Knott (1972); the components are found to be related to Fourier series expansions of the underlying distribution function. Asymptotic power properties of the statistic and its components in testing symmetry about the origin against location shift alternatives when observations have double…

混合线性模型的多变量方法AI 解读

The usual treatment of the two-way mixed model parallels that of the fixed models, with the usual sums of squares appearing in the F ratios. In this article, we argue in favor of a multivariate approach. We propose a new criterion for testing a general hypothesis under general conditions and offer an expression for the asymptotic expansion of the distribution function.

由 M 估计构造近似置信区间的新方法AI 解读

The empirical function used to define M estimates of location is similar to a distribution function when Ψ is nondecreasing. This similarity allows approximate confidence intervals to be constructed from the “percentiles” of the defining function.

基于删失数据的分布函数经验贝叶斯估计札记AI 解读

Susarla and Van Ryzin exhibited an empirical Bayes estimator of a distribution function $F$ based on randomly right-censored observations. In a later paper they obtained a different estimator which alleviates the weaknesses of their earlier estimator and showed that it is asymptotically optimal with rate of convergence $n^{-1}$. The purpose of this note is to present a slightly different estimator which is simpler and is also asymptotically optimal with the same rate of…

某些非参数模型中的分位数估计AI 解读

The deficiency of sample quantiles with respect to quasiquantiles is investigated under the assumption that the true density function has bounded derivatives. Then the sample quantile is still an efficient estimator of the true quantile but the relative deficiency of sample quantiles with respect to suitably defined quasiquantiles quickly tends to infinity for increasing sample sizes. If the second derivative of the true density function is bounded, then adaptive estimators…

非参数多重比较程序的前 k−1 组显著性水平AI 解读

We consider the nonparametric pairwise comparisons procedures derived from the Kruskal-Wallis $k$-sample test and from Friedman's test. For large samples the $(k - 1)$-mean significance level is determined, i.e., the probability of concluding incorrectly that some of the first $k - 1$ samples are unequal. We show that in general this probability may be larger than the simultaneous significance level $\alpha$. Even when the $k$th sample is a shift of the other $k - 1$ samples,…

Johnson 分布曲线参数的分位数估计AI 解读

Easy quantile estimators are given for the parameters of Johnson curves. The estimators are at least as good as moment estimators.

正态分布函数的计算AI 解读

A slight modification of a formula of A. J. Strecock provides a simple approximation to the normal distribution function which is accurate to nine decimal places.

右删失观测下递增失效率分布函数的最大似然估计AI 解读

The maximum likelihood estimator of a distribution function with increasing failure rate is derived based on a set of observations subject to arbitrary right censorship. This estimator is defined everywhere on the positive real line while the Kaplan-Meier estimator may not be. The small sample properties of this estimator are indicated by results of a Monte Carlo study for the Weibull distribution.

简单线性模型百分位数曲线的紧置信带与容忍带AI 解读

This article develops sharp confidence bands for percentiles of regression functions over finite intervals. Attention is focused on one-sided (upper) bands for these percentiles, but a simple extension allows construction of two-sided bands. These upper bands are useful for tolerance bands, since a 100-γ percent confidence band for the 100/βth percentile is also a γ coefficient β-tolerance band.

基于伽马分布的不同收入不平等指标性质分析AI 解读

The Gini, Theil entropy, and Pietra measures of inequality associated with the gamma distribution function are expressed in terms of the parameters defining the gamma distribution. Method of moments (MME) and maximum likelihood estimators (MLE) of these measures are obtained along with expressions for the asymptotic standard errors of the MLE measures. A table is presented that facilitates the calculation of MLE of inequality measures and the associated asymptotic standard…

利用复杂抽样设计的数据区分分布AI 解读

This article presents the statistical methodology for estimating stratum cumulative distribution functions (cdf's) when the sample is drawn according to a complex design. Justification for the use of this methodology is offered, and examples are presented to demonstrate the expanded inference possible when estimated cdf's are used in addition to stratum means. The methods are applied to data from a survey of the patterns of care in radiation therapy facilities in the United…