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线性回归模型中百分位数的置信带AI 解读

Simultaneous confidence intervals for percentiles of the normal regression model similar to those given by Steinhorst and Bowden (1971) are considered. Kanofsky's (1968) confidence band for a single normal distribution is modified and extended to the regression model. The confidence bands that are simultaneous in all percentiles provide corresponding confidence bands for the cumulative conditional normal distribution functions. The various procedures are compared with…

线性回归模型中百分位数的置信带AI 解读

Simultaneous confidence intervals for percentiles of the normal regression model similar to those given by Steinhorst and Bowden (1971) are considered. Kanofsky's (1968) confidence band for a single normal distribution is modified and extended to the regression model. The confidence bands that are simultaneous in all percentiles provide corresponding confidence bands for the cumulative conditional normal distribution functions. The various procedures are compared with…

分位数过程及其统计应用AI 解读

A Preliminary Study of Quantile Processes A Weak Convergence of the Normed Sample Quantile Process Strong Approximations of the Normed Quantile Process Two Approaches to Constructing Simultaneous Confidence Bounds for Quantiles Weak Convergence of Quantile Processes in Weighted Sup-Norm Metrics and Further Strong Approximations On Bahadur's Representation of Sample Quantiles and on Kiefer's Theory of Deviations Between the Sample Quantile and Empirical Processes Quadratic…

条件经验过程AI 解读

We prove a Donsker-type invariance principle for a nearest-neighbor-type conditional empirical process. As an application we show asymptotic normality of conditional quantiles and derive large-sample distribution-free tests and confidence bands for a conditional distribution function.

多元分布的置信集合AI 解读

The confidence sets for a $q$-dimensional distribution studied in this paper have several attractive features: affine invariance, correct asymptotic level whatever the actual distribution may be, numerical feasibility, and a local asymptotic minimax optimality property. When dimension $q$ equals one, the confidence sets reduce to the usual Kolmogorov-Smirnov confidence bands, except that critical values are determined by bootstrapping.

用于处理与对照比较的渐近最优平衡处理不完全区组设计子类AI 解读

Incomplete block designs for estimation of treatment-control differences are studied. A class of designs for this purpose, called balanced treatment incomplete block designs, has recently been proposed and studied by several authors. Here, a relatively small subclass of these designs is shown to contain the asymptotically optimal design under the criterion of minimizing the length of simultaneous confidence intervals for treatment-control differences. These results can be…

用于处理与对照比较的渐近最优平衡处理不完全区组设计子类AI 解读

Incomplete block designs for estimation of treatment-control differences are studied. A class of designs for this purpose, called balanced treatment incomplete block designs, has recently been proposed and studied by several authors. Here, a relatively small subclass of these designs is shown to contain the asymptotically optimal design under the criterion of minimizing the length of simultaneous confidence intervals for treatment-control differences. These results can be…

Bootstrap 在功率谱密度估计中的应用AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on estimated spectral density. The bootstrap method is applied to obtain nonparametric confidence bands and intervals. It is the aim of this paper to indicate how this can be done and to report on the outcome of some Monte Carlo studies of the properties of the resulting procedures. Some asymptotic theory concerning the properties of the…

非参数逐步多重比较程序AI 解读

Nonparametric multiple comparisons are discussed, with particular emphasis given to stepwise procedures. Nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc nonparametric analog of the Newman—Keuls procedure. These new procedures are compared among themselves and with nonstepwise procedures based on Type I error levels and comparisonwise power. It is shown that these stepwise nonparametric procedures control…

非参数逐步多重比较程序AI 解读

Nonparametric multiple comparisons are discussed, with particular emphasis given to stepwise procedures. Nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc nonparametric analog of the Newman—Keuls procedure. These new procedures are compared among themselves and with nonstepwise procedures based on Type I error levels and comparisonwise power. It is shown that these stepwise nonparametric procedures control…

回归函数的置信带AI 解读

A method for obtaining (conservative) confidence bands for regression functions in low dimensions is given. Of particular importance is the applicability of the method to nonparametric regression. Computations, examples, and comparisons indicate the effectiveness of the method.

简单线性回归置信带的平均宽度最优性AI 解读

The problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered. Optimality is defined as minimization of the average width of the bands weighted by a normalized function. This weight function is presented as an indicator of experimental interest in the varying width of the band. A comparison between the commonly seen hyperbolic bands and segmented-line bands is presented.

简单线性回归中的可容许与最优置信带AI 解读

A framework is presented for deciding among functional forms when constructing confidence bands in simple linear regression. Using the concept of tautness, definitions of admissibility and completeness are developed. These lead to a characterization of a minimal complete class of band forms. A type of average width optimality within this class is briefly discussed.

三个正态总体均值两两比较的精确同时置信区间AI 解读

The problem of simultaneously estimating the pairwise differences of means of three independent normal populations with equal variances is considered. A computational method involving a bivariate t density is used to form confidence intervals with simultaneous coverage probability equal to 1 — a. For equal sample sizes, the method is the Tukey studentized range procedure. With unequal sample sizes, the method is superior to the various generalized Tukey methods. A table of…

三个或四个均值多重比较的精确同时置信区间AI 解读

A procedure for constructing exact simultaneous confidence intervals for a finite set of multiple comparisons among three or four groups is presented. These confidence intervals are hyperbolic and based on an unbiased estimator of the mean values having a normal distribution with covariance matrix σ2V, where V is an arbitrary known positive definite matrix. This procedure is used to study the amount of conservativeness of Tukey—Kramer intervals for pairwise comparisons in an…

现代基础统计学AI 解读

Preface Chapter 1: Introduction 1.1 The Growth of Modern Statistics 1.2 Sources of Statistical Data 1.3 The Nature of Statistical Data Chapter 2: Summarizing Data: Listing and Grouping 2.1 Listing Numerical Data 2.2 Stem-and-Leaf Displays 2.3 Frequency Distribution 2.4 Graphical Presentations 2.5 Summarizing Two-Variable Data Chapter 3: Summarizing Data: Measures of Location 3.1 Population and Samples 3.2 The Mean 3.3 The Weighted Mean 3.4 The Median 3.5 Other Fractiles 3.6…

同时置信界的平均宽度最优性AI 解读

Simultaneous confidence bounds for multilinear regression functions over subregions $X$ of Euclidean space are defined to be $\mu$-optimal in a class of bounds $C$, if they minimize average width with respect to $\mu$ over $X$, among all bounds in $C$ with equal coverage probability. We show that for certain simultaneous confidence bounds we can find a measure $\mu$ relative to which the bounds are $\mu$-optimal in $C$, where $C$ is a large class of bounds. Such results are…

协方差分析中的同时两两比较AI 解读

Procedures for multiple comparisons among treatment means, in analysis of covariance with a random concomitant, are considered. A Tukey-Kramer (TK)-type procedure is introduced for a conditional analysis and is compared with Thigpen and Paulson's (1974) unconditional procedure. It is first established (by simulation) that the TK procedure controls the unconditional familywise error rate at the nominal level set for the conditional procedure. In the second part of this work,…

与最佳者多重比较的约束同时置信区间AI 解读

For comparing $k$ treatment effects $\theta_1, \theta_2, \cdots \theta_k$, often the parameters of primary interest are $\theta_i - \max_{j\neq i}\theta_j, i = 1, \cdots, k$. In this article, we develop constrained $100P^\ast{\tt\%}$ two-sided simultaneous confidence intervals for $\theta_i - \max_{j \neq i} \theta_j$ which we refer to as (constrained) MCB intervals. It turns out that the lower bounds of the intervals imply Indifference Zone selection inference, and the…

摘要暂缺

自回归谱的同时置信带AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on the estimated spectral density. We propose and illustrate a method for determining asymptotic simultaneous confidence bands using Scheffé projections.

一维多项式回归的精确置信带AI 解读

An exact piecewise polynomial simultaneous confidence band is described for one-dimensional (p—1)th order polynomial regression. The band is constructed by placing intervals around the estimated response at the zeros of the pth order orthogonal polynomial with respect to the design points. Since under the usual assumptions the response estimates are uncorrelated at these zeros, the construction of the exact band in the normal case is made easy.

自回归谱的同时置信带AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on the estimated spectral density. We propose and illustrate a method for determining asymptotic simultaneous confidence bands using Scheffé projections.

删失生存数据中风险率的非参数推断AI 解读

This paper concerns nonparametric inference for hazard rates with censored serial data. The focus is upon "delta sequence" estimators of the form $h_n(x) = \int K_b(x, y) dH_n(y)$ with $K_b$ integrating to 1 and concentrating mass near $x$ as $b \rightarrow 0. H_n$ is the Nelson-Aalen empirical cumulative hazard. Strong approximation and simultaneous confidence bands are derived for Rosenblatt-Parzen estimators, with $K_b(x, y) = w((x - y)/b)/b, b = o(n^{-1}),$ and $w(\cdot)$…