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Likelihood-Based Sufficient Dimension Reduction

基于似然的充分降维

We obtain the maximum likelihood estimator of the central subspace under conditional normality of the predictors given the response. Analytically and in simulations we found that our new estimator can preform much better than sliced inverse regression, sliced average variance estimation and directional regression, and that it seems quite robust to deviations from normality.

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Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons

GARCH 系数为零的检验:标准检验修正与相对效率比较

This article is concerned with testing the nullity of coefficients in generalized autoregressive conditionally heteroscedastic (GARCH) models. The problem is nonstandard because the quasi-maximum likelihood estimator is subject to positivity constraints. This article establishes the asymptotic null and local alternative distributions of Wald, score, and quasi-likelihood ratio tests. Efficiency comparisons under fixed alternatives are considered. Two cases of special interest…

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Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

离散观测扩散过程的蒙特卡洛最大似然估计

This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s. continuous estimators of the likelihood function for a family of diffusion models and its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffusions, and involves no discretization error. We show that, under regularity…

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MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL

用灵活系数 GARCH(1,1) 模型刻画金融波动的多重状态

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes…

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A note on semiparametric efficient inference for two-stage outcome-dependent sampling with a continuous outcome

连续结局两阶段结局依赖抽样的半参数有效推断

Outcome-dependent sampling designs have been shown to be a cost effective way to enhance study efficiency. We show that the outcome-dependent sampling design with a continuous outcome can be viewed as an extension of the two-stage case-control designs to the continuous-outcome case. We further show that the two-stage outcome-dependent sampling has a natural link with the missing-data and biased-sampling framework. Through the use of semiparametric inference and missing-data…

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A note on profile likelihood for exponential tilt mixture models

指数倾斜混合模型的剖面似然札记

Suppose that independent observations are drawn from multiple distributions, each of which is a mixture of two component distributions such that their log density ratio satisfies a linear model with a slope parameter and an intercept parameter. Inference for such models has been studied using empirical likelihood, and mixed results have been obtained. The profile empirical likelihood of the slope and intercept has an irregularity at the null hypothesis so that the two…

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Consistent Model Selection and Data-Driven Smooth Tests for Longitudinal Data in the Estimating Equations Approach

估计方程框架下纵向数据的一致模型选择与数据驱动光滑检验

Summary Model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood, particularly for correlated categorical data. The paper introduces a novel Bayesian information criterion type model selection procedure based on the quadratic inference function, which does not require the full likelihood or quasi-likelihood. With probability approaching 1, the criterion…

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Properties and estimation of asymmetric exponential power distribution

非对称指数幂分布的性质与估计

The new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces different decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum…

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Markov-switching models with endogenous explanatory variables II: A two-step MLE procedure

含内生解释变量的马尔可夫转换模型Ⅱ:两步极大似然估计

This paper proposes a two-step maximum likelihood estimation (MLE) procedure to deal with the problem of endogeneity in Markov-switching regression models. A joint estimation procedure provides us with an asymptotically most efficient estimator, but it is not always feasible, due to the 'curse of dimensionality' in the matrix of transition probabilities. A two-step estimation procedure, which ignores potential correlation between the latent state variables, suffers less from…

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Large-sample inference on spatial dependence

空间依赖的大样本推断

We consider cross-sectional data that exhibit no spatial correlation, but are feared to be spatially dependent. We demonstrate that a spatial version of the stochastic volatility model of financial econometrics, entailing a form of spatial autoregression, can explain such behaviour. The parameters are estimated by pseudo-Gaussian maximum likelihood based on log-transformed squares, and consistency and asymptotic normality are established. Asymptotically valid tests for…

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Model Selection Criteria for Missing-Data Problems Using the EM Algorithm

利用 EM 算法构造缺失数据问题的模型选择准则

We consider novel methods for the computation of model selection criteria in missing-data problems based on the output of the EM algorithm. The methodology is very general and can be applied to numerous situations involving incomplete data within an EM framework, from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and/or covariates. Toward this goal, we develop a class of information criteria for missing-data…

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Semiparametric Estimation of Covariance Matrixes for Longitudinal Data

纵向数据协方差矩阵的半参数估计

Estimation of longitudinal data covariance structure poses significant challenges because the data are usually collected at irregular time points. A viable semiparametric model for covariance matrices was proposed in Fan, Huang and Li (2007) that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically via aggregating information from irregular and sparse data points within each subject. However, the asymptotic…

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Domain-Level Covariance Analysis for Multilevel Survey Data With Structured Nonresponse

结构性无应答下多层调查数据的域级协方差分析

Health care quality surveys in the United States are administered to individual respondents (i.e., hospital patients, health plan members) to evaluate the performance of health care organizations (i.e., hospitals, health plans), which thus constitute estimation domains. For better understanding and more parsimonious reporting of dimensions of quality, we analyze relationships among quality measures at the domain level. Rather than specifying a full parametric model for the…

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Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets

大型空间数据集似然估计中的协方差截尾

Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on Gaussian processes. But calculating the likelihood can be computationally infeasible for large data sets, requiring O(n3) calculations for a data set with n observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approach, covariance matrixes are “tapered,” or multiplied element wise by a sparse…

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Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices

高斯对称矩阵特征值与特征向量的推断

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3×3 and 2×2 symmetric…

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A neural network demand system with heteroskedastic errors

具有异方差误差的神经网络需求系统

In this paper we consider estimation of demand systems with flexible functional forms, allowing an error term with a general conditional heteroskedasticity function that depends on observed covariates, such as demographic variables. We propose a general model that can be estimated either by quasi-maximum likelihood (in the case of exogenous regressors) or generalized method of moments (GMM) if the covariates are endogenous. The specification proposed in the paper nests…

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M -ESTIMATION IN GARCH MODELS

GARCH 模型中的 M 估计

This paper derives asymptotic normality of a class of M -estimators in the generalized autoregressive conditional heteroskedastic (GARCH) model. The class of estimators includes least absolute deviation and Huber's estimator in addition to the well-known quasi maximum likelihood estimator. For some estimators, the asymptotic normality results are obtained only under the existence of fractional unconditional moment assumption on the error distribution and some mild smoothness…

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Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data

二元生存数据正态变换模型的半参数极大似然估计

We consider a class of semiparametric normal transformation models for right censored bivariate failure times. Nonparametric hazard rate models are transformed to a standard normal model and a joint normal distribution is assumed for the bivariate vector of transformed variates. A semiparametric maximum likelihood estimation procedure is developed for estimating the marginal survival distribution and the pairwise correlation parameters. This produces an efficient estimator…

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Soap Film Smoothing

肥皂膜平滑

Summary Conventional smoothing methods sometimes perform badly when used to smooth data over complex domains, by smoothing inappropriately across boundary features, such as peninsulas. Solutions to this smoothing problem tend to be computationally complex, and not to provide model smooth functions which are appropriate for incorporating as components of other models, such as generalized additive models or mixed additive models. We propose a class of smoothers that are…

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Clarification: Regression Model Selection—A Residual Likelihood Approach

澄清:回归模型选择的残差似然方法

In regression models, Shi and Tsai (2002) applied the logarithm of the commonly used residual maximum likelihood function (2.2) to obtain the residual information criterion RIC in equation (2.10). Function (2.2) is the same as the modified profile likelihood function, but it is different from the complete residual maximum likelihood function that contains two additional terms, −12(n−k)log⁡(2π) and 12log⁡|X′X|⁠, on the right-hand side of expression (2.2). Because these two…

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Nonlinear models for strongly dependent processes with financial applications

强依赖过程的非线性模型及金融应用

This paper is motivated by recent evidence that many univariate economic and financial time series have both nonlinear and long memory characteristics. Hence, this paper considers a general nonlinear, smooth transition regime autoregression which is embedded within a strongly dependent, long memory process. A time domain MLE with simultaneous estimation of the long memory, linear AR and nonlinear parameters is shown to have desirable asymptotic properties. The Bayesian and…

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Econometric modelling in finance and risk management: An overview

金融与风险管理中的计量建模:概览

This paper gives an overview about the sixteen papers included in this special issue. The papers in this special issue cover a wide range of topics. Such topics include discussing a class of tests for correlation, estimation of realized volatility, modeling time series and continuous-time models with long-range dependence, estimation and specification testing of time series models, estimation in a factor model with high-dimensional problems, finite-sample examination of…

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Finite sample properties of the QMLE for the Log-ACD model: Application to Australian stocks

Log-ACD 模型准极大似然估计的有限样本性质:澳大利亚股票应用

This paper concerns the properties of the Quasi Maximum Likelihood Estimator (QMLE) of the Logarithmic Autoregressive Conditional Duration (Log-ACD) model. Proofs of consistency and asymptotic normality of QMLE for the Log-ACD model with log-normal density are presented. This is an important issue as the Log-ACD is used widely for testing various market microstructure models and effects. Knowledge of the distribution of the QMLE is crucial for purposes of valid inference and…

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Estimation of the stochastic conditional duration model via alternative methods

随机条件持续期模型的替代估计方法

This paper examines the estimation of the Stochastic Conditional Duration model by the empirical characteristic function and the generalized method of moments when maximum likelihood is unavailable. The joint characteristic function for the durations along with general expressions for the moments are derived, leading naturally to estimation via the empirical characteristic function and generalized method of moments. In a Monte Carlo study as well as an empirical application,…

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