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LOCAL RANK ESTIMATION OF TRANSFORMATION MODELS WITH FUNCTIONAL COEFFICIENTS

函数系数变换模型的局部秩估计

This paper considers a nonparametric functional coefficient model with an unknown link function. The model gives flexibility to the standard interaction-variable model by allowing an arbitrary functional form of heterogeneous marginal effects. A local rank estimation procedure is proposed for the functional coefficients along with its asymptotic property.

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TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR MODELS

部分线性模型的结构变化检验

We consider two tests of structural change for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and nonparametric components simultaneously, based on the cumulative sums of weighted residuals from the same semiparametric regression. We derive the limiting distributions of both tests…

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COINTEGRATION RANK TESTING UNDER CONDITIONAL HETEROSKEDASTICITY

条件异方差下的协整秩检验

We analyze the properties of the conventional Gaussian-based cointegrating rank tests of Johansen (1996, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either…

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BIAS CORRECTIONS IN TESTING AND ESTIMATING SEMIPARAMETRIC, SINGLE INDEX MODELS

半参数单指标模型估计与检验的偏差校正

Semiparametric methods are widely employed in applied work where the ability to conduct inferences is important. To establish asymptotic normality for making inferences, bias control mechanisms are often used in implementing semiparametric estimators. The first contribution of this paper is to propose a mechanism that enables us to establish asymptotic normality with regular kernels. In so doing, we argue that the resulting estimator performs very well in finite samples.…

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M -ESTIMATION FOR A SPATIAL UNILATERAL AUTOREGRESSIVE MODEL WITH INFINITE VARIANCE INNOVATIONS

无限方差创新下空间单向自回归模型的 M 估计

We study the limiting behavior of the M -estimators of parameters for a spatial unilateral autoregressive model with independent and identically distributed innovations in the domain of attraction of a stable law with index α ∈ (0, 2]. Both stationary and unit root models and some extensions are considered. It is also shown that self-normalized M -estimators are asymptotically normal. A numerical example and a simulation study are also given.

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LOCAL IDENTIFICATION IN EMPIRICAL GAMES OF INCOMPLETE INFORMATION

不完全信息经验博弈的局部识别

This paper studies identification for a broad class of empirical games in a general functional setting. Global identification results are known for some specific models, e.g., in some standard auction models. We use functional formulations to obtain general criteria for local identification. These criteria can be applied to both parametric and nonparametric models, and also to models with asymmetry among players and affiliated private information. A benchmark model is…

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SMOOTH VARYING-COEFFICIENT ESTIMATION AND INFERENCE FOR QUALITATIVE AND QUANTITATIVE DATA

兼容定性与定量数据的平滑变系数估计与推断

We propose a semiparametric varying-coefficient estimator that admits both qualitative and quantitative covariates along with a test for correct specification of parametric varying-coefficient models. The proposed estimator is exceedingly flexible and has a wide range of potential applications including hierarchical (mixed) settings, small area estimation, etc. A data-driven cross-validatory bandwidth selection method is proposed that can handle both the qualitative and…

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INSTRUMENTAL VARIABLE ESTIMATION IN A DATA RICH ENVIRONMENT

数据丰富环境中的工具变量估计

We consider estimation of parameters in a regression model with endogenous regressors. The endogenous regressors along with a large number of other endogenous variables are driven by a small number of unobservable exogenous common factors. We show that the estimated common factors can be used as instrumental variables and they are more efficient than the observed variables in our framework. Whereas standard optimal generalized method of moments estimator using a large number…

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MIXED NORMAL INFERENCE ON MULTICOINTEGRATION

多重协整的混合正态推断

Asymptotic likelihood analysis of cointegration in I (2) models (see Johansen, 1997, 2006; Boswijk, 2000; Paruolo, 2000) has shown that inference on most parameters is mixed normal, implying hypothesis test statistics with an asymptotic χ 2 null distribution. The asymptotic distribution of the multicointegration parameter estimator so far has been characterized by a Brownian motion functional, which has been conjectured to have a mixed normal distribution, based on…

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UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

局部多项式 M 回归估计的一致 Bahadur 表示及其加性模型应用

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {( Y i , X i )}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We…

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FULLY MODIFIED ESTIMATION OF SEASONALLY COINTEGRATED PROCESSES

季节协整过程的完全修正估计

We extend the framework of the fully modified, ordinary least squares (OLS) estimator introduced by Phillips and Hansen (1990) to the case of seasonally cointegrated processes at a given frequency. First we extend a weak convergence result of sample covariance matrices (Phillips, 1988) to the case of seasonal unit roots. Using a complex number framework, we then show that we can take into account the constraints that exist in a situation of seasonal cointegration as…

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TIME-VARYING COINTEGRATION

时变协整

In this paper we propose a time-varying vector error correction model in which the cointegrating relationship varies smoothly over time. The Johansen setup is a special case of our model. A likelihood ratio test for time-invariant cointegration is defined and its asymptotic chi-square distribution is derived. We apply our test to the purchasing power parity hypothesis of international prices and nominal exchange rates, and we find evidence of time-varying cointegration.

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RISK MINIMIZATION FOR TIME SERIES BINARY CHOICE WITH VARIABLE SELECTION

带变量选择的时间序列二元选择风险最小化

This paper considers the problem of predicting binary choices by selecting from a possibly large set of candidate explanatory variables, which can include both exogenous variables and lagged dependent variables. We consider risk minimization with the risk function being the predictive classification error. We study the convergence rates of empirical risk minimization in both the frequentist and Bayesian approaches. The Bayesian treatment uses a Gibbs posterior constructed…

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ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA

依赖且异质数据的尾指数估计

In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for processes with extremes that form mixingale sequences and asymptotically normal…

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ESTIMATION OF UNIT ROOT SPATIAL DYNAMIC PANEL DATA MODELS

单位根空间动态面板数据模型的估计

This paper examines the asymptotics of the QMLE for unit root dynamic panel data models with spatial effect and fixed effects. We consider a unit root dynamic panel data model with spatially correlated disturbances and a unit root spatial dynamic panel data model. For both models the estimate of the dynamic coefficient is $\root \of {nT^3 }$ consistent and the estimates of other parameters are $\root \of {nT}$ consistent, and all of them are asymptotically normal. For the…

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ASYMPTOTICALLY UNBIASED ESTIMATION OF AUTOCOVARIANCES AND AUTOCORRELATIONS WITH LONG PANEL DATA

长面板数据中自协方差与自相关的渐近无偏估计

An important reason for analyzing panel data is to observe the dynamic nature of an economic variable separately from its time-invariant unobserved heterogeneity. This paper examines how to estimate the autocovariances of a variable separately from its time-invariant unobserved heterogeneity. When both cross-sectional and time series sample sizes tend to infinity, we show that the within-group autocovariances are consistent, although they are severely biased when the time…

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TESTS OF THE MARTINGALE DIFFERENCE HYPOTHESIS USING BOOSTING AND RBF NEURAL NETWORK APPROXIMATIONS

基于 Boosting 与径向基神经网络近似的鞅差假设检验

The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function (RBF) neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a, 2003b). However, unlike that work we provide a formal theoretical justification for the validity of these tests and present some new general…

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UNIT ROOT TESTS WITH WAVELETS

基于小波的单位根检验

This paper develops a wavelet (spectral) approach to testing the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By decomposing the variance (energy) of the underlying process into the variance of its low frequency components and that of its high frequency components via the discrete wavelet…

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ON THE SPECTRAL PROPERTIES OF MATRICES ASSOCIATED WITH TREND FILTERS

趋势滤波器相关矩阵的谱性质

This note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties, such as the circulant and the generalized tau. These results are used to characterize the properties of a smoother in terms of an approximate eigen-decomposition of the associated…

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CONFIDENCE BANDS IN QUANTILE REGRESSION

分位数回归的置信带

Let ( X 1 , Y 1 ), …, ( X n , Y n ) be independent and identically distributed random variables and let l ( x ) be the unknown p -quantile regression curve of Y conditional on X . A quantile smoother l n ( x ) is a localized, nonlinear estimator of l ( x ). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process { l n ( x ) – l ( x )}. Using strong approximations of…

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ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES

谱密度估计的渐近理论

We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

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CHARACTERISTIC FUNCTION–BASED TESTING FOR MULTIFACTOR CONTINUOUS-TIME MARKOV MODELS VIA NONPARAMETRIC REGRESSION

通过非参数回归与特征函数检验多因子连续时间马尔可夫模型

We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed form or can be approximated accurately for many popular continuous-time Markov models in economics and finance. An omnibus test fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time…

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NONSTATIONARITY-EXTENDED WHITTLE ESTIMATION

扩展至非平稳情形的 Whittle 估计

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used fractional autoregressive integrated moving average models with generalized autoregressive conditional heteroskedastic-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso, and Giraitis (2007, Journal of Econometrics…

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ASYMPTOTIC THEORY FOR EMPIRICAL SIMILARITY MODELS

经验相似性模型的渐近理论

We consider the stochastic process $Y_t = \sum\nolimits_{i < t} {s_w } (x_t ,x_i)Y_i /\sum\nolimits_{i < t} {s_w } (x_t ,x_i) + \varepsilon _t$ , t = 2, …, n , where s w ( x t , x i ) is a similarity function between the t th and the i th observations and { ε t } is a random disturbance term. This process was originally axiomatized by Gilboa, Lieberman, and Schmeidler (2006, Review of Economics and Statistics 88, 433–444) as a way by which agents, or…

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