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离散指数族模型中混合密度的估计AI 解读

This paper concerns estimating a mixing density function $g$ and its derivatives based on iid observations from $f(x) = \int f(x \mid \theta)g(\theta)d\theta$, where $f(x \mid \theta)$ is a known exponential family of density functions with respect to the counting measure on the set of nonnegative integers. Fourier methods are used to derive kernel estimators, upper bounds for their rate of convergence and lower bounds for the optimal rate of convergence. If $f(x \mid \theta_0) \geq \varepsilon^{x + 1} \forall x$…

删失数据中样本分位数估计相对核分位数估计的样本量亏损AI 解读

Consider a statistical procedure (Method A) which is based on $n$ observations and a less effective procedure (Method B) which requires a larger number $k_n$ of observations to give equal performance under a certain criterion. To compare two different procedures, Hodges and Lehmann suggested that the difference $k_n - n$, called the deficiency of Method B with respect to Method A, is the most natural quantity to examine. In this article, the performance of two kernel…

用于分位数同时置信区间的上下界分布AI 解读

We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution…

超额收益的条件分布：一项实证分析AI 解读

In this article we describe the cumulative distribution function of excess returns conditional on a broad set of predictors that summarize the state of the economy. We do so by estimating a sequence of conditional logit models over a grid of values of the response variable. Our method uncovers higher-order multidimensional structure that cannot be found by modeling only the first two moments of the distribution. We compare two approaches to modeling: one based on a…

正态均值乘积的参考先验贝叶斯分析AI 解读

Two reference priors for the product of means of n normal distributions with common known variance are developed. One of them induces an improper posterior distribution and therefore is not of much interest. The other is a generalized form of the n = 2 case derived by Berger and Bernardo. The latter is compared with the uniform prior (the Jeffreys prior) in posterior inference and the optimal frequentist coverage criterion. The reference prior is shown to be better than the…

分布函数的非参数似然置信带AI 解读

Berk and Jones described a nonparametric likelihood test of uniformity with greater asymptotic Bahadur efficiency than any weighted Kolmogorov–Smirnov test at any alternative to U[0, 1]. We invert this test to form confidence bands for a distribution function using Noé's recursion. Nonparametric likelihood bands are narrower in the tails and wider in the center than Kolmogorov-Smirnov bands and are asymmetric about the empirical cumulative distribution function. This article…

用于分位数同时置信区间的上下界分布AI 解读

We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution…

自回归分位数及相关秩得分过程AI 解读

This paper develops extensions of the regression quantiles of Koenker and Bassett (1978) to autoregression. It generalizes several results of Jureckova (1992a) and Gutenbrunner and Jureckova (1992) in linear regression to autoregression models. In particular, it gives the asymptotic uniform linearity of linear rank-scores statistics based on residuals suitable in autoregression. It also discusses the two types of $L$-statistics appropriate in autoregression.

P{X<Y} 的最小方差无偏估计量的容许性与极小极大性AI 解读

Suppose that $X_1,\ldots, X_m$ are i.i.d. from a continuous distribution function $F$ and $Y_1,\ldots, Y_n$ are i.i.d. from a continuous distribution function $G; X$'s and $Y$'s are independent. A minimum variance unbiased estimator of $P\{X < Y\}$ is the Mann-Whitney statistic. We show that the Mann-Whitney statistic is admissible under a class of weighted squared error losses and is minimax under a proper weighted squared error loss.

形状约束密度的有限样本置信包络AI 解读

A conservative finite-sample simultaneous confidence envelope for a density can be found by solving a finite set of finite-dimensional linear programming problems if the density is known to be monotonic or to have at most $k$ modes relative to a positive weight function. The dimension of the problems is at most $(n/\log n)^{1/3}$, where $n$ is the number of observations. The linear programs find densities attaining the largest and smallest values at a point among cumulative…

生存时间与协变量独立性的综合检验AI 解读

It has been over 60 years since Kolmogorov introduced a distribution-free omnibus test for the simple null hypothesis that a distribution function coincides with a given distribution function. Doob subsequently observed that Kolmogorov's approach could be simplified by transforming the empirical process to an empirical process based on uniform random variables. Recent use of more sophisticated transformations has led to the construction of asymptotically distribution-free…

截断数据 Lynden–Bell 估计量的强一致收敛AI 解读

In this paper, we prove that the Lynden-Bell estimator of a distribution function in the random truncation model is uniformly strong consistent over the whole half line, a problem left open by Woodroofe.

Let $\hat{F}_n$ be the Kaplan-Meier estimator of a distribution function $F$ computed from randomly censored data. We show that under optimal integrability assumptions on a function $\varphi$, the Kaplan-Meier integral $\int \varphi d\hat{F}_n$, when properly standardized, is asymptotically normal.

一般责任法律改革与保险市场结果的分布AI 解读

Many states enacted tort liability reform laws in the late 1980s to limit liability costs and stabilize insurance markets. This paper uses firm-level data from two states that enacted reforms over the 1984-91 period--New York and Colorado--to assess their effects. The liability insurance performance in Pennsylvania and Kentucky--two states that did not adopt reforms--provides a reference point for how insurance markets might have performed. The quantile regression models…

个人收入分布：再考察AI 解读

Abstract In a recent paper, Majumder and Chakravarty (1990) propose a four‐parameter model which they find provides a better fit to some income data than the lognormal, gamma, Singh‐Maddala, Dagum, and generalized beta of the second kind (GB2) distributions. This note (1) demonstrates that the model proposed by Majumder and Chakravarty is a reparameterization of the GB2 and (2) reconciles the corresponding contradictory empirical findings reported by Majumder and Chakravarty.

摘要暂缺

半参数回归泛函AI 解读

A regression method is developed for a general class of functionals. A semiparametric linear model is adopted, and the regression parameters are estimated by maximizing a profiled nonparametric or empirical likelihood based on a local estimate of the conditional distribution function. Simulated and real data examples are shown, including an application of quantile regression to censored survival data from a clinical trial for myeloma.

使用 P-P 图比较处理效应AI 解读

This article examines the use of the probability-probability plot (p-p plot) as a method for comparing treatment effects. To begin in the context of three examples the p-p plot is contrasted with the quantile-quantile plot (q-q plot), which is an alternative means of describing treatment effects. In these examples it is shown that p-p plots representing different experimental conditions or patient populations allow scale-invariant comparisons of treatment effects but q-q…

基于中位数回归模型的生存分析AI 解读

The median is a simple and meaningful measure for the center of a long-tailed survival distribution. To examine the covariate effects on survival, a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates. In this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations. Our proposals can be…

半参数回归泛函AI 解读

A regression method is developed for a general class of functionals. A semiparametric linear model is adopted, and the regression parameters are estimated by maximizing a profiled nonparametric or empirical likelihood based on a local estimate of the conditional distribution function. Simulated and real data examples are shown, including an application of quantile regression to censored survival data from a clinical trial for myeloma.

摘要暂缺

平滑经验过程与分位数过程之间的距离AI 解读

We consider Bahadur-Kiefer representations for smoothed quantile processes. We prove that the asymptotics of the distance between smoothed empirical and quantile processes can be completely different from that of the unsmoothed ones. We obtain a complete characterization of the possible limits.

马尔可夫链经验估计量的效率AI 解读

Suppose we observe a uniformly ergodic Markov chain with unknown transition distribution. The empirical estimator for a linear functional of the (invariant) joint distribution of two successive observations is defined using the pairs of successive observations. Its efficiency is proved using a martingale approximation. As a corollary we show efficiency of the empirical joint distribution function in the sense of a functional convolution theorem.

近积分 AR 过程中若干检验统计量的渐近分布AI 解读

Asymptotic distributions of some test statistics in near-integrated AR processes are studied. Some exact formulas for the distribution functions are given as well as approximative results obtained by saddlepoint approximation techniques.