论文检索

某些复合假设的序贯检验AI 解读

Summary A sequential procedure is developed to distinguish between null and alternative hypotheses of the type H 0: θ ≤ θ0 and H 1: θ ≥ θ1 (θ0 ≤ θ1) for one-parameter exponential families in such a way that the risks of type I and type II errors are smaller than some predetermined bounds. This is accomplished using observations of a sequence of random variables whose distribution is known up to the parameter θ, and involves the theory of certain tests with power one. The…

高阶层级随机效应模型中的贝叶斯等变估计量AI 解读

Summary The Bayes equivariant estimators of the variance components (Zacks, 1970, 1971) are characterized in the case of r-stage hierarchical random effects models when the random effects are normally distributed and are mutually and completely independent. Non-trivial Bayes equivariant estimators are derived using a special prior distribution for the three-stage hierarchical model. It is observed that for the squared error loss function every Bayes equivariant estimator of…

检验回归关系随时间保持稳定的方法AI 解读

Summary Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are…

均方误差的推广及其在岭回归中的应用AI 解读

Summary Hoerl and Kennard (1970) have proposed a method of estimation for multiple regression problems which involves adding small positive quantities to the diagonal of XT X. They use a type of mean square error to justify the procedure. This paper considers some generalizations of mean square error and provides a stronger defence of the method.

正态分布的尺度混合AI 解读

Summary This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V 2 is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.

Watson分布的均值与方差AI 解读

Summary Watson's distribution is the distribution of the ratio of two linear combinations of independent x22 variables (the denominator being positive). Such ratios arise, for example, in the consideration of, or in approximations to, certain serial correlation coefficients. The moments of these ratios are known only in specialized cases. We derive the first two moments for the more general Watson distribution.

连续时间随机模型的若干离散近似AI 解读

Summary The paper considers the asymptotic biases in various econometric estimators when data generated by a stochastic differential equation system of the form d y d t − A y ( t ) = B z ( t ) + a ( t ) are estimated by approximating these equations in the form { y ( t + δ ) − y ( t ) } / δ = 1 2 A { y ( t + δ ) + y ( t ) } + 1 2 B { z ( t + δ ) + z ( t ) } + v ( t ) , where y(t) is a vector of endogenous variables, z(t) is a vector of exogenous variables and A and B are…

Wiener–Kolmogorov 预测器的渐近性质（一）AI 解读

Summary “Windowed” estimates of the spectral density function are used to carry out the factorization of the sample spectral density function and hence estimate the Wiener-Kolmogorov prediction coefficients. Expressions are derived for the asymptotic mean and variance of all the statistics necessary to estimate the predictor. The covariances and asymptotic normality of these estimates are also investigated. In particular, an expression for the asymptotic mean-square error or…

相依观测的最大似然方法AI 解读

Summary Under certain conditions on conditional probability densities, in the case of dependent observations, the maximum-likelihood estimate is proved to be consistent, asymptotically efficient and asymptotically normal.

复杂抽样下的统计推断AI 解读

Summary The design of complex samples induces correlations between element values. In stratification negative correlation reduces the variance; but that gain is less for subclass means, and even less for their differences and for complex statistics. Clustering induces larger and positive correlations between element values. The resulting increase in variance is measured by the ratio deff , and is often severe. This is reduced but persists for subclass means, their…

投影算子、广义逆与最佳线性无偏估计AI 解读

Summary It is well known that in the Gauss–Markov model (Y, Xβ, σ2 V) with | V | ≠ 0, the BLUE (best linear unbiased estimator) of Xβ is Y1, the orthogonal projection of Y on M(X), the space spanned by the columns of X, with inner product defined as (x, y) = x'V-1 y. A quadratic function of Y2, the projection of Y on the orthogonal complement of M(X), provides an estimate of σ2. It may be seen that Y = Y1 + Y2. When V is singular, the inner product definition as in…

统计模型的构建与比较AI 解读

Summary A general method of constructing mathematical models for probability distributions other than the normal, closely related to that of Nelder and Wedderburn (1972), is briefly outlined. A likelihood procedure for comparing statistical models based on different distributions is described and numerical examples, using models based on the exponential family, given to illustrate the techniques.

趋极布朗运动与鸟类导航AI 解读

Summary This paper is not concerned with identifying the mechanism of bird navigation, but rather with assessing the degree of success possible using very bad navigational aids of whatever sort. Flight-paths are simulated using virtually no hypotheses, and all numerical parameters are determined ornithologically. The results are compared with the performance of actual birds, and also with a brownian model which is analytically convenient. It turns out that some formulae for…

离散水库相关分布估计的期望与离散程度矩阵AI 解读

Summary Approximate expressions are found, in the case of a particular model for the input transition matrix, for the mean and dispersion matrix of its elements and of the elements of the storage distribution for Moran and Lloyd reservoirs.

分层配置及分层与非分层πPS抽样方案的相对效率AI 解读

Summary The problem of optimum allocation to strata has been earlier examined in the light of a priori distributions. In this context, under the criterion of minimum expected variance, the sampling strategy consisting of an unstratified πPS sampling scheme together with the Horvitz–Thompson (HT) estimator was shown to be inferior to the strategy consisting of a stratified πPS sampling scheme with the corresponding HT estimator with this optimum allocation. In this paper,…

回归分析中的岭型估计量AI 解读

Summary An examination of the mean-square error properties of a class of shrinkage estimators for the normal regression model leads to a new derivation of the Hoerl–Kennard (1970) Ridge estimator and its generalization. Comparison is made with the James–Stein estimator, and with the generalized-inverse estimator proposed by Marquardt (1970). A Bayesian approach is noted.

排序参数的区间估计AI 解读

Summary Let F(x; θ) denote a family of distributions on the real line, indexed by the real-valued parameter θ. It is assumed that the given family is stochastically increasing in θ, that is, F(x; θ) is non-increasing in θ for each x. Let θ l …, θk represent k unknown values of the parameter θ, and let X l …, Xk represent k independent observations from the distributions F(x; θ l), …, F(x; θk), respectively. Let X* and θ* denote the ith smallest values among the observations…

检验方差之间线性关系的若干程序AI 解读

Summary In this paper, procedures are given for testing the hypothesis that the relation σ32=σ12+σ22 holds among the three variances σ12,σ22 and α32. This hypothesis is tested against the alternatives (i) σ32>σ12+σ22, (ii) σ32<σ12+σ22 and (iii) σ32≠σ12+σ22. The test procedures satisfy the property that the size or the Type I error does not exceed the preassigned level α. Optimum properties of the tests and their size and power functions are also investigated. The…

单侧贝叶斯区间与频率学派置信区间不相容的一则说明AI 解读

Summary With a proper prior distribution the one-sided Bayes confidence interval for the scalar parameter θ in the density function f(x, θ) never coincides with the corresponding confidence interval based on frequency, whether the experiment is of fixed sample size or sequential.

空间相互作用与格点系统的统计分析AI 解读

Summary The formulation of conditional probability models for finite systems of spatially interacting random variables is examined. A simple alternative proof of the Hammersley–Clifford theorem is presented and the theorem is then used to construct specific spatial schemes on and off the lattice. Particular emphasis is placed upon practical applications of the models in plant ecology when the variates are binary or Gaussian. Some aspects of infinite lattice Gaussian…

类内相关模型中均值对比的 Tukey 置信区间AI 解读

Summary In the intraclass correlation model when the variance σ 2 and the intraclass correlation coefficient 'p are both unknown, Tukey's confidence intervals for the contrasts in the means are obtained for the fixed sample and the sequential case. In the latter case confidence intervals of fixed width are obtained and the cost of not knowing σ2 and ‘p has been studied. From these results parallel results for Scheffé's confidence intervals can easily be obtained. A…

摘要暂缺

二元负二项分布的参数估计AI 解读

Summary Edwards and Gurland (1961) and Subrahmaniam (1966) have considered a correlated model as an alternative to the Bates and Neyman (1952) model, appropriate in the theory of accident proneness. The latter has presented a test for suitability of Bates–Neyman model against the alternative of the correlated model. Edwards and Gurland, on the other hand, are mainly concerned with the estimation of the parameters. Unfortunately, they are restricted to moments estimators…

最优实验设计理论的若干一般问题AI 解读

Summary This paper is an expansion of comments made by the author in the discussion following the reading of papers by Laycock (1972) and Wynn (1972). Section 2 presents a direct proof and interpretation of the equivalence theorem for the general case of a concave criterion function. This has implications for iterative algorithms of the type suggested by Wynn, as indicated in Section 3. Section 4 is concerned with a characterization of D,-optimality as a criterion which…