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自回归模型中若干预测量的有限样本性质AI 解读

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O ( T −1 ), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three…

分段线性预算约束的计量经济学AI 解读

This article presents a Monte Carlo evaluation of some alternative estimators for a demand model when the budget constraint is piecewise-linear and the budget set is convex. We examine the performance of two maximum likelihood (ML) estimators and an ordinary least squares (OLS) estimator under varying sample sizes and error variances. A simple log-linear demand function, with income and price as the explanatory variables, is specified. Although I find that the OLS bias…

线性回归误差方差的预检验估计AI 解读

We derive exact finite-sample expressions for the biases and risks of several common pretest estimators of the scale parameter in the linear regression model. These estimators are associated with least squares, maximum likelihood and minimum mean squared error component estimators. Of these three criteria, the last is found to be superior (in terms of risk under quadratic loss) when pretesting in typical situations.

非平稳分类时间序列回归模型：渐近估计理论AI 解读

For the analysis of nonstationary categorical time series, a parsimonious and flexible class of models is proposed. These models are generalizations of regression models for stochastically independent categorical observations. Consistency, asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements. Some models for binary time series are discussed in detail. To demonstrate asymptotic properties, a theorem is…

有向图的贝叶斯模型AI 解读

Holland and Leinhardt (1981) proposed a simple exponential model called the p 1 model for analyzing digraphs that arise in studies of networks. A digraph consists of a set of g nodes and a g × g adjacency matrix (Xij ), where Xij = 1 if node i relates to node j and Xij = 0 otherwise. The underlying cell probabilities pij = Pr(Xij = 1) are to be estimated from these dichotomous responses. The p 1 model imposes an additive structure on a log-odds version of the pij . It…

发现新物种概率的非参数估计AI 解读

A random sample is taken from a population consisting of an unknown number of distinct species. A quantity of interest is the probability of discovering a new species when an additional draw from the population is made. An estimator of this quantity was introduced by Starr (1979). We prove a conjecture of Starr's that the estimator is uniformly minimum variance unbiased and give various asymptotic properties of the estimator. A nonparametric maximum likelihood estimator that…

改进的 Bootstrap 置信区间AI 解读

We consider the problem of setting approximate confidence intervals for a single parameter θ in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, , can be quite misleading. In practice, tricks based on transformations, bias corrections, and so forth, are often used to improve their accuracy. The bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to…

重复测量的最大似然计算：EM 算法的应用AI 解读

The purpose of this article is to consider the use of the EM algorithm (Dempster, Laird, and Rubin 1977) for both maximum likelihood (ML) and restricted maximum likelihood (REML) estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure (Anderson 1973). Several models and methods of analysis have been proposed in recent years for repeated measures data; Ware (1985) presented an overview. Because the EM…

共同相对风险的估计：平等就业中的应用AI 解读

To analyze hiring data in equal employment cases, the available positions should be stratified in accordance with the qualifications needed for the jobs. It is then necessary to combine the results of each stratum to obtain an overall test of equal hiring rates. Furthermore, a summary measure, which compares the hiring rate of a minority applicant to that of a majority one, is then estimated. Indeed, the relative risk measure is used by the government in assessing an…

非连续观测时间序列参数估计量的渐近分布AI 解读

The asymptotic normal distributions of two estimators, the maximum likelihood estimator and an alternative weighted least-squares estimator proposed by Wincek & Reinsel (1986) for parameter estimation of autoregressive-moving average models with nonconsecutively observed or missing data are derived for the stationary first-order autoregressive model, and also for the moving average model under periodic A-B sampling. Numerical comparisons of the explicit asymptotic variances…

共同主成分模型的两种推广AI 解读

Under the common principal component model the covariance matrices Ψi, of k populations are assumed to have identical eigenvectors, that is, the same orthogonal matrix diagonalizes all Ψi, simultaneously. This paper modifies the common principal component model by assuming that only q out of p eigenvectors are common to all Ψi, while the remaining p–q elgenvectors are specific in each group. This is called a partial common principal component model. A related modification…

半非参数最大似然估计AI 解读

Often maximum likelihood is the method of choice for fitting an econometric model to data but cannot be used because the correct specific ation of (multivariate) density that defines the likelihood is unknown. In this situation, simply put the density equal to a Hermite series and apply standard finite dimensional maximum likelihood methods. Model parameters and nearly all aspects of the unknown density itself will be estimated consistently provided that the length of the…

切比雪夫多项式逼近与特征函数估计AI 解读

SUMMARY A new procedure for estimating characteristic functions based on a Chebyshev polynomial expansion for the density of the Cosine is developed. Simulation results confirm the usefulness of the method. It is applied to the estimation of two stochastic process models for daily stock returns. The Press compound events model is also estimated by maximum likelihood methods. Results are suggestive of the adequacy of the compound events model and the vg model (a variant of…

自回归移动平均参数的稳健一致估计AI 解读

We aim at estimates of autoregressive-moving average parameters which are simultaneously consistent at the nominal Gaussian model and insensitive to outliers in the data. The estimates may be viewed as a robust version of maximum likelihood estimates of order r and, for purely autoregressive models, reduce to a special case of generalized M-estimates.

嵌套随机效应非平衡混合模型极大似然估计的快速评分算法AI 解读

A fast Fisher scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects is described. The algorithm uses explicit formulae for the inverse and the determinant of the covariance matrix, given by LaMotte (1972), and avoids inversion of large matrices. Description of the algorithm concentrates on computational aspects for large sets of data.

《自回归时间序列集合的估计与假设检验》的公式更正AI 解读

Formulae for ψ^(α) and σ^2(α) on p. 87 do not hold for all α, since they may not satisfy the constraint σ^2(α)≤ψ^(α) induced by the parameterization. Then the expressions do not give maximum likelihood estimates for given α. When the inequality fails, the maximum likelihood estimates are on the boundary of the parameter space, namely where σ2=ψ⁠. The maximum then occurs for σ^2(α)=ψ^(α) both equal to σ^2(α) given at p. 88, shortly after (7). Formula (6) still applies,…

一阶自回归参数的渐消窗估计AI 解读

In the estimation of autoregressive parameters, biases from ordinary least-squares or maximum likelihood estimator are big even for moderately large sample sizes. A new tapering estimation technique is developed to reduce the bias. Monte Carlo experiments show that the tapering estimation in the time domain yields a substantial reduction in the bias when autoregressive parameters are positive and not very near unity, over a wide range of sample sizes.

空间高斯过程协方差函数似然估计的问题AI 解读

Maximum likelihood has frequently been suggested as a way to estimate covariance parameters in spatial Gaussian processes. The results of some simple examples based on simulated data are discussed. It is shown by an example with real data that the profile likelihood can be multimodal, and that the global maximum may not correspond to a sensible value of the parameters.

关于多元岭回归AI 解读

A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p × q parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the ‘across regression’ correlations, and ignores the Stein effect. A remedy was offered by Brown & Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting…

二维格点上的内蕴自回归及相关模型AI 解读

Stationary autoregressions on a two-dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary. Prediction formulae and the asymptotic behaviour of the semivariogram are derived. For parameter estimation we propose an approximate maximum likelihood estimator, a generalization of Whittle's estimator; it is derived also for general intrinsic models.

利用平滑方法诊断二元 Logistic 回归AI 解读

The paper discusses some diagnostic tools for binary logistic regression which use smoothing techniques. Smoothed binary data are employed to devise a battery of diagnostic plots, from simple procedures which indicate only the adequacy or inadequacy of a maximum likelihood logistic fit, to partial residual plots and delta local deviance plots which reveal the type of model inadequacy, suggesting perhaps the addition of nonlinear terms or interactions. Properties of the…

球面角中心高斯分布的统计分析AI 解读

The angular central Gaussian distribution is an alternative to the Bingham distribution for modeling antipodal symmetric directional data. In this paper the statistical theory for the angular central Gaussian model is presented. Some topics treated are maximum likelihood estimation of the parameters, testing for uniformity and circularity, and principal components analysis. Comparisons to methods based upon the sample second moments are made via an example.

Frank 二元分布族AI 解读

This paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent. The proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the Fréchet bounds as well as the distribution corresponding to independent variables. Three nonparametric estimators of the association parameter are suggested and Monte Carlo experiments are used to…