论文检索

含误差成分动态模型的估计AI 解读

Observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit. Different assumptions about the initial conditions are (a) initial state fixed, (b) initial state random, (c) the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed, and (d) the unobserved individual effect independent of the unobserved…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

摘要暂缺

摘要暂缺

摘要暂缺

家族数据分析：线性模型方法AI 解读

A linear-model approach is proposed for deriving the maximum likelihood estimates of the mother–sib interclass correlation and other parameters from familial data when the families have unequal numbers of offspring. It leads to an algorithm which involves the maximization of an explicit function of a variable for estimating one parameter and direct substitutions for other parameters. The algorithm is believed to be much simpler and more practical than that proposed by Rosner…

二元响应数据的两类加性化变换AI 解读

Two families of power transformations for probabilites are introduced to model symmetric and asymmetric departures from the logistic model. The aim is to provide, in a comprehensive way, a representation of alternative scales in terms of which to carry out the analysis of binary response data. Maximum likelihood methods are empolyed to estimate an appropriate transformation using GLIM. Tests for detection of symmetric and asymmetric departures are proposed.

多变量线性关系：最大似然估计与回归界限AI 解读

Summary The well known result that, when the ratio of error variances is specified in normal theory bivariate linear relationships, the maximum likelihood estimator of the slope parameter takes the same form for both structural and functional relationships is extended to the multivariate case. Furthermore, it is well known that in the bivariate case the estimator of the slope is bounded by the two regression estimators. Analogous results are derived for the multivariate…

二项响应模型中最大似然估计量的存在性AI 解读

Summary Necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response (this includes Logit and Probit) models.

伪最大似然估计：理论与应用AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. random variables with probability distribution $F_{\theta, p}$ indexed by two real parameters. Let $\hat{p} = \hat{p}(X_1, \cdots, X_n)$ be an estimate of $p$ other than the maximum likelihood estimate, and let $\hat{\theta}$ be the solution of the likelihood equation $\partial/\partial \theta \ln L(\mathbf{x}, \theta, \hat{p}) = 0$ which maximizes the likelihood. We call $\hat{\theta}$ a pseudo maximum likelihood estimate of $\theta$, and…

固定样本量下向量参数极大似然估计的存在性与唯一性AI 解读

The maximum likelihood estimate is shown to exist and to be unique if a twice continuously differentiable likelihood function is constant on the boundary of the parameter space and if the Hessian matrix is negative definite whenever the gradient vector vanishes. The condition of constancy on the boundary cannot be completely removed, cf. Tarone and Gruenhage (1975). The theory is illustrated with several examples.

Logistic 回归诊断AI 解读

A maximum likelihood fit of a logistic regression model (and other similar models) is extremely sensitive to outlying responses and extreme points in the design space. We develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit. The elements of the fitting process which constitute the usual output (parameter estimates, standard errors, residuals, etc.) will be used for this…

用于统计推断的若干傅里叶方法AI 解读

Common statistical procedures such as maximum likelihood and M-estimation admit generalized representations in the Fourier domain. The Fourier domain provides fertile ground for approaching a number of difficult problems in inference. In particular, the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain…

改进有限信息最大似然估计量分布的渐近展开AI 解读

An improvement of the limited information maximum likelihood (LIML) estimator was proposed by Morimune (1978). In this note two asymptotic expansions of the distribution of the improved estimator are derived, both for large sample size and for large values of the noncentrality parameter. The improved estimator uniformly dominates the LIML estimator in terms of the probability of concentration around the true coefficient for both the parameter sequences. The distributions of…

协方差分量模型中的估计AI 解读

Estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes. The estimation of fixed and random effects when the variances and covariances are known is presented in Bayesian terms, Point estimates of the unknown variances and covariances are computed using the EM algorithm for maximum likelihood estimation from incomplete data. The techniques are illustrated with data on law schools,…

重新审视数据变换分析AI 解读

Following Box and Cox (1964), we assume that a transform Z i = h(Yi , λ) of our original data {Yi } satisfies a linear model. Consistency properties of the Box-Cox estimates (MLE's) of λ and the parameters in the linear model, as well as the asymptotic variances of these estimates, are considered. We find that in some structured models such as transformed linear regression with small to moderate error variances, the asymptotic variances of the estimates of the parameters in…

改进有限信息极大似然估计量分布的渐近展开AI 解读

An improvement of the limited information maximum likelihood (LIML) estimator was proposed by Morimune (1978). In this note two asymptotic expansions of the distribution of the improved estimator are derived, both for large sample size and for large values of the noncentrality parameter. The improved estimator uniformly dominates the LIML estimator in terms of the probability of concentration around the true coefficient for both the parameter sequences. The distributions of…

正态性下保序回归的平方损失AI 解读

The maximum likelihood estimator $\hat{\mu}$ of a nondecreasing regression function has been studied in detail in the literature. However, little is known about its quadratic loss pointwise. This paper shows that the mean square error of $\hat{\mu}_i$ is less than that of the usual estimator $\bar{X}_i$ for each $i$ when $\bar{X}_1,\cdots, \bar{X}_k$ are independent normal variates.

条件指数族与渐近推断的表示定理AI 解读

Conditional exponential families of Markov processes are defined and a representation of the score function martingale is established for the important conditionally additive case. This result unifies those obtained separately for different examples and provides the key to asymptotic normality results for the maximum likelihood estimate.

准确且简约的正态线性回归模型的可容许选择AI 解读

Let $M_0$ be a normal linear regression model and let $M_1,\cdots, M_K$ be distinct proper linear submodels of $M_0$. Let $\hat k \in \{0,\cdots, K\}$ be a model selection rule based on observed data from the true model. Given $\hat k$, let the unknown parameters of the selected model $M_{\hat k}$ be fitted by the maximum likelihood method. A loss function is introduced which depends additively on two parts: (i) a measure of the difference between the fitted model $M_{\hat k}$…

封闭种群多次重捕抽样的贝叶斯分析AI 解读

This paper considers from a Bayesian viewpoint inferences about the size of a closed animal population from data obtained by a multiple-recapture sampling scheme. The method developed enables prior information about the population size and the catch probabilities to be utilized to produce considerable improvements in certain cases on ordinary maximum likelihood methods. Several ways of expressing such prior information are explored and a practical example of the uses of…

多重匹配下的相对风险估计AI 解读

Under multiple matching, relative risk from a rare disease is estimated in a retrospective design. Maximum likelihood estimation is carried out using an unconditional probability model. In addition, this model is used to derive a new estimator of relative risk which is noniterative but is as efficient, asymptotically, as the maximum likelihood estimator.

稀疏数据下的优势比估计量AI 解读

The properties of four commonly used estimators of the odds ratio are studied under a large-sample scheme in which the number of 2 × 2 tables increases but the possible marginal configurations remain fixed. Neither the unconditional maximum likelihood nor the empirical logit estimators converge to the true odds ratio; their asymptotic bias is computed for certain special cases of interest. The conditional maximum likelihood and Mantel-Haenszel estimators, which are…