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基于单样本符号统计量的两样本检验之Bahadur效率AI 解读

SUMMARY This paper discusses the two-sample test of location based on the comparison of two distribution-free one-sample confidence intervals derived from sign statistics. This test procedure, first introduced by Hettmansperger (1984), rejects the null hypothesis of equal population medians when the two intervals are disjoint. He presents three different ways to select the two one-sample intervals and one choice leads to Mood's test. All solutions have the same Pitman…

学生化分位数的分布AI 解读

SUMMARY The asymptotic variance of a sample quantile depends on the value of the population density at the population quantile. Therefore Studentizing a sample quantile involves density estimation, either explicitly or implicitly. One popular way of Studentizing is to use the Siddiqui–Bloch–Gastwirth estimator, whose construction depends crucially on the choice of a smoothing parameter m. We examine the effect which the selection of m has on the level error of tests or…

多维福祉度量与密歇根调查数据的不平等分析AI 解读

We demonstrate a multidimensional approach for combining several indicators of well-being, including the traditional money-income indicators. This methodology avoids the difficult and much criticized task of computing imputed incomes for such indicators as net worth and schooling. Inequality in the proposed composite measures is computed using relative inequality indexes that permit simple analysis of both the contribution of each welfare indicator (and its factor…

截断数据非参数最大似然估计量的若干表示AI 解读

The nonparametric maximum likelihood estimators of the distribution functions of observations in the truncation model are represented as iid mean processes, with a remainder term of order $o(n^{-1/2})$ a.s.

用于贝叶斯非参数预测密度的逻辑斯蒂正态分布AI 解读

This article models the common density of an exchangeable sequence of observations by a generalization of the process derived from a logistic transform of a Gaussian process. The support of the logistic normal includes all distributions that are absolutely continuous with respect to the dominating measure of the observations. The logistic-normal family is closed in the prior to posterior Bayes analysis, with the observations entering the posterior distribution through the…

排序集样本的刻画及其在分布函数估计中的应用AI 解读

Ranked-set sampling has been shown to provide improved estimators of the mean and variance when actual measurement of the observations is difficult but ranking of the elements in a sample is relatively easy. This result holds even if the ranking is imperfect. In this article, we provide a characterization of a ranked-set sample that makes the source of this additional information intuitively clear. It is applied to show that the empirical distribution function of a…

指定分位数的拟单峰先验下后验概率的范围AI 解读

Suppose several quantiles of the prior distribution for θ are specified or, equivalently, the prior probabilities of a partitioning collection of intervals {Ii } are given. In addition, suppose that the prior distribution is assumed to be unimodal. Rather than selecting a single prior distribution to perform a Bayesian analysis, it is of interest to consider the class of all prior distributions compatible with these inputs. For this class and unimodal likelihood functions,…

给定分位数的拟单峰先验下后验概率的取值范围AI 解读

Suppose several quantiles of the prior distribution for θ are specified or, equivalently, the prior probabilities of a partitioning collection of intervals {Ii } are given. In addition, suppose that the prior distribution is assumed to be unimodal. Rather than selecting a single prior distribution to perform a Bayesian analysis, it is of interest to consider the class of all prior distributions compatible with these inputs. For this class and unimodal likelihood functions,…

随机删失下二元分布函数的估计AI 解读

Estimators are proposed of the underlying distribution function of independent bivariate ran vectors which are subject to random right censorship in each coordinate. The estimators satisy the monotonicity requirements of a distribution function, are uniformly strongly consistent rate equal to that of the empirical distribution function and are fairly simple to compute.

同时估计尺度曲线的稳健非参数回归AI 解读

Let $\{X_i, Y_i\}^n_{i=1} \subset \mathbb{R}^d \times \mathbb{R}$ be independent identically distributed random variables. If the conditional distribution $F(y \mid x)$ can be parametrized by $F(y \mid x) = F_0((y - m(x))/\sigma(x))$ with a fixed and known distribution $F_0$, the regression curve $m(x)$ and scale curve $\sigma(x)$ could be estimated by some parametric method. More generally, we assume that $F$ is unknown and consider nonparametric simultaneous $M$-type…

非参数回归中的自助法：局部自适应平滑与置信带AI 解读

The operation of the bootstrap in the context of nonparametric regression is considered. Bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator. The application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances. The technique of the bootstrap is to replace…

随机样本的双权预测区间AI 解读

This study takes a biweight approach to providing a prediction interval for a single future observation. This problem—equivalent to the problem of estimating quantiles—is of fundamental importance in ascertaining the nature of a process. The prediction or quantile problem is difficult for a robust estimator, since much of the desired information is in the extremes of the sample, whose influence the robust estimator is designed to resist. The situation is further complicated…

Pearson型拟合优度检验：单变量情形AI 解读

Chi-squared tests are proposed for testing goodness of fit when the data may or may not be subject to random censoring. Both the simple and compositive null hypotheses are considered. For the simple null hypothesis the resulting test statistic in the uncensored case differs from Pearson's statistic only in that the expected frequency for cell Aj is taken to be , where is the empirical distribution function, instead of n ∫ A j d F o ; this results in k df instead of the usual…

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基尼系数的方差估计：概率抽样AI 解读

An estimator of the Gini coefficient (the well-known income inequality measure) of a finite population is defined for an arbitrary probability sampling design, taking the sampling design into consideration. Alternative estimators of the variance of the estimated Gini coefficient are introduced. The sampling performance of the Gini coefficient estimator and its variance estimators is studied by means of a Monte Carlo study, using stratified sampling from a miniature…

M 分位数AI 解读

It is well known that a M-estimator of the centre of symmetry Θ of a symmetric distribution can be defined in terms of either a continuous symmetric loss function ρ or the associated influence functionψ. This estimator is robust if ψ is bounded. In this paper, we develop a generalization of the M-concept to estimation of a quantile analogue of Θ, called a M-quantile, by introducing a particular kind of asymmetry into ψ. A natural consequence is that the M- quantile parameter…

贝叶斯自助法的直方样条平滑AI 解读

This paper describes a version of the Bayesian bootstrap that assigns random Dirichlet mass uniformly across statistically equivalent blocks. The method requires prior knowledge that the underlying distribution is continuous with known compact support. Under these conditions, the resulting analysis has three advantages over traditional bootstrap competitors. First, it takes account of the probability integral transformation. Secondly, it often enables exact expressions for…

随机删失下二元分布函数的估计AI 解读

Estimators are proposed of the underlying distribution function of independent bivariate ran vectors which are subject to random right censorship in each coordinate. The estimators satisy the monotonicity requirements of a distribution function, are uniformly strongly consistent rate equal to that of the empirical distribution function and are fairly simple to compute.

单个统计泛函的经验似然比置信区间AI 解读

The empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken. In this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions. It is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean, for a class of M-estimates that includes quantiles, and for differentiable…

不等概率抽样下分布函数与中位数的估计AI 解读

We consider sampling with probability proportional to size or aggregate size and derive a number of estimators of the finite population distribution function. The estimators are compared theoretically and empirically. By inverting the distribution function estimators, we obtain estimators of the finite population median. The performance of these median estimators are investigated.

自助乘积极限过程的收敛速率AI 解读

We establish rates for strong approximations of the bootstrapped product-limit process and the corresponding quantile process. These results are used to show weak convergence of bootstrapped total time on test and Lorenz curve processes to the same limiting Gaussian processes as for the unbootstrapped versions. We develop fully nonparametric confidence bands and tests for these curves and apply these results to prostate cancer. We also present almost sure results for the…

无模型一步向前预测区间：渐近理论与小样本模拟AI 解读

We show that the empirical quantile process from an ARMA$(1, q)$ process which is strongly mixing $\Delta_s$, and is either Gaussian or double exponential, converges to a Gaussian process. This result is used to derive model-free one-step-ahead prediction intervals for such processes. Simulations demonstrate where the asymptotic theory can and cannot be applied to small samples.

多样本 Anderson–Darling 检验AI 解读

Two k-sample versions of an Anderson–Darling rank statistic are proposed for testing the homogeneity of samples. Their asymptotic null distributions are derived for the continuous as well as the discrete case. In the continuous case the asymptotic distributions coincide with the (k – 1)-fold convolution of the asymptotic distribution for the Anderson–Darling one-sample statistic. The quality of this large sample approximation is investigated for small samples through Monte…

密度估计的半参数方法AI 解读

One method of fitting a parametric density function f(x, θ) is first to estimate θ by maximum likelihood, say, and then to estimate f(x, θ) by . On the other hand, when the parametric model does not hold, the true density f(x) may be estimated nonparametrically, as in the case of a kernel estimate . The key idea proposed is to fit a combination of the parametric and nonparametric estimates, namely where π (0 ≤ π ≤ 1) is unknown. The parameter π is estimated from the data,…