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人口预测的准确性AI 解读

Population projections are key elements of many planning and policy studies but are inherently inaccurate. This study of past population projection errors provides a means for constructing confidence intervals for future projections. We first define a statistic to measure projection errors independently of the size of the population and the length of the projection period. A sample of U.S. Census Bureau and United Nations projections indicates that the distributions of…

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二项分布似然函数的单峰性AI 解读

A maximum likelihood estimate exists for both parameters of the binomial distribution if and only if the sample mean exceeds the sample variance. The derivative of the log-likelihood function has at most one finite root; consequently the likelihood function is unimodular.

合并列联表中 Pearson 卡方统计量的可分解性、单调性及应用AI 解读

The Pearson chi-square statistic for a contingency table is decomposed into a sum of components. Each component involves the Pearson chi-square statistic for tables that are formed by collapsing (i.e., combining) rows and/or columns of the original table. Since the terms in the decomposition are necessarily nonnegative, this leads to a monotonicity in the statistic; the Pearson chi-square value for any table N is never smaller than the corresponding values for tables formed…

确定时间序列周期的一种方法AI 解读

The periods corresponding to peaks in the autoregressive and window spectral density estimators are shown to be consistent and asymptotically normal estimators of peak periods in the true spectral density under assumptions of known autoregressive order and under slight modifications of the assumptions often made to show the asymptotic normality of window estimators, respectively. The asymptotic variances are obtained, and the use of the theory is illustrated by obtaining an…

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公共项目分析：一种新的分类数据方法AI 解读

I: Foundations.- 1. Multidimensional Contingency Tables.- 2. Guidelines for Analysis.- What Are Categorical Data?.- Is This a Categorical Data Problem?.- What Function Should Be Analyzed?.- What Sample Size Is Required?.- Are Zero Cells a Problem?.- How Many Analyses Should Be Performed?.- What Levels of Significance Should Be used?.- Summary.- 3. Contingency Table Analysis: The WLS Approach.- The Contingency Table.- Formation of Functions.- The Variance of a Function.- The…

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模型选择中的样本量选择与可区分性评估AI 解读

In this article we present a general Bayesian approach to discrimination. We describe how the difference between two separate families of distributions can be assessed in terms of differences between two binomial models. Two examples that illustrate the methodology are included. Specifically, we investigate the extent to which it is possible to discriminate between the von Mises and the wrapped normal distributions and also between the normal and a family of t distributions.

基于简单秩阶梯得分统计量的位置模型推断AI 解读

A class of estimation procedures that are robust, relatively efficient, and yet computationally simple is proposed for the one- and two-sample location problems. Particular emphasis is placed on the problem of determining confidence intervals, a topic that has seen limited exposure in the literature. As a by-product, some interesting point estimates are obtained. A class of score functions that are ordinary step functions is considered for the location model. Point estimates…

适度多元非正态性对 Roy 最大根检验的影响AI 解读

The asymptotic distribution of Roy's largest root statistic in multivariate Edgeworth populations is expanded to terms of the first order. To this order, the effects of non-normality are expressed by Mardia's measures of multivariate skewness and kurtosis, together with a supplementary skewness measure. Tables of corrections to the nominal significance level are presented for the k-sample MANOVA situation. Comparison with simulation results indicates that the correction…

设定不确定时的潜变量系统估计：广义成分分析与消元法AI 解读

This article argues that, to relieve the specification difficulties that frequently accompany latent variable models, a first application should in most cases employ an estimator that makes no assumption about the nature of the unobservables. The two possibilities are generalized component analysis, with the unobservables treated as incidental parameters; and the eliminant method, where they are removed by transformation of the model before estimation. It is shown that these…

乘法交互模型中不完全可加性的检验AI 解读

Consider the multiplicative interaction model defined by yij = μ + τ i + β j + λα i γ j + ∈ ij , i = 1, 2, …, t, j = 1, 2, …, b, where it is assumed that Σ i τ i = Σ j β j = Σ i α i = σ j γ j = 0 and γ i α i 2 = γ j γ j 2 = 1. It is also assumed that the ∈ ij are distributed NID (0, σ2). This article derives the likelihood ratio test of H 0: Hα = 0 and Gγ = 0 vs. Ha :Hα ≈ 0 or Gγ ≈ 0, where H is a q × t matrix of row contrasts of rank q and G is a r × b matrix of row…

删失生存分析中一般统计量的重复显著性检验AI 解读

The asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow-up. These results are used for constructing repeated significance tests over real time.

含Box–Cox变换模型参数估计的快速高效算法AI 解读

A modified Newton algorithm for the estimation of parameters in models containing the Box-Cox transformation is presented. It is shown that the usual maximum likelihood estimator for the k linear parameters and the m power transformation parameters may be specified as an m-parameter nonlinear least squares estimator. Several models containing Box-Cox transformations are estimated and the speed and efficiency of the modified algorithm compared with three other gradient…

用B样条对微量荧光测定直方图进行反卷积AI 解读

We consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors. We propose a method of estimation using spline functions, discuss the numerical implementation of the method, and prove its consistency. The problem is motivated by the analysis of DNA content obtained by microfluorometry, and an example of such an analysis is included.

鱼类种群年龄构成估计的贝叶斯优化AI 解读

To estimate the age distribution of a fish population, a two-phase stratified sample design is proposed. Bayesian methods are employed to determine (a) optimal estimators of the desired population proportions; and (b) the optimal choice of second-phase sample sizes subject to a fixed budget. A summary of the results of some numerical examples is presented. These examples demonstrate typical expected gains obtained by using the Bayesian optima as compared to alternative…

多项式回归中的若干稳健型 D 最优设计AI 解读

Consider a polynomial regression situation on an interval and also a robustness-type formulation of Stigler's. A technique involving canonical moments is discussed and some explicit solutions are given.