scholarly journals Additive Nonparametric Instrumental Regressions: A Guide to Implementation

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Samuele Centorrino ◽  
Frederique Feve ◽  
Jean-Pierre Florens
Keyword(s):  
Instrumental Variables ◽  
Regularization Method ◽  
Regression Models ◽  
Regression Function ◽  
Data Driven ◽  
Finite Sample ◽  
Partially Linear ◽  
Regularization Parameters ◽  
Finite Sample Properties ◽  
Additive Nonparametric Regression

AbstractWe present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

scholarly journals Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

1990 ◽  
Vol 6 (4) ◽  
pp. 466-479 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Yoon-Jae Whang
Keyword(s):  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Regression Models ◽  
Regression Function ◽  
Curse Of Dimensionality ◽  
Finite Sample ◽  
Squared Error ◽  
Convergence Results ◽  
Additive Regression ◽  
Parametric Regression Models

This paper considers series estimators of additive interactive regression (AIR) models. AIR models are nonparametric regression models that generalize additive regression models by allowing interactions between different regressor variables. They place more restrictions on the regression function, however, than do fully nonparametric regression models. By doing so, they attempt to circumvent the curse of dimensionality that afflicts the estimation of fully non-parametric regression models.In this paper, we present a finite sample bound and asymptotic rate of convergence results for the mean average squared error of series estimators that show that AIR models do circumvent the curse of dimensionality. A lower bound on the rate of convergence of these estimators is shown to depend on the order of the AIR model and the smoothness of the regression function, but not on the dimension of the regressor vector. Series estimators with fixed and data-dependent truncation parameters are considered.

NONPARAMETRIC FILTERING OF THE REALIZED SPOT VOLATILITY: A KERNEL-BASED APPROACH

2009 ◽  
Vol 26 (1) ◽  
pp. 60-93 ◽  
Author(s):  
Dennis Kristensen
Keyword(s):  
Realized Volatility ◽  
Data Driven ◽  
Selection Methods ◽  
Finite Sample ◽  
Weighted Version ◽  
Integrated Volatility ◽  
Finite Sample Properties ◽  
Boundary Issues ◽  
Consistency And Asymptotic Normality ◽  
Spot Volatility

A kernel weighted version of the standard realized integrated volatility estimator is proposed. By different choices of the kernel and bandwidth, the measure allows us to focus on specific characteristics of the volatility process. In particular, as the bandwidth vanishes, an estimator of the realized spot volatility is obtained. We denote this the filtered spot volatility. We show consistency and asymptotic normality of the kernel smoothed realized volatility and the filtered spot volatility. We consider boundary issues and propose two methods to handle these. The choice of bandwidth is discussed and data-driven selection methods are proposed. A simulation study examines the finite sample properties of the estimators.

scholarly journals Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 22 ◽  
Author(s):  
Pierre Perron ◽  
Yohei Yamamoto
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Structural Changes ◽  
Error Variance ◽  
Regression Coefficients ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Joint Approach ◽  
Size Distortions

In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that testing for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron et al. (2019) provide tests with good size and power.

scholarly journals TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR MODELS

2010 ◽  
Vol 26 (6) ◽  
pp. 1761-1806 ◽  
Author(s):  
Liangjun Su ◽  
Halbert White
Keyword(s):  
Structural Change ◽  
Linear Models ◽  
Linear Time ◽  
Semiparametric Regression ◽  
Parametric Models ◽  
Finite Sample ◽  
Weighted Residuals ◽  
Partially Linear ◽  
Finite Sample Properties ◽  
Cumulative Sums

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 under the null hypothesis of no structural change and for sequences of local alternatives. We show that the tests are generally not asymptotically pivotal under the null but may be free of nuisance parameters asymptotically under further asymptotic stationarity conditions. Our tests thus complement the conventional instability tests for parametric models. To improve the finite-sample performance of our tests, we also propose a wild bootstrap version of our tests and justify its validity. Finally, we conduct a small set of Monte Carlo simulations to investigate the finite-sample properties of the tests.

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