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似然比统计量的几何理解AI 解读

It is well known that twice a log-likelihood ratio statistic follows asymptotically a chi-square distribution. The result is usually understood and proved via Taylor's expansions of likelihood functions and by assuming asymptotic normality of maximum likelihood estimators (MLEs). We obtain more general results by using a different approach: The Wilks type of results hold as long as likelihood contour sets are fan-shaped. The classical Wilks theorem corresponds to the…

非平稳二元选择AI 解读

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the…

二元变量分布中多元全正性的似然比检验AI 解读

Multivariate Totally Positive $(MTP_2)$ binary distributions have been studied in many fields, such as statistical mechanics, computer storage and latent variable models. We show that $MTP_2$ is equivalent to the requirement that the parameters of a saturated log-linear model belong to a convex cone, and we provide a Fisher-scoring algorithm for maximum likelihood estimation.We also show that the asymptotic distribution of the log-likelihood ratio is a mixture of chi-squares…

形状约束回归中的自由度AI 解读

For the problem of estimating a regression function, $\mu$ say, subject to shape constraints, like monotonicity or convexity, it is argued that the divergence of the maximum likelihood estimator provides a useful measure of the effective dimension of the model. Inequalities are derived for the expected mean squared error of the maximum likelihood estimator and the expected residual sum of squares. These generalize equalities from the case of linear regression. As an…

面板 Probit 中的异方差误设：GMM 与模拟最大似然的小样本比较AI 解读

This paper compares generalized method of moments (GMM) and simulated maximum likelihood (SML) approaches to the estimation of the panel probit model. Both techniques circumvent multiple integration of joint density functions without the need to restrict the error term variance-covariance matrix of the latent normal regression model. Particular attention is paid to a three-stage GMM estimator based on nonparametric estimation of the optimal instruments for given conditional…

I(2) 系统中两阶段估计量的渐近效率AI 解读

This paper derives the distribution of the two stage estimator of cointegrating parameters in I (2) systems, abbreviated 2SI2, under several assumptions regarding the drift of the process. The asymptotic distribution is compared with that of the maximum likelihood (ML) estimator derived in Johansen (1997, Scandinavian Journal of Statistics 24, 433–462). It is found that the two asymptotic distributions are the same, thus showing that the 2SI2 estimator is asymptotically as…

多元正态层级模型的推断AI 解读

Summary This paper provides a new method and algorithm for making inferences about the parameters of a two-level multivariate normal hierarchical model. One has observed J p-dimensional vector outcomes, distributed at level 1 as multivariate normal with unknown mean vectors and with known covariance matrices. At level 2, the unknown mean vectors also have normal distributions, with common unknown covariance matrix A and with means depending on known covariates and on unknown…

EM估计的标准误AI 解读

Summary The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the…

多元正态协方差矩阵广义线性模型的极大似然估计AI 解读

The positive-definiteness constraint is the most awkward stumbling block in modelling the covariance matrix. Pourahmadi's (1999) unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models. The new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors. In this paper, the…

多种稀有特征流行比例的有效估计AI 解读

We consider a population with multiple traits of interest, where our goal is to estimate the proportions of individuals with the traits. When traits are rare, group testing can improve efficiency. Previous work of Hughes-Oliver & Swallow (1994) developed an adaptive two-stage design for group testing of only one trait. We extend this work to the multi-trait case. We derive the optimum group sizes using compound D-optimum design theory. Estimation is based on maximum…

持续时间依赖与非参数异质性：蒙特卡洛研究AI 解读

We examine the behaviour of the nonparametric maximum likelihood estimator (NPMLE) for a discrete duration model with unobserved heterogeneity and unknown duration dependence. We find that a nonparametric specification of either the duration dependence or unobserved heterogeneity, when the other feature of the hazard is known to be absent, leads to estimators that are well behaved even in modestly sized samples. In contrast, there is a large and systematic bias in the…

论剖面似然AI 解读

We show that semiparametric profile likelihoods, where the nuisance parameter has been profiled out, behave like ordinary likelihoods in that they have a quadratic expansion. In this expansion the score function and the Fisher information are replaced by the efficient score function and efficient Fisher information. The expansion may be used, among others, to prove the asymptotic normality of the maximum likelihood estimator, to derive the asymptotic chi-squared distribution…

单调平均剩余寿命的估计AI 解读

In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age $x, M(x)$, defined by $$M(x) = E[X - x|X > x],$$ where $X$ is a lifetime. $M$ is called the mean residual life function.In many applications it is reasonable to assume that $M$ is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of $M$ and…

约束局部 M 估计量的渐近性质AI 解读

We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and,more generally, $M$-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set $S$.We give a counterexample showing that regularity of $S$ in the sense of Clarke is not sufficient for asymptotic equivalence of $\sqrt{n}$-consistent locally optimal $M$-estimators.We argue further that stronger properties, such as so-called near…

平滑单调密度与单峰密度的极大似然估计AI 解读

We study the nonparametric estimation of univariate monotone and unimodal densities usingthe maximum smoothed likelihood approach. The monotone estimator is the derivative of the least concave majorant of the distribution correspondingto a kernel estimator.We prove that the mapping on distributions $\Phi$ with density $\varphi$, $$\varphi \mapsto \text{the derivative of the least concave majorant of $\Phi},$$ is a contraction in all $L^P$ norms $(1 \leq p \leq \infty)$, and…

面板计数数据下计数过程均值的两种估计量AI 解读

We study two estimators of the mean function of a countingprocess based on “panel count data.” The setting for “panel count data” is one in which $n$ independent subjects, each with a counting process with common mean function, are observed at several possibly different times duringa study. Following a model proposed by Schick and Yu, we allow the number of observation times, and the observation times themselves, to be random variables. Our goal is to estimate the mean…

光滑高斯随机场模型中结构化相关矩阵的估计AI 解读

This article considers the estimation of structured correlation matrices in infinitely differentiable Gaussian random field models.The problem is essentially motivated by the stochastic modeling of smooth deterministic responses in computer experiments.In particular, the log-likelihood function is determined explicitly in closed-form and the sieve maximum likelihood estimators are shown to be strongly consistent under mild conditions.

摘要暂缺

广义线性模型中的置信带AI 解读

Generalized linear models (GLM) include many useful models. This paper studies simultaneous confidence regions for the mean response function in these models. The coverage probabilities of these regions are related to tail probabilities of maxima of Gaussian random fields, asymptotically, and hence, the so-called tube formula is applicable without any modification. However, in the generalized linear models, the errors are often nonadditive and non-Gaussian and may be…

加性逻辑回归：提升法的统计视角（含讨论与作者回应）AI 解读

Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of…

半参数 ARCH 模型：估计函数方法AI 解读

We introduce the method of estimating functions to study the class of autoregressive conditional heteroscedasticity (ARCH) models. We derive the optimal estimating functions by combining linear and quadratic estimating functions. The resultant estimators are more efficient than the quasi-maximum likelihood estimator. If the assumption of conditional normality is imposed, the estimator obtained by using the theory of estimating functions is identical to that obtained by using…

ARFIMA 模型中基于似然的小样本推断AI 解读

The autoregressive fractionally integrated moving average (ARFIMA) model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there have been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood estimates and formulation of procedures for their computation. Small-sample inference, however, has not to date been studied. Here we…

一类双重删失现时状态模型的非参数极大似然估计及伴侣研究应用AI 解读

The California Partners' Study is an ongoing investigation of heterosexual HIV transmission in partners of infected index cases (Padian, et al., 1987; Shiboski & Jewell, 1990). In addition to the HIV-status of the partner at the recruiting time one also observes the initial time of the partnership and a lower bound for the infection time of the index case. Following Jewell, Malani & Vittinghoff (1994) we assume that the infection time of the index case is uniformly…

一类单纯形约束下的离散分布估计AI 解读

Simplex constraints, such as monotonicity and convexity or concavity on the probabilities of a set of discrete distributions, are useful for modeling and analyzing discrete data. This article considers both maximum likelihood estimation and Bayesian estimation of discrete distribution with a class of simplex constraints using the Expectation-Maximization (EM) algorithm and the data augmentation (DA) algorithm. The formulation and implementation of EM and DA for binomial,…