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列联表典型分析的最大似然方法AI 解读

Canonical analysis has often been employed instead of log-linear models to analyze the relationship of two polytomous random variables; however, until the last few years, analysis has been informal. In this article, models are examined that place nontrivial restrictions on the values of the canonical parameters so that a parsimonious description of association is obtained. Maximum likelihood is used to obtain parameter estimates for these restricted models. Approximate…

抽样设计对主成分分析的影响AI 解读

Most sample surveys are multivariate and many lend themselves to multivariate methods of analysis. The most usual mode of such analysis is a standard statistical package, such as BMDP or SPSS, in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution. This assumption ignores the sample selection procedure involved in the survey, which leads to the following basic…

部分删失数据的半马尔可夫模型札记AI 解读

A recharacterization of the semi-Markov model described by Lagakos, Sommer & Zelen (1978) permits the nonparametric maximum likelihood estimators to be expressed in terms of familiar and easily computable quantities, such as event-specific hazard estimators and Kaplan & Meier (1958) survival estimators. In addition to simplifying the calculation and clarifying the interpretation of the previously derived estimators, this reformulation also facilitates the estimation of…

近似预测似然AI 解读

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot…

允许非连续观测的回归—ARMA时间序列模型精确极大似然估计AI 解读

SUMMARY An explicit procedure is given to obtain the exact maximum likelihood estimates of the parameters in a regression model with ARMA time series errors with possibly nonconsecutive data. The method is based on an innovation transformation approach from which an explicit recursive procedure is derived for the efficient calculation of the exact likelihood function and associated derivatives. The innovations and associated derivatives are used to develop a modified…

摘要暂缺

分段线性预算约束的计量经济学：综述与最大似然方法阐释AI 解读

Robert Moffitt, The Econometrics of Piecewise-Linear Budget Constraints: A Survey and Exposition of the Maximum Likelihood Method, Journal of Business & Economic Statistics, Vol. 4, No. 3 (Jul., 1986), pp. 317-328

分段线性预算约束的计量经济学AI 解读

In this article maximum likelihood techniques for estimating consumer demand functions when budget constraints are piecewise linear are exposited and surveyed. Consumer demand functions are formally derived under such constraints, and it is shown that the functions are themselves nonlinear as a result. The econometric problems in estimating such functions are exposited, and the importance of the stochastic specification is stressed, in particular the specification of both…

随机删失数据的卡方拟合优度检验AI 解读

Two Pearson-type goodness-of-fit test statistics for parametric families are considered for randomly right-censored data. Asymptotic distribution theory for the test statistics is based on the result that the product-limit process with MLE for nuisance parameters converges weakly to a Gaussian process. The Chernoff-Lehmann (1954) result extends to a generalized Pearson statistic. A modified Pearson statistic is shown to have a limiting chi-square null distribution.

估计量的大偏差AI 解读

The performance of a sequence of estimators $\{T_n\}$ of $g(\theta)$ can be measured by its inaccuracy rate $-\lim \inf_{n\rightarrow\infty} n^{-1} \log \mathbb{P}_\theta(\|T_n - g(\theta)\| > \varepsilon)$. For fixed $\varepsilon > 0$ optimality of consistent estimators $\operatorname{wrt}$ the inaccuracy rate is investigated. It is shown that for exponential families in standard representation with a convex parameter space the maximum likelihood estimator is optimal. If…

广义加性模型的降维原理AI 解读

Let $(X, Y)$ be a pair of random variables such that $X = (X_1,\cdots, X_J)$ ranges over $C = \lbrack 0, 1\rbrack^J$. The conditional distribution of $Y$ given $X = x$ is assumed to belong to a suitable exponential family having parameter $\eta \in \mathbb{R}$. Let $\eta = f(x)$ denote the dependence of $\eta$ on $x$. Let $f^\ast$ denote the additive approximation to $f$ having the maximum possible expected log-likelihood under the model. Maximum likelihood is used to fit an…

共同主成分分析的渐近理论AI 解读

Under the common principal component model $k$ covariance matrices $\mathbf{\Sigma}_1,\cdots,\mathbf{\Sigma}_k$ are simultaneously diagonalizable, i.e., there exists an orthogonal matrix $\mathbf{\beta}$ such that $\mathbf{\beta'\Sigma_i\beta = \Lambda_i}$ is diagonal for $i = 1,\cdots, k$. In this article we give the asymptotic distribution of the maximum likelihood estimates of $\mathbf{\beta}$ and $\mathbf{\Lambda}_i$. Using these results, we derive tests for (a) equality…

多元方差分量模型的极大似然估计与似然比准则AI 解读

Maximum likelihood estimators are obtained for multivariate components of variance models under the condition that the effect covariance matrix is positive semidefinite with a maximum rank. The rank of the estimator is random. The estimation procedure leads to a likelihood ratio test that the rank of the effect matrix is not greater than a given number against the alternative that the rank is not greater than a larger specified number. Linear structural relationship models…

ε 污染先验下的稳健贝叶斯与经验贝叶斯分析AI 解读

For Bayesian analysis, an attractive method of modelling uncertainty in the prior distribution is through use of $\varepsilon$-contamination classes, i.e., classes of distributions which have the form $\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, \pi_0$ being the base elicited prior, $q$ being a "contamination," and $\varepsilon$ reflecting the amount of error in $\pi_0$ that is deemed possible. Classes of contaminations that are considered include (i) all possible…

期望频数受线性约束时对数线性模型的最大似然方法AI 解读

Hypotheses relating to log-linear models may be defined in terms of constraints on the frequencies or on the logarithms of the frequencies. A two-step algorithm is developed to allow fitting models containing constraints of both types. This algorithm is shown to yield maximum likelihood estimates of the log-linear parameters. Three examples are presented to illustrate cases in which these models are of interest.

死因数据不完整时动物实验患病率与死亡率的非参数估计AI 解读

Age-specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity. Nonparametric maximum likelihood estimators for the prevalence and mortality functions are available for the case in which incidental and fatal occurrences of a disease can always be distinguished. This article generalizes these methods to allow the role of a disease in causing death to be uncertain for a subset of the…

稀疏列联表中对数线性模型的拟合优度检验AI 解读

The asymptotic normality of the likelihood ratio goodness-of-fit statistic is demonstrated for testing the fit of log-linear models with closed form maximum likelihood estimates in sparse contingency tables. Unlike the traditional chi-squared theory, the number of categories in the table increases as the sample size increases, but not all of the expected frequencies are required to become large. Some results of a small Monte Carlo study are presented. The traditional…

摘要暂缺

零贝塔收益最大似然估计量的几何结构AI 解读

ABSTRACT This paper explores geometric relations, in mean‐variance space, among the sample frontier, the maximum likelihood estimator, and two other estimators of the zerobeta return. It is also demonstrated that a partition of the portfolio space is determined by a family of parabolas; the zeros of each parabola are the maximum likelihood estimators associated with all portfolios on the parabola. This observation is the basis for an additional interpretation of the…

摘要暂缺

关于线性模型中可行 GLS、准极大似然、稳健、自适应和谱估计量无偏性的札记AI 解读

Donald W. K. Andrews, A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust, Adaptive, and Spectral Estimators of the Linear Model, Econometrica, Vol. 54, No. 3 (May, 1986), pp. 687-698

联立方程 Tobit 模型的外生性检验及其劳动供给应用AI 解读

A test of weak exogeneity in the simultaneous equation Tobit model is proposed and illustrated using a female labour supply model estimated using cross-section data. The test statistic can be simply output from any standard Tobit maximum likelihood package, and is asymptotically efficient. The procedure provides consistent estimators for the simultaneous Tobit model whose asymptotic covariance matrix is a simple extension of the usual Tobit formula. We also provide the…

二元泊松分布的偶点估计AI 解读

Estimation of the parameters in the bivariate Poisson distribution by the methods of maximum likelihood, moments and double zero proportion was considered by Holgate (1964). An alternative estimation procedure, the even points method, is studied, asymptotic efficiencies are examined and comparisons with moment estimators are given.

分数差分时间序列建模AI 解读

Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy.