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第二类区间删失下光滑泛函的渐近最优估计AI 解读

For a version of the interval censoring model, case 2, in which the observation intervals are allowed to be arbitrarily small, we consider estimation of functionals that are differentiable along Hellinger differentiable paths. The asymptotic information lower bound for such functionals can be represented as the squared $L_{2}$-norm of the canonical gradient in the observation space. This canonical gradient has an implicit expression as a solution of an integral equation that…

状态空间模型中最大似然估计量的渐近正态性AI 解读

State space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way. Inference in such models has been studied by Bickel, Ritov and Rydén, who consider hidden Markov models, which are special kinds of state space models, and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions. In this paper we generalize the results of Bickel, Ritov and Rydén to state…

近不稳定 AR(p) 过程的渐近推断AI 解读

In this paper nearly unstable AR( p ) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR( p ) models. In this case the…

半参数选择偏差模型的最大似然估计及其艾滋病疫苗试验应用AI 解读

The following problem is treated: given s possibly selection biased samples from an unknown distribution function, and assuming that the sampling rule weight functions for each of the samples are mathematically specified up to a common unknown finite-dimensional parameter, how can we use the data to estimate the unknown parameters? We propose a simple maximum partial likelihood method for deriving the semiparametric maximum likelihood estimator. A discussion of assumptions…

缺失数据非参数分析的递归算法AI 解读

The mixture of Dirichlet processes posterior that arises in nonparametric Bayesian analysis has been analysed most effectively using Markov chain Monte Carlo. As a computationally simple alternative, we introduce a recursive approximation based on one-step posterior predictive distributions. Asymptotic calculations provide theoretical support for this approximation, and we investigate its actual behaviour in several numerical examples. From a non-Bayesian perspective, this…

刻画变点最大似然估计量的分布行为AI 解读

We consider the problem of estimating the unknown changepoint in a sequence of time-ordered observations. Upper and lower bounds are derived for the asymptotic distribution of the maximum likelihood estimator and methods of approximation are suggested. A computationally efficient algorithm is presented for deriving the bounds and approximations for the asymptotic probabilities of the maximum likelihood estimator when the parameters before and after the changepoint are…

The quasi-likelihood function proposed by Wedderburn broadened the scope of generalized linear models by specifying the variance function in-stead of the entire distribution. However, complete specification of variance functions in the quasi-likelihood approach may not be realistic. We define a nonparametric quasi-likelihood by replacing the specified variance function in the conventional quasi-likelihood with a nonparametric variance function estimate. This nonparametric…

随机逼近版 EM 算法的收敛性AI 解读

The expectation-maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations, however, this method is not applicable because the expectation step cannot be performed in closed form. To deal with these problems, a novel method is introduced, the stochastic approximation EM (SAEM), which replaces the…

泊松过程同质性的调整得分检验AI 解读

Tests of homogeneity are being increasingly used for the analysis of event time data, but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes. Here we consider tests of homogeneity for recurrent event data in which the null model is a Poisson process and the alternative is a mixed Poisson process. We examine score and adjusted score statistics in the context of parametric and semiparametric regression…

比例优势回归模型中的半参数推断AI 解读

For fitting the proportional odds regression model with right-censored survival times, we introduce some weighted empirical odds functions. These functions are solutions of some self-consistency equations and have a nice martingale representation. From these functions, several classes of new regression estimators, such as the pseudo–maximum likelihood estimator, martingale residual-based estimators, and minimum distance estimators, are derived. These estimators have…

泊松过程同质性的调整得分检验AI 解读

Tests of homogeneity are being increasingly used for the analysis of event time data, but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes. Here we consider tests of homogeneity for recurrent event data in which the null model is a Poisson process and the alternative is a mixed Poisson process. We examine score and adjusted score statistics in the context of parametric and semiparametric regression…

比例优势回归模型的半参数推断AI 解读

For fitting the proportional odds regression model with right-censored survival times, we introduce some weighted empirical odds functions. These functions are solutions of some self-consistency equations and have a nice martingale representation. From these functions, several classes of new regression estimators, such as the pseudo–maximum likelihood estimator, martingale residual-based estimators, and minimum distance estimators, are derived. These estimators have…

季节性协整的似然分析AI 解读

The error correction model for seasonal cointegration is analyzed. Conditions are found under which the process is integrated of order 1 and cointegrated at seasonal frequency, and a representation theorem is given. The likelihood function is analyzed and the numerical calculation of the maximum likelihood estimators is discussed. The asymptotic distribution of the likelihood ratio test for cointegrating rank is given. It is shown that the estimated cointegrating vectors are…

基于自适应最大似然估计的单位根检验AI 解读

Adaptive maximum likelihood estimators of unit roots in autoregressive processes with possibly non-Gaussian innovations are considered. Unit root tests based on the adaptive estimators are constructed. Limiting distributions of the test statistics are derived, which are linear combinations of two functionals of Brownian motions. A Monte Carlo simulation reveals that the proposed tests have improved powers over the classical Dickey–Fuller tests when the distribution of the…

自动化 Monte Carlo EM 算法最大化广义线性混合模型似然AI 解读

Summary Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method…

缺失机制不可忽略时广义线性模型中的协变量缺失AI 解读

Summary We propose a method for estimating parameters in generalized linear models with missing covariates and a non-ignorable missing data mechanism. We use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one-dimensional conditional distributions, with each one-dimensional conditional distribution consisting of a logistic regression. We allow the covariates to be either categorical or…

VAR 维度对估计量偏误的影响AI 解读

Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not address questions regarding the influence of the number and nature of the system's variates on parameter estimates. Clearly, both questions will have repercussions on the way VARs are…

面板数据的对称归一化工具变量估计AI 解读

The authors discuss the estimation of linear panel-data models with sequential moment restrictions using symmetrically normalized generalized method of moments (SNM) estimators and limited information maximum likelihood (LIML) analogues. These estimators are asymptotically equivalent to standard generalized method of moments (GMM) estimators but are invariant to normalization and tend to have a smaller finite-sample bias, especially when the instruments are poor. The authors…

Jackknife 工具变量估计AI 解读

Two-stage-least-squares (2SLS) estimates are biased towards the probability limit of OLS estimates. This bias grows with the degree of over-identification and can generate highly misleading results. In this paper we propose two simple alternatives to 2SLS and limited-information-maximum-likelihood (LIML) estimators for models with more instruments than endogenous regressors. These estimators can be interpreted as instrumental variables procedures using an instrument that is…

短札：通过正态近似由条件信息计算信息矩阵AI 解读

This paper provides a method for computing the asymptotic covariance matrix from a likelihood function with known maximum likelihood estimate of the parameters. Philosophically, the basic idea is to assume that the likelihood function should be well approximated by a normal density when asymptotic results about the maximum likelihood estimate are applied for statistical inference. Technically, the method makes use of two facts: the information for a one-dimensional parameter…

杂论：含缺失值图模型的最大似然估计AI 解读

In this paper we discuss maximum likelihood estimation when some observations are missing in mixed graphical interaction models assuming a conditional Gaussian distribution as introduced by Lauritzen & Wermuth (1989). The approach via the EM algorithm of Little & Schluchter (1985) for the saturated case is expanded to cover the special restrictions in graphical models. A more efficient way to compute the E-step is indicated. The main purpose of the paper is to show that for…

平稳与非平稳短记忆及长记忆自回归过程的统一模型选择AI 解读

The question of model choice for the class of stationary and nonstationary, fractional and nonfractional autoregressive processes is considered. This class is defined by the property that the dth difference, for −½ ≪ d ≪ ∞, is a stationary autoregressive process of order po ≪ ∞. A version of the Akaike information criterion, AIC, for determining an appropriate autoregressive order when d and the autoregressive parameters are estimated simultaneously by a maximum likelihood…

最大似然先验AI 解读

Consider an estimate $\theta^*$ of a parameter $\theta$ based on repeated observations from a family of densities $f_\theta$ evaluated by the Kullback–Leibler loss function $K(\theta, \theta^*) = \int \log(f_\theta/f_{\theta^*})f_\theta$. The maximum likelihood prior density, if it exists, is the density for which the corresponding Bayes estimate is asymptotically negligibly different from the maximum likelihood estimate. The Bayes estimate corresponding to the maximum…

动态回归模型中扰动方差估计量的自由度调整AI 解读

In the classical regression model with fixed regressors the statistic S 2 , i.e. the sum of squared residuals (SSR) divided by the number of degrees of freedom, is an unbiased estimator of the variance of the disturbances. If the model is dynamic and contains lagged-dependent explanatory variables, then the least-squares coefficient estimators are biased in finite samples, and so is S 2 . By deriving the expectation of the initial terms in an expansion of the expression for…