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不等间隔纵向数据中的序列相关AI 解读

Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed…

服从 Gamma 分布的随机前沿模型AI 解读

We modify the stochastic frontier model of Aigner, Lovell, and Schmidt to allow the one-sided part of the disturbance to have a two-parameter Gamma distribution rather than the less flexible half-normal distribution. Maximum-likelihood estimation and the estimation of firm-specific inefficiency estimates require the evaluation of integrals which have no closed form and for which there are no polynomial approximations available. We consider two methods of computing these…

多元自回归移动平均时间序列理论自协方差矩阵的计算AI 解读

SUMMARY Matrix expressions relating the theoretical autocovariances of autoregressive moving average (ARMA) processes to their parameters are derived and used to design an efficient procedure for computing autocovariance sequences of multivariate ARMA processes. The method proposed is more efficient than others suggested in the literature and, in particular, reduces the computational burden associated with exact maximum likelihood estimation of ARMA models. The closed form…

L-矩：利用次序统计量的线性组合分析与估计分布AI 解读

SUMMARY L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves…

检验偏离常数均值的综合检验AI 解读

Observations $y_i$ are made at points $x_i$ according to the model $y_i = F(x_i) + e_i$, where the $e_i$ are independent normals with constant variance. In order to decide whether or not $F(x)$ is constant, a likelihood ratio test is constructed, comparing $F(x) \equiv \mu$ with $F(x) = \mu + Z(x)$, where $Z(x)$ is a Brownian motion. The ratio of error variance to Brownian motion variance is chosen to maximize the likelihood, and the resulting maximum likelihood statistic $B$…

基于累积风险率的生命历程数据模型拟合优度检验AI 解读

To check the validity of an assumed parametric model for survival data, one may compare $\hat{A}(t)$, the nonparametric Nelson-Aalen plot of the cumulative hazard rate, with $A(t, \hat{\theta})$, the estimated parametric cumulative hazard rate, $\hat{\theta}$ being for example the maximum likelihood estimator. Convergence in distribution of $\sqrt n (\hat{A}(t) - A(t, \hat{\theta}))$ and more general processes is studied in the present paper, employing the general framework…

扩散过程不完全观测渐近充分性的一个充分条件AI 解读

Consider an $m$-dimensional diffusion process $(X_t)$ with unknown drift and small known variance observed on a time interval $\lbrack 0, T\rbrack$. We derive here a general condition ensuring the asymptotic sufficiency, in the sense of Le Cam, of incomplete observations of $(X_t)_{0 \leq t \leq T}$ with respect to the complete observation of the diffusion as the variance goes to 0. We then construct estimators based on these partial observations which are consistent,…

随机过程参数估计中广义交叉验证与修正最大似然的比较AI 解读

Wahba compared the performance of generalized cross validation (GCV) and modified maximum likelihood (MML) procedures for choosing the smoothing parameter of a smoothing spline. This work makes a more careful study of the two procedures when the stochastic model motivating the modified maximum likelihood estimate is correct. In particular, it is shown that in the case of the linear smoothing spline with equally spaced observations, both estimates are asymptotically normal…

Let $l(\theta) = n^{-1} \log p(x, \theta)$ be the log likelihood of an $n$-dimensional $X$ under a $p$-dimensional $\theta$. Let $\hat{\theta}_j$ be the mle under $H_j: \theta^1 = \theta^1_0, \ldots, \theta^j = \theta^j_0$ and $\hat{\theta}_0$ be the unrestricted mle. Define $T_j$ as $\lbrack 2n\{l(\hat{\theta}_{j - 1}) - l(\hat{\theta}_j)\}\rbrack^{1/2} \operatorname{sgn}(\hat{\theta}^j_{j - 1} - \theta^j_0).$ Let $T = (T_1, \ldots, T_p)$. Then under regularity conditions,…

广义线性模型中的不完全数据AI 解读

This article examines incomplete data for the class of generalized linear models, in which incompleteness is due to partially missing covariates on some observations. Under the assumption that the missing data are missing at random, it is shown that the E step of the EM algorithm for any generalized linear model can be expressed as a weighted complete data log-likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range.…

利用正交级数指数形式进行密度估计AI 解读

If a density is represented as an exponential of a series of orthogonal polynomials, it has a simple likelihood with a complete set of sufficient statistics. To ensure that the maximum likelihood equations are well conditioned, the polynomials should be orthogonal with respect to the estimated density. The optimal number of terms in the series can be determined by minimizing an estimate of a loss function. The penalized likelihood equations can be solved with little extra…

含替代预测变量模型的近似拟似然估计AI 解读

We consider quasi-likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error. We review and extend four approaches to estimation in this problem, all of them based on small measurement error approximations. A taxonomy of the data sets likely to be available in measurement error studies is developed. An asymptotic theory based on this taxonomy is obtained and includes measurement error and Berkson error models…

采用广义Mantel–Haenszel估计量的列联表齐性检验AI 解读

A conditional test for the homogeneity of the odds ratios in L2 × K (K > 2) tables is developed based on a multiple hypergeometric distribution. The test is a generalization of the Breslow-Day test (1980) and is useful in sparse tables. For computational feasibility, the conditional maximum likelihood estimator is replaced by a consistent but inefficient estimator in the test statistic. If this is the case, it is shown that the asymptotic distribution is not chi squared, as…

利用正交级数指数形式进行密度估计AI 解读

If a density is represented as an exponential of a series of orthogonal polynomials, it has a simple likelihood with a complete set of sufficient statistics. To ensure that the maximum likelihood equations are well conditioned, the polynomials should be orthogonal with respect to the estimated density. The optimal number of terms in the series can be determined by minimizing an estimate of a loss function. The penalized likelihood equations can be solved with little extra…

利用二次指数模型分析相关二元响应AI 解读

A model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data. Pseudo-maximum likelihood methods using a special case termed the multiplicative model are proposed, but are noted to be computationally unattractive if the ‘blocks’ of correlated responses are at all large. On the other hand score estimating functions for mean and correlation parameters are shown to be of a…

利用逻辑回归调整无应答偏差AI 解读

A method of adjustment for nonresponse is considered. No information about the nonrespondents is required, but the respondents are assumed to answer all questions of interest. One or more call-backs are assumed. The probabilities of response are represented by a logistic regression model, in which variables in the survey are explanatory variables. The probabilities are estimated using a modified conditional maximum likelihood approach, based on the respondents. The estimated…

多个变化点的最大似然估计AI 解读

Maximum likelihood estimation of the locations of changes in sequences of independent categorical random variables when there are known lower bounds on the lengths of the sub-sequences between the change points is discussed. A method is developed which finds one of the maximum likelihood solutions. The problem of estimating the number of changed segments is discussed and some numerical results about the precision of the estimates of the locations of changes are presented.…

亲代与子代相关系数的估计AI 解读

When families have different numbers of offspring, Srivastava (1984) provided an easily computable estimator as an alternative to the maximum likelihood estimator of parent-offspring correlation. Some properties of this estimator are discussed vis-à-vis with those of ensemble and pairwise estimators. Further, we derive the small sample distribution of Srivastava's estimator under the assumption of null parent-offspring correlation. In the process, we demonstrate that a…

家庭数据中组内相关的最大似然估计：估计方程方法AI 解读

We introduce a generalized model for estimating intraclass correlation in the analysis of familial data. This model incorporates the models of Donner & Koval (1980), Donner & Bull (1983), Rosner (1984) and Münoz, Rosner & Carey (1986) as special cases. We then obtain the maximum likelihood estimates of the parameters of the model. In particular we obtain a single estimating equation, to be solved iteratively, for the estimation of the intraclass correlation p and discuss all…

结构方程的归一化：方向估计量的性质AI 解读

In the general structural equation model only the direction of the vector of coefficients of the endogenous variables is determined.The traditional normalization rule defines the coefficients that are of interest but should not be embodied in the estimation procedure: we show that the properties of the traditionally defined ordinary least squares and two stage least squares estimators are distorted by their dependence on the normalization rule.Symmetrically normalized…

理性预期模型的全信息估计与随机模拟AI 解读

Abstract A computationally feasible method for the full information maximum‐likelihood estimation of models with rational expectations is described in this paper. The stochastic simulation of such models is also described. The methods discussed in this paper should open the way for many more tests of the rational expectations hypothesis within macroeconomic models.

宏观经济系统中的协整AI 解读

Abstract This paper investigates the long‐run relationships within a set of six quarterly time‐series on the Austrian economy by means of cointegration. After analysing the univariate properties, especially with respect to the appropriate seasonal filter, the maximum‐likelihood method proposed by Johansen (1988) is applied to estimate and test the cointegrating relationships. We found three such relations, implying that the system is driven by three independent stochastic…

EM 算法在惩罚似然估计中的应用AI 解读

SUMMARY The EM algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation. This paper discusses properties of the EM algorithm in such contexts, concentrating on rates of convergence, and presents an alternative that is usually more practical and converges at least as quickly.

工作离职的动态：联邦雇员案例AI 解读

Abstract In this paper we develop a model of workers' quit decisions . Using panel data on a sample of US Federal government employees we use maximum‐likelihood techniques to determine how much of the observed decline in quits with job tenure is a result of declining individual quit propensities (‘state dependence’) rather than dynamic sample self‐selection (‘heterogeneity’). The latter is found to be much more important than the former. The effects of relative Federal…