论文检索

自变量取值受限时线性回归的置信带AI 解读

Several writers have studied the problem of obtaining confidence bands for a straight line regression under the requirement that the bands be at a specified confidence level, (1 – α) say, for values of the independent variable restricted to a pre-specified closed interval. The bands studied by other writers have been either bands of equal width throughout the interval or trapezoidal bands. This paper studies confidence bands of the classical hyperbolic type under the…

摘要暂缺

Wishart 矩阵极端特征根的分位点AI 解读

SUMMARY This paper tabulates the distribution of the largest and smallest characteristic roots of a Wishart matrix; the computation is based on an approximation derived from work of Pillai. As an application, we present simultaneous confidence intervals for the variance components of the two-way layout with unequal variances.

线性回归中更窄的置信带AI 解读

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function for all values of the independent variable have…

线性回归中更窄的置信带AI 解读

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function for all values of the independent variable have…

简单线性模型的线段置信带AI 解读

In this paper confidence bands are given for the entire line for simple linear regressions. The conventional bands that have been given in the past are curvilinear. In this paper we consider confidence bands that are straight lines. It is shown that under certain conditions the “width” of these straight line bands is less than the width of the conventional curvilinear bands.

In the paper, exact tests are proposed for testing the trend in the presence of autocorrelation and also for testing the trend and autocorrelation simultaneously in a first order Markov process. Also, the simultaneous confidence intervals associated with these tests are derived. These results are extended to a higher order Markov process.

线性模型中等宽与比例宽度的置信带AI 解读

In this paper confidence bands are given for simple linear models. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval.

平衡单因素与双因素分类的简便多重比较：第二部分，推导与近似AI 解读

Part 1 of this paper (Kurtz, Link, Tukey & Wallace, 1965a) presents tables of approximate percentage points of the ratio of a range to a sum of ranges and discusses their use in multiple-comparison procedures for balanced single and double classifications. The methods of approximation used in the construction of these tables are described here with emphasis on results and methods likely to be of use in other connexions. The basic approximation and the multiple comparison…

利用 t 分布估计多个对比AI 解读

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions…

列联表三因素交互作用的简便分析方法AI 解读

The earlier literature on three-factor interactions in a three-way contingency table was concerned mainly with the null hypothesis H 0 that these interactions are all nil. In the present article, we present methods for testing H 0 which are easier to apply than those suggested by earlier writers on this subject, and in addition we develop methods for obtaining simultaneous confidence intervals for estimating the magnitudes of the three-factor interactions in the three-way…

直线回归的置信带AI 解读

This paper develops a method for obtaining confidence bands in polynomial regression when the observations are independently distributed with constant but unknown variance. The bands may be obtained, in principle, over arbitrary sets of the independent variable with exact preassigned confidence coefficients. In general, difficult distribution problems result when specific applications are attempted. The major portion of this paper is concerned with first degree polynomials…

列联表交叉乘积比的同时置信限AI 解读

Summary Fisher (1962) has proposed a method for obtaining confidence limits for the cross-product ratio in a 2 × 2 table which requires that the user solve a quartic equation. Based on a different mathematical derivation, Cornfield (1956) had proposed a similar method. In the present article, we shall present simpler methods for obtaining confidence limits for the cross-product ratio in a 2 × 2 table, and we shall extend these methods to obtain simultaneous confidence…

多元方差分析中的 Hotelling 广义 T²AI 解读

SUMMARY Hotelling’s generalized T2 is the sum of the roots of the determinantal equation |Z - θY/n| = 0, where Y and Z have central and non-central p-dimensional Wishart distributions with d.f. Q and n. Y and Z are obtained as the sum of products matrices for p-variate normal distributions N(0, σ1) and N(b(q), σ1). The distribution of this statistic is shown to be a monotonic increasing function of each of the population roots. An unbiased estimate of a linear function of…

回归中的同时容忍区间AI 解读

Joint prediction intervals (based upon the original fitted model) for K future responses at each of K separate settings of the independent variable have been treated by Lieberman (1961). When K is unknown and possibly arbitrarily large, these results do not apply. A solution to the problem of arbitrary K is given in terms of tolerance intervals on the distributions of future observations, the intervals being (probabilistically) simultaneous in each possible value of the…

摘要暂缺

多个均值之间的多重比较AI 解读

Methods for constructing simultaneous confidence intervals for all possible linear contrasts among several means of normally distributed variables have been given by Scheffé and Tukey. In this paper the possibility is considered of picking in advance a number (say m) of linear contrasts among k means, and then estimating these m linear contrasts by confidence intervals based on a Student t statistic, in such a way that the overall confidence level for the m intervals is…

摘要暂缺

平稳时间序列的统计分析AI 解读

Stationary Stochastic Processes and Their Representations: 1.0 Introduction 1.1 What is a stochastic process? 1.2 Continuity in the mean 1.3 Stochastic set functions of orthogonal increments 1.4 Orthogonal representations of stochastic processes 1.5 Stationary processes 1.6 Representations of stationary processes 1.7 Time and ensemble averages 1.8 Vector processes 1.9 Operations on stationary processes 1.10 Harmonizable stochastic processes Statistical Questions when the…

摘要暂缺

摘要暂缺

多组最小二乘问题及其相关正交多项式的意义AI 解读

A multiple group least squares’ problem is presented and solved which involves determination of certain coefficients separately for each of several samples with a final coefficient given a single optimum value for all samples grouped together. The computation of orthogonal polynomials implicit in the normal equations is discussed relative to the forward solution of these equations. Certain significant advantages of computing orthogonal predictors are pointed out. A numerical…

非参数情形下的置信界限AI 解读

The purpose of this article is to give a survey 1 1I should like to thank Professor Wolfowits for pointing out the need for such a survey. of certain methods available for finding confidence limits when nothing is assumed about the population from which a sample has been drawn except possibly that it has a continuous distribution. The following three cases are treated: a confidence band for the unknown cumulative distribution function, a confidence interval for the…

非参数情形下的置信限AI 解读

The purpose of this article is to give a survey 1 1I should like to thank Professor Wolfowits for pointing out the need for such a survey. of certain methods available for finding confidence limits when nothing is assumed about the population from which a sample has been drawn except possibly that it has a continuous distribution. The following three cases are treated: a confidence band for the unknown cumulative distribution function, a confidence interval for the…