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用最小二乘平滑分析田间试验AI 解读

SUMMARY Assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment, least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend. Treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form. However, the main emphases are on the accuracy of…

概率分布下尾的最大似然估计AI 解读

SUMMARY We consider the estimation of the three parameters of the lower tail of a distribution function based on the k smallest out of n observations. The likelihood function has a singularity but it is argued that a local maximum, when it exists, should be taken as the m.l.e. Asymptotic results as k → ∞, n → ∞, k/n → 0 show that such a local maximum does exist, and provides consistent estimators whenever the shape parameter is greater than one; otherwise there is no local…

删失与分组数据的再加权最小二乘估计：EM 算法应用AI 解读

SUMMARY We consider the problem of adapting weighted least squares estimation so that estimates can be found with censored or grouped data. The EM algorithm is implemented for the linear model where the errors are assumed to be generated by a scale mixture of normal distributions. In particular, explicit results are given for the case where the marginal distribution of the error is Student-t with an even number of degrees of freedom. Expressions for the observed information…

非参数曲线估计的核函数AI 解读

SUMMARY The choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated. Explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error, IMSE (the present proof of the optimality of the latter kernels is restricted up to order k = 5). These kernels are also of interest for the nonparametric estimation of probability densities and spectral densities. A…

自回归时间序列残差方差与阶数的估计AI 解读

SUMMARY We study the bias of Yule-Walker, least squares and Burg-type estimates of the residual variance of autoregressive processes. Both simulations and theory indicate that Yule-Walker estimates are inferior to least squares and Burg-type estimates. The effect on order determination is also studied, and we extend the results on overestimation of the AIC criterion to the general multivariate case. For strongly autocorrelated processes, Yule-Walker estimates of residual…

利用重复观测估计多变量线性结构关系AI 解读

SUMMARY We derive maximum likelihood estimators for parameters of a multivariate linear structural relationship in the replicated case. The asymptotic covariance matrix of the maximum likelihood estimator of the coefficient of the relationship is obtained by using the delta method when the sample size tends to infinity.

二元响应的方差成分模型：访员间变异AI 解读

SUMMARY Interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non-normal family. The maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire. This raises some interesting questions about the use of unbalanced ANOVA methods with these data.

指数边际非线性自回归时间序列的建模与残差分析AI 解读

SUMMARY An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by an analysis of a long series of wind velocity data which has first been detrended and then transformed into a stationary series with an exponential marginal distribution. The stationary series is modelled with a newly developed type of second order autoregressive process with random coefficients, called the…

动态线性模型的递归估计AI 解读

SUMMARY A dynamic, linear model for the analysis of univariate time series is proposed. It encompasses many of the common statistical models as special cases such as multiple regression, exponential smoothing and mixed autoregressive-moving average processes. its distinguishing feature is that it relies on only one primary source of randomness. It therefore not only provides a simpler framework for the study of dynamic models but also eliminates the need for the contentious…

Gauss–Markov 定理向随机回归系数情形的扩展AI 解读

SUMMARY Several theorems which extend the Gauss-Markov theorem to the case of stochastic vectors of coefficients are presented in the literature. Some of these theorems, although differently formulated and proved, are based on the same assumptions and arrive at similar results. Some theorems are special cases of theorems, already existing in the literature. In other cases, theorems, which appear to be similar in their underlying assumptions and conclusions, differ in ways…

概率密度核估计量的一项最优性质AI 解读

SUMMARY Let f̂(x) be an asymptotically unbiased, nonparametric estimator of the density f(x) based on observations falling within the interval (x – ∈, x + ∈), where ∈ → 0 as the sample size diverges. We derive a lower bound to the variance of f(x), and prove that the bound is attained by a kernel estimator. This result is extended to estimates of f (r)(x), and to estimates of derivatives whose bias is improved by taking out the effects of unwanted terms.

回归模型贝叶斯分析中的最小二乘近似AI 解读

SUMMARY Least-Squares approximation of the parameters in a regression model are worked out in a Bayesian framework and shown to provide, at a low computational cost, a setup to handle non-normal models and/or non-natural conjugate prior distributions. This allows one to balance an approximate solution to a reasonable model against an exact solution to a simplified model.

使用因子模型对二元响应进行量表评分AI 解读

SUMMARY A simple method for scaling a set of binary responses is proposed using the logit factor model of Bartholomew (1980). It is shown that individuals may be ranked on the basis of a linear combination, ∑αi x i of the responses (xi = 0 or 1) where the αi's are the appropriate factor loadings. This completely avoids the need to calculate the y-scores suggested in Bartholomew (1980) and hence the heavy numerical integration which that method involves.

多元线性模型条件预测的一则注记AI 解读

SUMMARY In this paper we investigate the effects of errors in the estimation of the covariance structure of a multivariate random vector on the prediction of unobserved components of a further vector conditional on the values of the remaining observed components of the vector. We derive an exact expression for the increase in the mean square error of the usual least squares predictor due to these estimation errors which shows that the increase is substantial for small…

典范参数化与零参数效应曲率AI 解读

SUMMARY An equation derived by Hougaard (1982) characterizes certain canonical parameterizations of curved exponential families. The geometrical interpretation of Hougaard's equation is presented and, with this background, the relationship of work on Gaussian non-linear regression, by Bates and Watts (1980) and others, to that on general asymptotic inference, by Efron (1975) and Amari (1982a, b), is discussed. Hougaard's δ-parameterization is that in which there is zero…

von Mises–Fisher 分布的拟合优度检验AI 解读

SUMMARY We derive a goodness-of-fit test for the von Mises-Fisher distribution which is an extension of a goodness-of-fit test for the von Mises distribution given by Cox (1975). A robust version of the test is also given. Computational aspects of the test statistic are discussed and a numerical example is given.

缺失数据下秩相关指标的不等式AI 解读

SUMMARY New inequalities are obtained for Spearman's footrule, its associated sum of the absolute values of rank differences, the number of discordant pairs associated with Kendall's tau and the coefficient of concordance of several rankings when one or more individuals are missing or added to the data.

ARMA 模型极大似然估计量的渐近展开AI 解读

SUMMARY A technique is given for the Edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving-average (ARMA) models. Our methodology is illustrated and results on the expansions for some simple ARMA models are presented.

稳健非参数函数拟合AI 解读

SUMMARY A robust non-parametric function fitting method is introduced. The estimate is motivated from the theory of M-estimation and of kernel estimation of regression functions. Consistency and asymptotic normality are shown. Bias and variance rates are the same as those previously obtained by Gasser and Müller (1979) for linear smoothers. The estimate satisfies a minimax property, i.e. it minimizes the maximal asymptotic variance as the error distributions vary over a…

回归模型与有序分类变量AI 解读

SUMMARY A general approach to regression modelling for ordered categorical response variables, y, is given, which is equally applicable to ordered and unordered y. The regressor variables xT = (x 1 ,…,xp) may be continuous or categorical. The method is based on the logistic family which contains a hierarchy of regression models, ranging from ordered to unordered models. Ordered properties of the former, the stereotype model, are established. The choice between models is made…

若干入样概率与规模成比例的抽样方法AI 解读

SUMMARY This article proposes a sampling scheme which involves creating a sampling design to ensure inclusion probability proportional to size selection. The sampling design is created through constructing a sample space in which the population units occur in proportion to their sizes and every pair of units occurs in such a way as to provide a non-negative and stable variance estimator. The selection procedure is then extremely simple and the values of the inclusion…

主成分的敏感性AI 解读

SUMMARY Simple analytical expressions are derived for the maximum changes in the coefficients of any principal component that are associated with a given (small) change in the variance of the component. This enables a sensitivity analysis to be conducted simultaneously with any principal component analysis, to investigate the stability of the derived components. This has implications for the interpretation of any set of components. A brief illustration is provided, and…

岭估计与 Stein 估计的另一种经验贝叶斯解释AI 解读

SUMMARY Ridge and Stein-like estimators have been motivated as being empirical Bayes estimates with respect to the prior β ~ N(0, τ2 V- 1) for the vector of regression coefficients β in the usual model y = Xβ + ϵ, where the hyperparameter τ2 is estimated from the data. V = I results in a ridge pattern of shrinkage while V = Xt X gives a Stein-like pattern. In this article an alternative formulation is considered, according to which the data represent a sample from a…

空间点模式的似然分析AI 解读

SUMMARY The likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns. Approximation methods of the normalizing factor of Gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness (or hardness) of repulsive interactions. The approximations are useful up to a considerably high density. The validity of our procedure is demonstrated…