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Semiparametric Estimation of a Single-Index Model with Nonparametrically Generated Regressors

含非参数生成解释变量的单指标模型半参数估计

This paper develops a theory of estimating parameters of a generated regressor model in which some explanatory variables in the equation of interest are the unknown conditional means of certain observable variables given other observable regressors. The paper imposes a weak nonparametric restriction on the form of the conditional means and maintains a single-index assumption on the distribution of the dependent variable in the equation of interest. The estimation method…

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The Encompassing Principle and Hypothesis Testing

涵盖原则与假设检验

The exponentially tilted family of densities is used to discuss the relationship between the encompassing principle and the M -test or conditional moment testing principle. It is shown that the two principles are capable of generating the same test statistics and in this sense equivalent. However, there are differences in motivation and emphasis underlying the principles that are important in econometric modeling. In addition, parsimonious encompassing interpretations for…

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Infinite-Order Cointegrated Vector Autoregressive Processes

无限阶协整向量自回归过程

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the…

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Spectral Analysis for Bivariate Time Series with Long Memory

双变量长记忆时间序列的谱分析

This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time…

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Sobolev Estimation of Approximate Regressions

近似回归的 Sobolev 估计

This paper focuses on the estimation of an approximated function and its derivatives. Let us assume that the data-generating process can be described by a family of regression models , where a is a multi-index of differentiation such that D α ϕ(x i ) is the αth derivative of ϕ( x i ) with respect to x i . The estimated model is characterized by a family D α f(X i |θ), where D α f(X i |θ) is the αth derivative of f(x i ,|θ) and θ is an unknown parameter. The model is in…

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Conditional Quantile Estimation and Inference for Arch Models

ARCH 模型的条件分位数估计与推断

Quantile regression methods are suggested for a class of ARCH models. Because conditional quantiles are readily interpretable in semiparametric ARCH models and are inherendy easier to estimate robustly than population moments, they offer some advantages over more familiar methods based on Gaussian likelihoods. Related inference methods, including the construction of prediction intervals, are also briefly discussed.

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Modeling Stock Prices without Knowing How to Induce Stationarity

无需预先确定平稳化方式的股票价格建模:计算更正

In “Modeling Stock Prices without Knowing How to Induce Stationarity” (1994, Econometric Theory 10, 701–719), we used posterior-odds calculations to evaluate restrictions imposed by a present-value model of stock prices across the equations of a VAR representation of stock prices and dividends. The results we reported are tainted by the omission of two factors: the Jacobians induced by the mapping of our priors over VAR parameters β into the restricted sample spaces relevant…

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The Identifiability of the Mixed Proportional Hazards Model with Time-Varying Coefficients

时变系数混合比例风险模型的可识别性

This paper establishes conditions for the nonparametric identifiability of the mixed proportional hazards model with time-varying coefficients. Unlike the mixed proportional hazards model, a regressor with two distinct values is not sufficient to identify this model. An unbounded regressor, however, is sufficient for identification.

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Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

近观测等价与单位根检验的理论尺寸问题

Said and Dickey (1984, Biometrika 71, 599–608) and Phillips and Perron (1988, Biometrika 75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is…

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The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test

随机游走水平穿越次数的极限分布与简单单位根检验

We derive the limit distribution of the number of crossings of a level by a random walk with continuously distributed increments, using a Brownian motion local time approximation. This complements the well-known result for the random walk on the integers. Use of the frequency of level crossings to test for a unit root is examined.

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Which Moments to Match?

应该匹配哪些矩?

We describe an intuitive, simple, and systematic approach to generating moment conditions for generalized method of moments (GMM) estimation of the parameters of a structural model. The idea is to use the score of a density that has an analytic expression to define the GMM criterion. The auxiliary model that generates the score should closely approximate the distribution' of the observed data but is not required to nest it. If the auxiliary model nests the structural model…

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