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非线性预测理论与有限总体比例估计AI 解读

The prediction approach to finite population inference is developed for a general nonlinear model. An estimator of the finite population total and an estimator of its variance are derived, and the asymptotic properties of both are obtained when the random variables in the model are independent. The theory is applied to the problem of estimating the total number of units that have a specified characteristic. An empirical study is presented, which confirms that a nonlinear…

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分析中的布朗运动与鞅AI 解读

Brownian motion. Stochastic integration. Conditioned Brownian motions. Boundary limits of harmonic functions. Complex Brownian motion and analytic functions. Hardy spaces and related spaces of martingales. H1 and BMO, m1 and BMO. PDE's which can be solved by running a Brownian motion. Stochastic differential equations.

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高级计量经济学：通向文献的桥梁AI 解读

TOPICS IN LARGE SAMPLE THEORY AND APPROXIMATION METHODS. A Review of Asymptotic Distribution Theory and Maximum Likelihood Estimation. Methods of Approximating Distribution Functions, Density Functions, and Moments. TOPICS IN TIME SERIES ANALYSIS. An Introduction to Time Series Analysis. Identification, Estimation, and Prediction in Time Series Models. The Relationship Between Time Series Models and Econometric Models. TOPICS IN ESTIMATION UNDER A QUADRATIC LOSS CRITERION.…

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随机区组设计中污染分布备择下对齐秩检验的渐近接受性质AI 解读

Asymptotic noncentral X 2 distributions of aligned rank test statistics under a contiguous sequence of alternatives of contaminated distributions are obtained as the number of blocks tends to infinity in a randomized-blocks design with one observation per cell. I show that the asymptotic relative efficiency of the aligned rank test, with respect to the likelihood ratio F test under the sequence of these alternatives, is one in the case of normal scores and is nearly equal to…

积分比值的一个实用不等式及其极大似然估计应用AI 解读

A generalization of a well-known covariance inequality is proved and is used to furnish sufficient conditions for the strict concavity of the log-likelihood of an observable random variable Y as a function of a real parameter θ that governs the distribution of an unobservable random variable X on which the distribution of Y depends in a known way.

贝叶斯集合估计与可容许集合估计AI 解读

We consider the problem of set estimation of a parameter θ based on an observation X, with the goal of simultaneous control of the noncoverage probability and expected size of the estimating set. Several notions of being Bayes for set estimates are studied, and their relationship to a natural notion of admissibility for confidence procedures is investigated.

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…

关于二项分布中试验次数 N 估计量的说明AI 解读

Consider k success counts from a binomial distribution with unknown N and success probability p. We examine the problem of estimating N. By integrating the likelihood for N and p over a beta density for p, we obtain the beta-binomial distribution resulting in stable and reasonably efficient estimators of N, which compare favorably with and are often better than the estimates introduced by Olkin et al. (1981).

非同分布观测下泊松假设的拟合优度检验AI 解读

Tests for detecting negative binomial departures from a Poisson model are studied for the one-way-layout and regression-through-the-origin cases. Approximations to the null and alternative distributions of these test statistics are presented. Locally optimal tests and tests suggested in the literature are compared in terms of asymptotic relative efficiency. Small sample comparisons are included.

基于 II 型删失数据的极大似然及相关估计量的渐近性质AI 解读

Some simple procedures are provided for establishing the asymptotic normality and uniform strong convergence of a class of functions that arise in the context of estimating parameters from a Type II censored sample. These lead to an elementary yet rigorous treatment of the asymptotic properties of maximum likelihood estimators based on Type II censored data. Further applications include the treatment of asymptotics of some modified maximum likelihood (MML) estimators. In…

结合 Kendall 秩相关与符号检验的非参数线性回归检验AI 解读

A nonparametric test for hypotheses concerning linear regression parameters is based on the signs of the residuals and their Kendall correlation with the independent variable. The small-sample distribution of the test statistic is tabulated, asymptotic approximations are derived, and the corresponding confidence region is presented. Furthermore, the Pitman asymptotic relative efficiency of the test is calculated with respect to the classical test based on least squares and…

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检验分离假设族的一种新方法AI 解读

Theoretical and empirical evidence are reported showing that the tests given in Cox (1961) and Williams (1970a, b) for the problem of testing separate families of hypotheses suffer from fundamental difficulties. Neither test is guaranteed to be asymptotically level a, even for very smooth problems. A new method proposed here as an alternative works adaptively by repeated application of the parametric bootstrap idea over slowly shrinking confidence regions. Theoretical…

在频域中探索臭氧的空间时间序列AI 解读

In 1974, atmospheric scientists (Molina and Rowland; Cicerone et al.) first postulated that man-made chemicals known as CFC's (e.g., freon) deplete the earth's ozone when released into the atmosphere. This article presents an exploratory data analysis (EDA) of a spatial time series of ozone measurements. Frequency domain techniques for the EDA are introduced and used to graphically display global, long-term trends relevant to the CFC issue. My intention is to illustrate the…

利用集中度比率数据估计 Herfindahl 指数AI 解读

High concentration ratio (C)—Herfindahl (H) index correlations found in United States studies may be biased upward by using estimated H. For New Zealand data, correlations between C and actual H are lower; the H—C relationship appears to be nonlinear. Guided by income distribution studies, a new family of H estimators—derived from H's upper and lower bounds rather than generalized assumptions about firm size distributions—is proposed. The methodology for calculating the…

Gauss–Markov 定理的一个非线性版本AI 解读

This article gives a nonlinear version of the Gauss—Markov theorem. It is shown that in a linear regression model y = Xβ + u, the lower bound for the risk matrix of a nonlinear estimator of β belonging to a certain class is the covariance matrix of the Gauss—Markov estimator, provided the distribution of error term u belongs to the class of elliptically symmetric distributions with second moments.

估计正参数乘积的样本分配方案AI 解读

Suppose that for i = 1, …, I, a random variable whose distribution depends on parameter μ i , > 0 is observable from population i. The problem is to estimate θ = IIμ i , using a Bayesian approach with squared error estimation loss in θ and allowing sequential allocation. That is, k observations may be taken one at a time and the decision to take an observation from population i may depend on past observations from all populations. For estimating θ, the best nonrandom…

通过 Box–Cox 变换获得偏态分布的位置度量AI 解读

Box—Cox power transformations are used to transform a set of observations to symmetry. A measure of location of the original data is obtained by applying the inverse transformation to the center of the transformed data. Its properties are discussed, and it is compared with other measures of location.

删失配对数据中位置差的无分布估计方法AI 解读

Nonparametric point and interval estimators of location difference in matched pairs data with arbitrary right censorship are proposed, based on a generalized Gehan—Gilbert test (Wei 1980). The point estimator is shown to be asymptotically normal and strongly consistent. The limits of the corresponding interval estimator are readily computable. An example is also provided to illustrate the techniques to problems in survival data analysis.

秩删失数据的最大似然回归AI 解读

Linear regression is a common method for analyzing continuous, cardinal data, but it is inappropriate when the dependent variable is an ordinal ranking. The model proposed for analyzing these data sets is the general linear model u = Xβ + ε, where the rank of the dependent variable u is observed instead of its value. A description is given for a numerical algorithm to evaluate the likelihood function that is efficient enough to permit maximum likelihood estimation of…