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变化率与初始值之间的关系AI 解读

Given a series of consecutive measurements on a random sample of individuals, it is often of interest to investigate whether there exists a relationship between the rate of change and the initial value. Assuming that the observations deviate in a random manner from the true values, straightforward regression computations will yield biased results. It is shown that, in the case of the normal distribution, the maximum likelihood (ML) estimates of the second-order moments of…

平衡单因素随机效应方差分析模型的单侧容忍限因子AI 解读

A technique based on the noncentral t distribution for obtaining one-sided tolerance limits for a balanced one-way-anova random-effects model is developed. These limits are such that the probability is γ that at least a proportion p of the population consisting of very many specimens from very many batches exceeds the calculated lower limit. A few selected tables are given, and an example illustrates the use of the derived tolerance factors.

多元分析中的非参数单侧检验及医学应用AI 解读

Permutation tests are applied to the maximal t statistic in two-sample, completely randomized designs, and in two-sample, matched-pair designs, where the response is a vector and the experimenter is interested in one specific direction in each component. Recommendations for subsampling are also included for cases when the number of permutations required to complete the test is prohibitive. These procedures are then applied to data from two medical trials.

检验匹配比例相等时 Q 统计量的分布AI 解读

The asymptotic distribution of Cochran's Q statistic is obtained under the null hypothesis H 0 for comparing proportions in matched samples under the multinomial model. Simulation studies show that a Satterthwaithe-type approximation provides a better approximation to the limiting distribution than does the chi-square distribution. Also, if by the nature of the problem, H 0 implies the side condition H, which is necessary for Q to have a limiting chi-square distribution,…

极小极大准则下的目的性调查抽样设计AI 解读

The linear regression superpopulation model for survey sampling allows a formulation of the survey design problem which is close to optimum experimental design theory. This article introduces an alternative criterion to that of Royall (1970). A sampling design can be chosen to minimize the maximum mean squared error (mse) of “prediction” over the unsampled units. An upper bound for this maximum mse is derived and an algorithm given for obtaining samples satisfying the bound.…

二元分布的一族依赖性概念AI 解读

A family of concepts of stochastic dependence for bivariate distribution functions is introduced. Each concept gives rise to a family of bivariate distribution functions. We show the equivalence of some of these families with families of positively dependent distribution functions, which are known in the literature, and characterize some of them by notions from reliability theory. Interrelations among the various families are studied, and some moment inequalities are…

若干单变量 Bradley–Terry 模型的加权最小二乘分析AI 解读

The approach of Grizzle, Starmer, and Koch (1969) to analyzing categorical data using linear and loglinear transformations is applied to the analysis of univariate paired and triple comparison experiments. This method of analysis produces noniterative weighted least-squares estimates of the preference ratings corresponding to the treatments under test and allows for testing hypotheses relative to their values within the framework of the general linear hypothesis. Further,…

回归中的有偏估计：基于均方误差的评价AI 解读

A mean squared error criterion is used to compare five estimators of the coefficients in a linear regression model: least squares, principal components, ridge regression, latent root, and a shrunken estimator. Each of the biased estimators is shown to offer improvement in mean squared error over least squares for a wide range of choices of the parameters of the model. The results of a simulation involving all five estimators indicate that the principal components and latent…

卡方拟合优度检验的功效近似：简单假设情形AI 解读

The limiting distribution of the chi-square goodness-of-fit statistic Tn under alternatives is noncentral chi-square if the alternative probabilities approach the null probabilities at an appropriate rate as n → ∞. It is shown that for fixed alternative probabilities, the limiting distribution of (Tn − μ n )/σ n is standard normal. Both of these asymptotic results can be used to approximate the power of the goodness-of-fit test. Numerical comparisons between these two…

再论回归计算精度AI 解读

Issue is taken with a previous article which examines Longley's analysis of computation error in regression models. Specifically, the singular value decomposition is used to analyze a set of data which relates to employment levels. This decomposition is used to analyze near multicollinearity in the data. It is suggested that a previous Monte Carlo study of this problem is noninformative, misleading, and possibly irrelevant.

小批量计量抽样方案的预测区间方法：正态过程的单次抽样AI 解读

A prediction-interval approach is used to derive variables sampling plans applicable to finite lots. A normally distributed process is assumed, and lots ranging in size from 5 to 70 are considered. The plans are such that, with high probability, accepted lots will have zero defects (defined in terms of one-sided specification limits). Further, tabulations provide information which is useful for selecting sample size for a specified combination of lot size and acceptable…

按总规模比例抽样中的方差估计AI 解读

The problem of estimating the variance of the ratio estimator in sampling with probability proportional to aggregate size is investigated. The form of nonnegative unbiased variance estimators is found. For sample size n = 2, it is shown that there is at most one nonnegative unbiased variance estimator, whereas for n > 2, two different, possibly nonnegative, unbiased variance estimators are proposed. The performance of the proposed unbiased variance estimators, as regards…

分数阶次序统计量及其应用AI 解读

Based upon Ferguson's Dirichlet process, we introduce an order-statistic process, a technical device which may be viewed as defining a continuum of fractional order statistics for any sample size. The order-statistic process provides an alternative to the quantile function essentially based on stochastic rather than linear interpolation. Its use in large-sample theory is suggested, and a simple proof is given that the order-statistic process, suitably normalized, converges…

非线性回归设定检验：一个非正则情形AI 解读

A statistical test of whether an additive nonlinear term in the response function should be omitted from a nonlinear regression specification is considered. The regularity conditions used to obtain the asymptotic distributions of the customary test statistics are violated when the null hypothesis of omission is true. Moreover, standard iterative algorithms are likely to perform poorly when the data support the null hypothesis. Methods designed to circumvent these…

货币供给估计中的抽样问题AI 解读

In this article, the selection and testing of a sample of member banks of the Federal Reserve System are described. The objectives are timely and accurate estimation of monetary aggregates for the population of member banks. This sampling problem is unusual for two reasons: the need to produce regular weekly estimates on an accelerated time schedule, and the extensive historical data available. These past data afford an opportunity to improve the precision of estimation and…

卡方分布分位点的直接近似AI 解读

In contrast to the customary approximations based on normalizing transformations, direct approximations involve only simple functions of parameters (such as degrees of freedom and tail area in the chi-squared distributions). This article uses techniques of exploratory data analysis to develop direct approximations for percentage points in the commonly used portions of both tails of the chi-squared distributions with small to moderate numbers of degrees of freedom. These…

会计总体抽样中统计估计量的表现AI 解读

Auditors usually have information on both the book amount and the audit amount available for each sample audit unit. Problems in using difference and ratio estimators, as well as some other estimators, for constructing large-sample normal confidence intervals when the population error rate is low are explored empirically in this article. The findings indicate the need for great care in using large-sample normal confidence intervals for sample sizes of 100 or 200 (sizes…

八个世纪的抽样检验：钱币检验仪式AI 解读

A sampling inspection scheme bearing striking similarities to modern procedures has been in more or less continuous operation at the Royal Mint in London for about eight centuries. The history of this scheme is reviewed, and a defect in the manner in which the critical levels were set is noted. The possibility that Master of the Mint, Isaac Newton might have grasped the nature of the defect is discussed. Finally, we review the situation at the United States Mint, where…

截断样本的原始规模估计AI 解读

Consider N (unknown) values of a variable X (discrete or continuous) independently sampled from a distribution with density f(x, θ), where θ is an unknown vector parameter. Suppose that the values of X belonging to a certain region R are not observable. This article deals with the problem of estimating N and θ in such situations which arise, for instance, in life testing and capture-recapture census. Asymptotic theory for maximum likelihood estimation of N and θ is presented…

线性回归模型设定误差检验的若干性质AI 解读

This article considers the test reset which is intended to detect a nonzero mean of the disturbance in a linear regression model. Analysis of an approximation to the test statistic's distribution and Monte Carlo experiments reveal that the power of the test may decline as the size of the disturbance mean increases. However, the possibility is remote and declines with increasing sample size. Alternative sets of test variables are considered, and their effect on the power of…

线性回归中斜率、截距与尺度的若干稳健估计比较AI 解读

Three classes of M estimates for robust linear regression are investigated for various contaminated normal distributions, sample sizes, and distributions of the independent variable. These are the Lp estimates, the amt estimate, and a new class of estimates (Ea ) with bounded influence function. It is found that the Ea class consistently outperforms the Lp class, performs about as well as the amt estimate, and solutions for Ea estimates can be obtained rapidly and reliably.…

回归解的可接受性：重新审视计算精度AI 解读

This note examines the experiment performed by Beaton, Rubin, and Barone (1976) to study the effect of rounding errors in published figures, when these data are used in regression analysis. The experiment could be vitiated by the fact that the error introduced in the trend variable is by no means trivial when one measures the data in deviation from the mean. For this reason, the results presented in Beaton, Rubin, and Barone (1976) do not contain enough evidence to suggest…

检测时间序列模型参数变化的序贯程序AI 解读

Procedures are proposed for monitoring forecast errors in order to detect changes in a time-series model. These procedures are based on likelihood ratio statistics which consist of cumulative sums. An extension of Page's method is presented which tests for changes in the parameter values of autoregressive integrated moving average (arima) models. The distributional properties of the statistics are approximated under the assumption that the series follows an integrated…

Cox 删失数据似然函数的效率AI 解读

D.R. Cox has suggested a simple method for the regression analysis of censored data. We carry out an information calculation which shows that Cox's method has full asymptotic efficiency under conditions which are likely to be satisfied in many realistic situations. The connection of Cox's method with the Kaplan-Meier estimator of a survival curve is made explicit.