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似然比统计量的 Bartlett 调整与最大似然估计量的分布AI 解读

SUMMARY For rather general parametric models, a simple connection is established between the Bartlett adjustment factor of the log-likelihood ratio statistic and the normalizing constant c of the formula c | ĵ |½ L̄ for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested. This leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or…

随机效应模型的一种新贝叶斯分析AI 解读

SUMMARY For a typical random effects model in the one way analysis of variance a new Bayesian analysis is offered. An exchangeable prior distribution is defined over the parameters. It is suggested that rather than use the usual “F” test one should consider this as an estimation problem. The posterior distribution of a function of the parameters which measures the amount of variation present is found.

混合比例的有效非参数估计AI 解读

SUMMARY By constructing a sequence of multinomial approximations and related maximum likelihood estimators, we derive a Cramér-Rao lower bound for nonparametric estimators of the mixture proportions and thereby characterize asymptotically optimal estimators. For the case of the sampling model M2 of Hosmer (1973) it is shown that the sequence of maximum likelihood estimators, which can be obtained explicitly, is asymptotically optimal in this sense. The results hold true even…

多项分布的拟合优度检验AI 解读

SUMMARY This article investigates the family {I λ;λ ϵ ℝ} of power divergence statistics for testing the fit of observed frequencies {Xi; i = 1, …, k} to expected frequencies {Ei; i = 1, …, k}. From the definition 2nIλ=2λ(λ+1)∑i=1kXi{(XiEi)λ−1};λ∈ℝ it can easily be seen that Pearson's X 2 (λ = 1), the log likelihood ratio statistic (λ = 0), the Freeman-Tukey statistic (λ = –½) the modified log likelihood ratio statistic (λ = –1) and the Neyman modified X 2 (λ = –2), are all…

某类指数模型中条件极大似然估计量的渐近行为AI 解读

SUMMARY In this paper we investigate the asymptotic behaviour of the conditional maximum likelihood estimator in an exponential model of order 2 introduced in Bar-Lev and Reiser (1982). This model, with natural parameters θ1 and θ2 (the latter a nuisance parameter), is characterized by expressing θ2 as a particular function of the mixed parameters. A direct proof is given for the asymptotic equivalence of the conditional maximum likelihood estimator and the maximum…

累积量具有幂级数形式时的分布与分位数渐近展开AI 解读

SUMMARY Cornish and Fisher (1937) gave the first few terms of the formal expansions for the distribution and percentiles of an asymptotically normal random variable (r.v.) in terms of its cumulants. They also showed that these expansions can sometimes produce extremely accurate approximations. In practice the cumulants are first expanded as a power series in a known parameter n (such as the sample size or degrees of freedom), and these expansions are substituted into the…

贝叶斯线性回归中的异常值模型与先验分布AI 解读

SUMMARY Bayesian inference in regression models is considered using heavy-tailed error distributions to accommodate outliers. The particular class of distributions that can be constructed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in Bayesian linear modelling, including simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters.

含外生变量的向量时间序列模型误设检验AI 解读

SUMMARY In this paper we consider the application of hypothesis testing procedures to ARMAX systems. The score, or Lagrangian multiplier, principle is used to obtain mis-specification tests appropriate to these models. The structure of the information or sensitivity matrix is investigated in order to discuss the identifiability of alternative models and is used to show the existence of a set of admissible alternatives that are locally equivalent to one another. This notion…

一种预测导向的模型选择准则AI 解读

SUMMARY A procedure for model selection is presented which chooses the model that gives the best prediction of the future observation. The predictive distributions associated with each model are compared by means of the logarithmic utility function. For two nested normal linear models, the choice criterion is the product of the posterior odds ratio and a factor depending on the design point of the future observation. Taking appropriate mean values, a criterion is obtained…

广义均方误差准则下比较估计量的检验AI 解读

SUMMARY This paper presents an asymptotic test for comparing alternative estimators of regression coefficients in terms of the generalized mean square error criterion. The paper also reports the outcome of a Monte Carlo experiment which was conducted to determine the small sample properties of the test statistic. These results indicate that the asymptotic test may be applied successfully even when the sample size is small.

关于《调查数据的卡方检验》的一则说明AI 解读

SUMMARY In their paper “Chi-squared tests with survey data”, Holt et al. give a correction factor for the chi-squared test of independence from survey data. We obtain an expression for this factor in terms of the cell and marginal proportions and the asymptotic variances of their estimates.

回归估计量的可容许性AI 解读

SUMMARY Admissibility of the regression estimator is established for two types of sampling designs: single stage sampling using probability proportional to a size variable and double sampling.

利用不完整数据递归估计参数AI 解读

SUMMARY Stochastic approximation procedures are considered for the estimation of parameters using incomplete data. One procedure is stated and illustrated which often leads to asymptotically efficient estimators. Others are developed which, although possibly not optimal in the above sense, will be very much easier to apply. This will be particularly advantageous when quick recursive estimates are required. Examples are given and a link is made between one of the sub-optimal…

比例优势模型中干扰参数的消除AI 解读

SUMMARY The problem of eliminating nuisance parameters in the context of the proportional odds model is considered. The technique used involves a form of sequential conditioning but it is not equivalent to a conditional or partial likelihood. Applications to ordered responses in the context of a matched pairs design are considered but the method can also be used where the responses are continuous.

被选中负指数分布总体的均值估计AI 解读

SUMMARY Let Xi be independent, negative exponentially distributed with unknown expectation λi, i = 1, …, k. Let J and M denote the (random) indices of the maximal and minimal observation, respectively. The paper considers estimation of the random quantities λJ and λM. The loss function is (a – λM)2/λ2 M for λM, and correspondingly for λJ. UMVUE and minimax estimators are shown to exist and are exhibited, and certain other reasonable estimators are discussed.

Greenwood统计量及其若干推广的渐近结果AI 解读

SUMMARY There has been a renewed interest in the Greenwood statistic for goodness of fit and its percentage points. See Burrows (1979), Currie (1981) and Stephens (1981). This statistic, which is based on the sum of squares of the sample spacings, is known to be locally most powerful among all tests based symmetrically on the simple one-step spacings. This paper discusses some generalizations of this statistic based on higher-order or m-step spacings and shows them to be…

隐式统计模型推断的蒙特卡洛方法AI 解读

SUMMARY A prescribed statistical model is a parametric specification of the distribution of a random vector, whilst an implicit statistical model is one defined at a more fundamental level in terms of a generating stochastic mechanism. This paper develops methods of inference which can be used for implicit statistical models whose distribution theory is intractable. The kernel method of probability density estimation is advocated for estimating a log-likelihood from…

用于极大似然估计及稳健替代准则的迭代重加权最小二乘AI 解读

SUMMARY The scope of application of iteratively reweighted least squares to statistical estimation problems is considerably wider than is generally appreciated. It extends beyond the exponential-family-type generalized linear models to other distributions, to non-linear parameterizations, and to dependent observations. Various criteria for estimation other than maximum likelihood, including resistant alternatives, may be used. The algorithms are generally numerically stable,…

利用样本自相关估计时间序列参数AI 解读

SUMMARY Consider a scalar linear process {xt} whose spectral density is σ 2 k(λ, θ 0) where σ2 is the innovation variance and k(⋅,θ0)∈{k(⋅,θ):θ∈S⊂ℝq}. We introduce a class of estimators of θ0 based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is…

列联表中的序列依赖AI 解读

SUMMARY A simple and useful representation is given for the asymptotic behaviour of the Pearson χ 2 test of independence in two-way contingency tables. This is used to analyse the statistic when the data are generated by Markov chains. A robustness result, showing when the Markov dependence has no effect on the usual limiting χ2 distribution, is also given.

分布函数的正交级数估计及其应用AI 解读

SUMMARY Motivated by applications to the non-parametric estimation of mixture proportions, we develop techniques for multivariate orthogonal series estimation of distribution functions. We approximate the empiric distribution function, rather than the true distribution function. This enables us to use trigonometric series methods to estimate distribution functions with unbounded support.

AR(p)模型对含测量误差AR(p)模型的单侧拉格朗日乘子检验AI 解读

SUMMARY The one-sided Lagrange multiplier test is suggested for testing the null autoregressive (AR) model against the AR model with measurement error. The test statistic is shown to be asymptotically N(0, 1) under the null. Finite sample properties of the test both under the null and under the alternative are examined briefly by simulations.

利用先验信息估计列联表概率AI 解读

SUMMARY Prior beliefs of association and independence in a two-way contingency table are discussed, and estimators of the cell probabilities are proposed which can incorporate this prior information. In the 2 × 2 table where the cell counts are assumed to have a multinomial distribution, estimators are developed which can incorporate prior beliefs about the correlation coefficient and the cross-product ratio. In the I × 2 table in which one set of marginal totals is fixed,…

回归中的舍入误差：Sheppard 修正的适用性AI 解读

SUMMARY We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, “regular” independent…