Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence…
Kung-Yee Liang · Daniel Tsou·刊期 1992-06 · 卷 79（2）·Biometrika已编入正刊
大量干扰参数下的经验贝叶斯与条件推断AI 解读
This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…
Jean-Marie Dufour · Marc Hallin·刊期 1992-06 · 卷 8（2）·Econometric Theory已编入正刊
改进的 Berry–Esseen–Chebyshev 界及统计应用AI 解读
A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later generalized by Kolodjažnyĭ–who also proved that they are, in some sense, optimal–is proposed. Further, the corresponding inequalities are shown to provide uniformly improved Chebyshev bounds for the tail probabilities of the distribution functions to be approximated. In contrast with most results on Berry–Esseen bounds, which emphasize rates of convergence to normality, the…
In the intuitive approach, a distribution function $F$ is said to be not more heavily tailed than $G$ if $\lim \sup_{x \rightarrow \infty} \bar{F}/\bar{G} < \infty$. An alternative is to consider the behavior of the ratio $F^{-1}(u)/G^{-1}(u)$, in a neighborhood of one. The present paper examines the relationship between these two criteria and concludes that the intuitive approach gives a more thorough comparison of distribution functions than the ratio of the quantile…
In this paper we consider the product-limit estimator of the survival distribution function in the context of independent but nonidentically distributed censoring times. An upper bound on the mean square increment of the stopped Kaplan-Meier process is obtained. Also, a representation is given for the ratio of the survival distribution function to the product-limit estimator as the product of a bounded process and a martingale. From this representation bounds on the mean…
Suppose $\hat{\theta}_n$ is a strongly consistent estimator for $\theta_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be, respectively, the last $n$ and the total number of $n$ for which $\hat{\theta}_n$ is at least $\varepsilon$ away from $\theta_0$. The limit distributions for $\varepsilon^2N_\varepsilon$ and $\varepsilon^2Q_\varepsilon$ as $\varepsilon$ goes to zero are obtained under natural and weak conditions. The theory covers both parametric…
We show that regression quantiles, which could be computed as solutions of a linear programming problem, and the solutions of the corresponding dual problem, which we call the regression rank-scores, generalize the duality of order statistics and of ranks from the location to the linear model. Noting this fact, we study the regression quantile and regression rank-score processes in the heteroscedastic linear regression model, obtaining some new estimators and interesting…
D. L. Hawkins · Subhash Kochar · Clive Loader·刊期 1992-03-01 · 卷 20（1）·The Annals of Statistics已编入正刊
转折点未知时针对平均剩余寿命先增后减分布的指数性检验AI 解读
Guess, Hollander and Proschan proposed tests for exponentiality versus IDMRL (increasing initially and then decreasing mean residual life) distributions when the change point, or corresponding quantile, is known. In this paper we propose two tests which do not require such knowledge of the change point. The tests are based on estimates of functionals of the $\operatorname{cdf}$ which discriminate between the exponential and IDMRL families.
Consider a stationary time series $(\mathbf{X}_t, Y_t), t = 0, \pm 1,\ldots,$ with $\mathbf{X}_t$ being $\mathbb{R}^d$-valued and $Y_t$ real-valued. The conditional mean function is given by $\theta(\mathbf{X}_0) = E(Y_0\mid\mathbf{X}_0)$. Under appropriate regularity conditions, a local average estimator of this function based on a finite realization $(\mathbf{X}_1, Y_1),\ldots,(\mathbf{X}_n, Y_n)$ can be chosen to achieve the optimal rate of convergence $n^{-1/(2 + d)}$ bot…
Methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of Koenker and Bassett. Spline parameterizations of the conditional quantile functions are used. The methods are illustrated by estimating hierarchical models for household electricity demand using data from the Chicago metropolitan area. The empirical results show that lower quantiles of demand (“base-load”) vary only slightly across residential…
A fast algorithm for calculating the nonparametric maximum likelihood estimate (MLE) of a mixing distribution, G(·). in a mixture model is discussed. The literature contains several methods for computing the nonparametric MLE of G, but these methods are slow. In this article we develop an algorithm for maximizing the log-likelihood l(G) over the family ℊ, of all distribution functions, that yields the nonparametric MLE of G. In some semiparametric problems, a structural or…
A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…
A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…
R. A. MALLER · S. ZHOU·刊期 1992 · 卷 79（4）·Biometrika已编入正刊
删失样本中免疫个体比例的估计AI 解读
An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…
NIALL H. ANDERSON · PETER HALL · D. M. TITTERINGTON·刊期 1992 · 卷 79（3）·Biometrika已编入正刊
由渐近展开启发的插值规则AI 解读
We suggest a simple interpolation rule, based on Edgeworth and Cornish-Fisher expansions, which permits highly accurate numerical approximation in problems involving calculation of distributions or quantiles without requiring explicit calculation of terms in the expansions.
R. L. CHAMBERS · ALAN H. DORFMAN · PETER HALL·刊期 1992 · 卷 79（3）·Biometrika已编入正刊
有限总体分布函数估计量的性质AI 解读
Two leading estimators of the finite population distribution function are studied. Their large-sample mean squared errors are compared, under a given model. Neither estimator is universally better; circumstances are identified where the model-based estimator would do poorly, despite employing the correct model.
A saddlepoint expansion is derived for the cumulative distribution function of the least squares estimator of the autoregressive coefficient. The new method is shown to be superior both analytically and numerically to many existing approximations. Unlike other methods the new approximation performs uniformly well over the whole range of the distribution including the extreme tail, even when the sample size is as small as 10.
KUNG-YEE LIANG · DANIEL TSOU·刊期 1992 · 卷 79（2）·Biometrika已编入正刊
存在大量干扰参数时的经验贝叶斯与条件推断AI 解读
This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…
In this paper we shall discuss the estimation of the mean of a normal distribution with variance 1. The main question in this work is the existence and computation of a least favorable distribution among all the prior distributions satisfying a given set of constraints. In the following we show that if this distribution is bounded from above on some even moment, then the least favorable distribution exists and it is either normal or discrete. The support of the discrete…
Consider a $\mathscr{Y}$-valued response variable having a density function $f(\cdot\mid x)$ that depends on an $\mathscr{X}$-valued input variable $x.$ It is assumed that $\mathscr{X}$ and $\mathscr{Y}$ are compact intervals and that $f(\cdot\mid\cdot)$ is continuous and positive on $\mathscr{X} \times \mathscr{Y}.$ Let $F(\cdot\mid x)$ denote the distribution function of $f(\cdot\mid x)$ and let $Q(\cdot\mid x)$ denote its quantile function. A finite-parameter exponential…
Miklos Csorgo · Edit Gombay · Lajos Horvath·刊期 1991-12-01 · 卷 19（4）·The Annals of Statistics已编入正刊
随机删失下核密度估计Lp距离的中心极限定理AI 解读
A sequence of independent nonnegative random variables with common distribution function $F$ is censored on the right by another sequence of independent identically distributed random variables. These two sequences are also assumed to be independent. We estimate the density function $f$ of $F$ by a sequence of kernel estimators $f_n(t) = (\int^\infty_{-\infty}K((t - x)/h(n))d\hat{F}_n(x))/h(n),$ where $h(n)$ is a sequence of numbers, $K$ is kernel density function and $\hat{F}_n$…
The estimation of the treatment effect in the two-sample problem with right censoring is of interest in survival analysis. In this article we consider both the location shift model and the scale change model. We establish the large-sample properties of a generalized Hodges-Lehmann type estimator. The strong consistency is established under the minimal possible conditions. The asymptotic normality is also obtained without imposing any conditions on the censoring mechanisms.…
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…
Thomas J. Diciccio · Christopher A. Field·刊期 1991-12 · 卷 78（4）·Biometrika已编入正刊
删失数据线性回归模型的精确近似条件推断与贝叶斯推断方法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…
In the intuitive approach, a distribution function F is said to be not more heavily tailed than G if limsupx→∞Fˉ/Gˉ<∞. An alternative is to consider the behavior of the ratio F−1(u)/G−1(u), in a neighborhood of one. The present paper examines the relationship between these two criteria and concludes that the intuitive approach gives a more thorough comparison of distribution functions than the ratio of the quantile…
On the Last Time and the Number of Times an Estimator is More than ε From its Target Value
Suppose θ^n is a strongly consistent estimator for θ0 in some i.i.d. situation. Let Nε and Qε be, respectively, the last n and the total number of n for which θ^n is at least ε away from θ0. The limit distributions for ε2Nε and ε2Qε as ε goes to zero are obtained under natural and weak conditions. The theory covers both parametric…
Guess, Hollander and Proschan proposed tests for exponentiality versus IDMRL (increasing initially and then decreasing mean residual life) distributions when the change point, or corresponding quantile, is known. In this paper we propose two tests which do not require such knowledge of the change point. The tests are based on estimates of functionals of the cdf which discriminate between the exponential and IDMRL families.
Consider a stationary time series (Xt,Yt),t=0,±1,…, with Xt being Rd-valued and Yt real-valued. The conditional mean function is given by θ(X0)=E(Y0∣X0). Under appropriate regularity conditions, a local average estimator of this function based on a finite realization (X1,Y1),…,(Xn,Yn) can be chosen to achieve the optimal rate of convergence n−1/(2+d) bot…
Consider a Y-valued response variable having a density function f(⋅∣x) that depends on an X-valued input variable x. It is assumed that X and Y are compact intervals and that f(⋅∣⋅) is continuous and positive on X×Y. Let F(⋅∣x) denote the distribution function of f(⋅∣x) and let Q(⋅∣x) denote its quantile function. A finite-parameter exponential…
Central Limit Theorems for Lp Distances of Kernel Estimators of Densities Under Random Censorship
A sequence of independent nonnegative random variables with common distribution function F is censored on the right by another sequence of independent identically distributed random variables. These two sequences are also assumed to be independent. We estimate the density function f of F by a sequence of kernel estimators fn(t)=(∫−∞∞K((t−x)/h(n))dF^n(x))/h(n), where h(n) is a sequence of numbers, K is kernel density function and F^n…