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基于谱分析的鞅假设检验AI 解读

This paper proposes a method of testing whether a time series is a martingale. A general asymptotic theory is developed for the spectral distribution function of the first differences. Under the null hypothesis, the spectral distribution function is shaped as a straight line. Several tests are developed which determine whether the sample spectral distribution function possesses this shape. These tests are consistent against all MA alternatives. Additional tests are developed…

从特征函数到分布函数：一个简明理论框架AI 解读

A unified framework is established for the study of the computation of the distribution function from the characteristic function. A new approach to the proof of Gurland's and Gil-Pelaez's univariate inversion theorem is suggested. A multivariate inversion theorem is then derived using this technique.

一致鞍点近似与对数凹密度AI 解读

SUMMARY For a one-dimensional variable with a log-concave density it is shown that the saddlepoint approximations to the density and the distribution function of the mean are uniformly valid. A double-saddlepoint approximation to a conditional distribution function is introduced, which is uniformly valid for a two-dimensional log-concave density. The results are illustrated with the log-normal distribution and the gamma distribution.

污染分布部分已知时的 ε 污染稳健贝叶斯分析AI 解读

SUMMARY Prior distributions of the form π=(1−ϵ)π0+ϵq,π0 being the base elicited prior, q being contamination and ϵ reflecting the amount of error in π0 that is deemed possible, are considered. It is assumed that π0 is completely specified and that only some quantiles of q are known. As π varies over this class, the ranges of the posterior mean and of the posterior probabilities of an arbitrary set are determined. Some examples including hypotheses testing related to a…

两个连续分布函数交叉点的统计推断AI 解读

Let $\mathscr{F}$ denote the set of cdf's on $\mathbb{R}$ with density everywhere positive. Let $C_A = \{(F,G) \in \mathscr{F} \times \mathscr{F}$: there exists a unique $x^\ast \in \mathbb{R}$ such that $F(x) > G(x) \text{for} x << x^\ast \text{and} F(x) < G(x) \text{for} x > x^\ast\}, C_B - \{(F,G) \in \mathscr{F} \times \mathscr{F}: (G,F) \in C_A\}$. Based on independent random samples from $F$ and $G$ (assumed unknown), we give distribution-free tests of $H_0: F = G$ vers…

大量观测下核平滑条件分位数的计算AI 解读

Quantiles of a variable Y conditional on another variable X, when plotted against X, can be a useful descriptive tool. These plots give a quick impression of the functional form of the relation between X and the location, spread, and shape of the conditional distribution of Y. If several Y are observed for each X, then sample quantiles could be calculated for each X. The resulting quantile plot may be quite noisy, however, and smoothing across X may be desired. This article…

光滑迭代程序的一步Bootstrap方法AI 解读

SUMMARY Resampling techniques have the potential to provide useful information about the sampling distribution of estimators of many population characteristics. Ambitious schemes such as the bootstrap and iterated bootstrap imply a substantial increase in computational effort. For some iterative procedures, such as generalized least squares or the EM algorithm, it is possible to avoid fully iterating each bootstrap replication to convergence. By analysing expansions of the…

均匀重抽样与重要性重抽样的 Bahadur 表示及渐近相对效率AI 解读

We derive Bahadur-type representations for quantile estimates obtained from two different types of nonparametric bootstrap resampling--the commonly used uniform resampling method, where each sample value is drawn with the same probability, and importance resampling, where different sample values are assigned different resampling weights. These results are applied to obtain the relative efficiency of uniform resampling and importance resampling and to derive exact convergence…

不变估计中经验分布函数的极小极大性AI 解读

Consider the problem of continuous invariant estimation of a distribution function with the weighted Cramer-von Mises loss. The minimaxity of the empirical distribution function, which is also the best invariant estimator, is proved for any sample size. This solves a long-standing conjecture.

多个总体一致随机序的统计推断AI 解读

Stochastic ordering between probability distributions is a widely studied concept. It arises in numerous settings and has useful applications. Since it is often easy to make value judgments when such orderings exist, it is desirable to recognize their occurrence and to model distributional structure under such orderings. Unfortunately, the necessary theory for statistical inference procedures has not been developed for many problems involving stochastic ordering and this…

回归分位数的非参数估计及局部 Bahadur 表示AI 解读

Let $(X, Y)$ be a random vector such that $X$ is $d$-dimensional, $Y$ is real valued and $Y = \theta(X) + \varepsilon$, where $X$ and $\varepsilon$ are independent and the $\alpha$th quantile of $\varepsilon$ is $0$ ($\alpha$ is fixed such that $0 < \alpha < 1$). Assume that $\theta$ is a smooth function with order of smoothness $p > 0$, and set $r = (p - m)/(2p + d)$, where $m$ is a nonnegative integer smaller than $p$. Let $T(\theta)$ denote a derivative of $\theta$ of…

平滑拟合优度检验：分位数函数方法AI 解读

A quantile function based analog to Neyman's smooth tests for goodness-of-fit hypotheses is developed. These procedures possess asymptotic and small-sample power properties similar to those for smooth tests. They are, however, computationally simple, applicable to both complete and Type II censored data, and easily focused in the direction of any specific set of alternatives. These results are used to develop a new test for exponentiality. Only location/scale null hypotheses…

多维参数空间中的稳健贝叶斯分析方法AI 解读

In some multiparameter Bayesian problems the prior is more naturally described as a joint density for all of the parameters and in others it is more naturally described as a product of marginal and conditional densities. Although ordinary quantile, ε-contamination, and density-ratio classes of priors may be sensible choices for robust Bayesian analyses in the former case, they may be less satisfactory in the latter. This article shows how to construct product classes of…

统计推断：从似然到显著性AI 解读

The concepts of likelihood and significance were defined and initially developed by R. A. Fisher, but followed almost separate and distinct routes. We suggest that a central function of statistical inference is in fact the conversion of the first, likelihood, into the second, significance: a linking of the Fisher concepts. A first-order asymptotic route for this is incorporated into most statistical packages. It uses the standardized maximum likelihood estimate, the…

具有子群一致性的贫困指数AI 解读

It seems desirable that the overall level of poverty should fall whenever poverty decreases within some subgroup of the population and is unchanged outside that group. Yet this simple and attractive property, which we call "subgroup consistency," is violated by many of the poverty indices suggested in recent years. This paper characterizes the class of subgroup consistent poverty indices, and identifies the special features associated with this property. Copyright 1991 by…

样本分位数删 d 刀切法的若干渐近结果AI 解读

This note studies the asymptotic behavior of the delete-$d$ jackknife in the irregular case of a sample $p$-quantile, calculated from a sample of $n$ iid r.v.'s. Two results are obtained: (a) an almost sure rate of convergence of the delete-$d$ jackknife histogram to the normal distribution; (b) almost sure convergence of the delete-$d$ jackknife variance estimate to the asymptotic variance of the sample $p$-quantile.

分位数自助置信区间的覆盖概率AI 解读

An asymptotic expansion of length 2 is established for the coverage probabilities of confidence intervals for the underlying $q$-quantile which are derived by bootstrapping the sample $q$-quantile. The corresponding level error turns out to be of order $O(n^{-1/2})$ which is unexpectedly low. A confidence interval of even more practical use is derived by using backward critical points. The resulting confidence interval is of the same length as the one derived by ordinary…

复杂调查设计下的分位数估计AI 解读

Estimation of the finite population distribution function and related statistics, such as the median and interquartile range, is considered. Large-sample properties of estimators constructed from stratified cluster samples, and properties of large-sample confidence intervals, are established. The results are obtained within the context of a sequence of finite populations generated from a superpopulation.

截断与删失数据下的分布函数估计AI 解读

A minor modification of the product-limit estimator is proposed for estimating a distribution function (not necessarily continuous) when the data are subject to either truncation or censoring, or to both, by independent but not necessarily identically distributed truncation-censoring variables. Making use of martingale integral representations and empirical process theory, uniform strong consistency of the estimator is established and weak convergence results are proved for…

加性异常值模型中的最小距离估计AI 解读

In the additive effects outliers (A.O.) model considered here one observes $Y_{j,n} = X_j + \upsilon_{j,n}, 0 \leq j \leq n$, where $\{X_j\}$ is the first order autoregressive [AR(1)] process with the autoregressive parameter $|\rho| < 1$. The A.O.'s $\{\upsilon_{j,n}, 0 \leq j \leq n\}$ are i.i.d. with distribution function (d.f.) $(1 - \gamma_n)I\lbrack x \geq 0\rbrack + \gamma_n L_n(x), x \in \mathbb{R}, 0 \leq \gamma_n \leq 1$, where the d.f.'s $\{L_n, n \geq 0\}$ are…

加权 Kaplan–Meier 统计量的大样本性质与最优性AI 解读

SUMMARY We propose a cumulative weighted difference in the Kaplan-Meier estimates as a test statistic for equality of distributions in the two-sample censored data survival analysis problem. For stability of such a statistic, the absolute value of the possibly random weight function must be bounded above by a multiple of (C −)1/2 + δ where 1 – C − is the left continuous censoring distribution function and δ > 0. For these weighted Kaplan–Meier (WKM) statistics, asymptotic…

删失数据线性回归的精确近似条件推断与贝叶斯推断AI 解读

A method to approximate marginal posterior distribution functions of regression coefficients and scale parameters is presented. It is based on a general asymptotic formula of DiCiccio, Field & Fraser (1990) for approximating marginal tail probabilities. In developing the method, it is shown that the accuracy of the approximation of DiCiccio et al. can be substantially increased in certain cases by using a suitable change of variables, and a general approach to deriving such…

重度删失数据下处理效应的一般估计量AI 解读

A generalized Hodges-Lehmann type estimator for the treatment effect in the two-sample problem with right censoring, is proposed based on an inverse-quantile-type idea using truncated versions of the Kaplan-Meier estimators over the subspace where they are consistent. Its strong consistency and asymptotic normality can be obtained, under no conditions on the uninformative censorings, and the resulting variance is easily estimable from the data. In simulation studies the…

迈向可实施的贝叶斯非参数密度估计AI 解读

SUMMARY Nonparametric density estimators smooth the empirical distribution function and are sensitive to the choice of smoothing parameters. This paper develops an hierarchical Bayes formulation for the smoothing problem. The prior distribution for the density function is the logistic normal process, which is a logistic transform of a Gaussian process. The covariance of the Gaussian process is a smoothing kernel and has parameters that control the degree of smoothness. The…