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列联表的齐次线性预测模型AI 解读

Maximum likelihood (ML) inference for the class of homogeneous linear predictor (HLP) models for contingency tables is described. HLP models constrain the expected table counts m through L(m) = Xβ, where the link L is allowed to be a many-to-one, nonlinear function. Generalized log-linear, association trend, marginal cumulative probit, and conditional marginal homogeneity models are given as specific examples. ML fit results, which include point estimates, goodness-of-fit…

广义线性模型的缺失数据方法AI 解读

Missing data is a major issue in many applied problems, especially in the biomedical sciences. We review four common approaches for inference in generalized linear models (GLMs) with missing covariate data: maximum likelihood (ML), multiple imputation (MI), fully Bayesian (FB), and weighted estimating equations (WEEs). There is considerable interest in how these four methodologies are related, the properties of each approach, the advantages and disadvantages of each…

量子层析入门AI 解读

Summary We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on identical quantum systems. The state can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We present consistency results for pattern function projection estimators and for sieve maximum likelihood…

回归分析中的二元位置—尺度模型及寿命数据应用AI 解读

Summary The literature on multivariate linear regression includes multivariate normal models, models that are used in survival analysis and a variety of models that are used in other areas such as econometrics. The paper considers the class of location–scale models, which includes a large proportion of the preceding models. It is shown that, for complete data, the maximum likelihood estimators for regression coefficients in a linear location–scale framework are consistent…

支撑集位于对角线上方的多元分布AI 解读

A general family of distributions for the empirical modelling of ordered multivariate data is proposed. The family is based on, but greatly extends, the joint distribution of order statistics from an independent and identically distributed univariate sample. General properties, including marginal and conditional distributions, bivariate dependence, limiting distributions and links to the Dirichlet distribution are described. Univariate and bivariate special cases of the…

一种半参数变点模型AI 解读

A semiparametric changepoint model is considered and the empirical likelihood method is applied to detect the change from a distribution to a weighted distribution in a sequence of independent random variables. The maximum likelihood changepoint estimator is shown to be consistent. The empirical likelihood ratio test statistic is proved to have the same limit null distribution as that with parametric models. A data-based test for the validity of the models is also proposed.…

协整误差序列相关时ADL与动态OLS协整估计量的比较AI 解读

This paper deals with a family of parametric, single-equation cointegration estimators that arise in the context of the autoregressive distributed lag (ADL) models. We particularly focus on a subclass of the ADL models, those that do not involve lagged values of the dependent variable, referred to as augmented static (AS) models. The general ADL and the restricted AS models give rise to the ADL and dynamic OLS (DOLS) estimators, respectively. The relative performance of…

发现新类别的条件概率预测AI 解读

Consider a population comprising disjoint classes. An important problem arising from various fields is prediction of the random conditional probability of discovering a new class. The asymptotic normality of the discovery probability is established in a Poisson model, where the number of individuals from each class is a Poisson process with a class-specific rate. A new derivation is presented for the well-known Good–Toulmin predictor as a moment-based estimator for the…

局部—全局神经网络AI 解读

We propose the local-global neural networks model within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the mixture of experts approach. We emphasize the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. The proposed model consists of a mixture of…

蒙特卡洛积分的似然方法AI 解读

The use of estimating equations has been a common approach for constructing Monte Carlo estimators. Recently, Kong et al. proposed a formulation of Monte Carlo integration as a statistical model, making explicit what information is ignored and what is retained about the baseline measure. From simulated data, the baseline measure is estimated by maximum likelihood, and then integrals of interest are estimated by substituting the estimated measure. For two different situations…

平滑样条非线性非参数回归模型AI 解读

Almost all of the current nonparametric regression methods, such as smoothing splines, generalized additive models, and varyingcoefficients models, assume a linear relationship when nonparametric functions are regarded as parameters. In this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly. They arise in many fields as either theoretical or empirical models. Our new estimation methods…

受约束的间接估计AI 解读

We develop generalized indirect estimation procedures that handle equality and inequality constraints on the auxiliary model parameters by extracting information from the relevant multipliers, and compare their asymptotic efficiency to maximum likelihood. We also show that, regardless of the validity of the restrictions, the asymptotic efficiency of such estimators can never decrease by explicitly considering the multipliers associated with additional equality constraints.…

非平稳 GARCH 模型的渐近推断AI 解读

Consistency and asymptotic normality are established for the highly applied quasi-maximum likelihood estimator in the GARCH(1,1) model. Contrary to existing literature we allow the parameters to be in the region where no stationary version of the process exists. This has the important implication that the likelihood-based estimator for the GARCH parameters is consistent and asymptotically normal in the entire parameter region including both stationary and explosive behavior.…

GARCH(p,q) 模型的序贯变点检测AI 解读

We suggest a sequential monitoring scheme to detect changes in the parameters of a GARCH(p,q) sequence. The procedure is based on quasi-likelihood scores and does not use model residuals. Unlike for linear regression models, the squared residuals of nonlinear time series models such as generalized autoregressive conditional heteroskedasticity (GARCH) do not satisfy a functional central limit theorem with a Wiener process as a limit, so its boundary crossing probabilities…

利用混合样条模型进行限制似然比失拟检验AI 解读

Summary Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one-sided testing problem a further complication is that the variance component…

空间自回归模型准最大似然估计量的渐近分布AI 解读

This paper investigates asymptotic properties of the maximum likelihood estimator and the quasi-maximum likelihood estimator for the spatial autoregressive model. The rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model. It is important to make the distinction with different spatial scenarios. Under the scenario that each unit will be influenced by only a few neighboring units, the estimators may have -rate…

马尔可夫状态切换自回归模型中极大似然估计的渐近性质AI 解读

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the…

随机间隔离散观测下扩散过程估计量的一般理论AI 解读

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are…

摘要暂缺

关于由边际密度构造伪似然的说明AI 解读

For likelihood‐based inference involving distributions in which high‐dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single q×1 vector of observations is observed are examined. Conditions under which consistent estimators of…

失效原因被遮蔽的竞争风险模型：基于 EM 算法的推断AI 解读

In this paper we propose inference methods based on the EM algorithm for estimating the parameters of a weakly parameterised competing risks model with masked causes of failure and second‐stage data. With a carefully chosen definition of complete data, the maximum likelihood estimation of the cause‐specific hazard functions and of the masking probabilities is performed via an EM algorithm. Both the E‐ and M‐steps can be solved in closed form under the full model and under…

病例对照抽样下的现状数据AI 解读

In this paper, we show that the distribution function of survival times is identified, up to a one‐parameter family of distribution functions, based on information from case‐control current status data. With supplementary information on the population frequency of cases relative to controls, a simple weighted version of the nonparametric maximum likelihood estimator for prospective current status data provides a natural estimator for case‐control samples. Following the…

Higher‐order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on θ. A modified likelihood ratio statistic is…

一类非正规计量经济模型中的似然估计与推断AI 解读

We study inference in structural models with a jump in the conditional density, where location and size of the jump are described by regression curves. Two prominent examples are auction models, where the bid density jumps from zero to a positive value at the lowest cost, and equilibrium job-search models, where the wage density jumps from one positive level to another at the reservation wage. General inference in such models remained a long-standing, unresolved problem,…