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ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

弱依赖下非线性分位数回归的渐近理论

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

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SPATIAL SEMIPARAMETRIC MODEL WITH ENDOGENOUS REGRESSORS

含内生解释变量的空间半参数模型

This paper proposes a semiparametric generalized method of moments estimator (GMM) estimator for a partially parametric spatial model with endogenous spatially dependent regressors. The finite-dimensional estimator is shown to be consistent and root-n asymptotically normal under some reasonable conditions. A spatial heteroscedasticity and autocorrelation consistent covariance estimator is constructed for the GMM estimator. The leading application is nonlinear spatial…

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TARGETING ESTIMATION OF CCC-GARCH MODELS WITH INFINITE FOURTH MOMENTS

无限四阶矩下 CCC-GARCH 模型的目标估计

As an alternative to quasi-maximum likelihood, targeting estimation is a much applied estimation method for univariate and multivariate GARCH models. In terms of variance targeting estimation, recent research has pointed out that at least finite fourth moments of the data generating process is required, if one wants to perform inference in GARCH models by relying on asymptotic normality of the estimator. Such moment conditions may not be satisfied in practice for financial…

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ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS

异方差与自相关稳健检验的检验水平和功效

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well…

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INFERENCE ON NONSTATIONARY TIME SERIES WITH MOVING MEAN

具有变化均值的非平稳时间序列推断

A semiparametric model is proposed in which a parametric filtering of a nonstationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I (1) and other hypotheses are…

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SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR TRANSFORMATION MODELS UNDER CONDITIONAL QUANTILE RESTRICTION

条件分位数约束下部分线性变换模型的半参数估计

This article is concerned with semiparametric estimation of a partially linear transformation model under conditional quantile restriction with no parametric restriction imposed either on the link functional form or on the error term distribution. We describe for the finite-dimensional parameter a $\sqrt n$ -consistent estimator which combines the features of Chen (2010)’s maximum integrated score estimator as well as Lee (2003)’s average quantile regression. We show the…

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NONPARAMETRIC COINTEGRATING REGRESSION WITH ENDOGENEITY AND LONG MEMORY

存在内生性与长记忆的非参数协整回归

This paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a,b, Econometric Theory 25, 710–738, Econometrica 77, 1901–1948), the conventional nonparametric local level kernel estimator is shown to be consistent…

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ESTIMATION OF CHANGE-POINTS IN LINEAR AND NONLINEAR TIME SERIES MODELS

线性与非线性时间序列模型的变点估计

This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude d of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as…

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CONSISTENT AND CONSERVATIVE MODEL SELECTION WITH THE ADAPTIVE LASSO IN STATIONARY AND NONSTATIONARY AUTOREGRESSIONS

平稳与非平稳自回归中自适应 Lasso 的一致及保守模型选择

We show that the adaptive Lasso is oracle efficient in stationary and nonstationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as if only these had been included in the model from the outset. In particular, this implies that it is able to discriminate between stationary and nonstationary autoregressions and it…

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AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

数量随样本增长的矩条件估计量平均

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of $\sqrt n$ -consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the…

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FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS

空间依赖稳健非参数协方差矩阵估计的 fixed-b 渐近理论

This paper develops a method for performing inference using spatially dependent data. We consider test statistics formed using nonparametric covariance matrix estimators that account for heteroskedasticity and spatial correlation (spatial HAC). We provide distributions of commonly used test statistics under “fixed- b ” asymptotics, in which HAC smoothing parameters are proportional to the sample size. Under this sequence, spatial HAC estimators are not consistent but…

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COMPARISON OF INFERENTIAL METHODS IN PARTIALLY IDENTIFIED MODELS IN TERMS OF ERROR IN COVERAGE PROBABILITY

按覆盖概率误差比较部分识别模型的推断方法

This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: bootstrap, subsampling, and asymptotic approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the…

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MODEL-FREE INFERENCE FOR TAIL RISK MEASURES

尾部风险度量的无模型推断

Understanding uncertainty in estimating risk measures is important in modern financial risk management. In this paper we consider a nonparametric framework that incorporates auxiliary information available in covariates and propose a family of inferential methods for the value at risk, expected shortfall, and related risk measures. A two-step generalized empirical likelihood test statistic is constructed and is shown to be asymptotically pivotal without requiring variance…

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REGULARIZING PRIORS FOR LINEAR INVERSE PROBLEMS

线性逆问题的正则化先验

This paper proposes a new Bayesian approach for estimating, nonparametrically, functional parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior we propose the posterior mean as an estimator and prove frequentist consistency of the posterior distribution. The latter provides the frequentist validation of our Bayesian procedure. We show that the minimax rate of contraction of the posterior…

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NONPARAMETRIC TRANSFORMATION REGRESSION WITH NONSTATIONARY DATA

非平稳数据的非参数变换回归

We examine a kernel regression estimator for time series that takes account of the error correlation structure as proposed by Xiao et al. (2003, Journal of the American Statistical Association 98, 980–992). We show that this method continues to improve estimation in the case where the regressor is a unit root or a near unit root process.

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A NONPARAMETRIC ESTIMATOR FOR THE COVARIANCE FUNCTION OF FUNCTIONAL DATA

函数型数据协方差函数的非参数估计

Many quantities of interest in economics and finance can be represented as partially observed functional data. Examples include structural business cycle estimation, implied volatility smile, the yield curve. Having embedded these quantities into continuous random curves, estimation of the covariance function is needed to extract factors, perform dimensionality reduction, and conduct inference on the factor scores. A series expansion for the covariance function is…

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SUBSET HYPOTHESES TESTING AND INSTRUMENT EXCLUSION IN THE LINEAR IV REGRESSION

线性工具变量回归中的子集假设检验与工具变量遗漏

This paper explores the sensitivity of plug-in subset tests to instrument exclusion in structural models. Identification-robust statistics based on the plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in…

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REFINED TESTS FOR SPATIAL CORRELATION

空间相关性的精化检验

We consider testing the null hypothesis of no spatial correlation against the alternative of pure first order spatial autoregression. A test statistic based on the least squares estimate has good first-order asymptotic properties, but these may not be relevant in small- or moderate-sized samples, especially as (depending on properties of the spatial weight matrix) the usual parametric rate of convergence may not be attained. We thus develop tests with more accurate size…

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SIGNAL EXTRACTION IN LONG MEMORY STOCHASTIC VOLATILITY

长记忆随机波动模型中的信号提取

Long memory in stochastic volatility (LMSV) models are flexible tools for the modeling of persistent dynamic volatility, which is a typical characteristic of financial time series. However, their empirical applicability is limited because of the complications inherent in the estimation of the model and in the extraction of the volatility component. This paper proposes a new technique for volatility extraction, based on a semiparametric version of the optimal…

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DIFFERENCING TRANSFORMATIONS AND INFERENCE IN PREDICTIVE REGRESSION MODELS

预测回归模型中的差分变换与推断

The limit distribution of conventional test statistics for predictability may depend on the degree of persistence of the predictors. Therefore, diverging results and conclusions may arise because of the different asymptotic theories adopted. Using differencing transformations, we introduce a new class of estimators and test statistics for predictive regression models with Gaussian limit distribution that is instead insensitive to the degree of persistence of the predictors.…

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NONPARAMETRIC IDENTIFICATION OF POSITIVE EIGENFUNCTIONS

正特征函数的非参数识别

Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk–return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models. This paper provides identification conditions for positive eigenfunctions in nonparametric models. Identification is achieved if the operator satisfies two mild positivity conditions…

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SPECIFICATION TESTING WHEN THE NULL IS NONPARAMETRIC OR SEMIPARAMETRIC

原假设为非参数或半参数模型时的设定检验

This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudo-ML methods like, for example, limited dependent variable or gravity models. Second, often one might not want to fully specify the null hypothesis. Instead, one…

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REGULAR VARIATION AND THE IDENTIFICATION OF GENERALIZED ACCELERATED FAILURE-TIME MODELS

正则变动与广义加速失效时间模型的识别

Ridder (1990, Review of Economic Studies 57, 167–182) provides an identification result for the Generalized Accelerated Failure-Time (GAFT) model. We point out that Ridder’s proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at 0 and ∞. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior…

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ADAPTIVE NONPARAMETRIC REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY

条件异方差下的自适应非参数回归

In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton–Raphson estimator and the local profile likelihood estimator are investigated. We show that the proposed estimators are…

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