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My research interests are in theoretical/applied Econometrics and Statistics. I am particularly interested in nonparametric and semiparametric models for regression. My research has appeared in the Journal of Econometrics, International Economic Review, Journal of Multivariate Analysis, Annals of Statistical Mathematics, Journal of Nonparametric Statistics, Econometric Reviews, RAND Journal of Economics, etc.
I have served as a referee for journals such as: Annals of Statistics, Journal of Econometrics, Journal of the American Statistical Association, Journal of Applied Econometrics, Econometric Reviews, Journal of Nonparametric Statistics, Journal of Multivariate Analysis, RAND Journal of Economics, etc. I am also a reviewer for Mathematical Reviews.
Recent Published or Forthcoming Papers:
Nonparametric regression estimation with general parametric error covariance (with F. Yao), Journal of Multivariate Analysis, forthcoming.
Abstract: The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the error covariance matrix is proposed. Sufficient conditions for its asymptotic normality are given and its efficiency relative to the local linear estimator is established. We give examples of how our results are useful in some recently studied regression models. A Monte Carlo study confirms the asymptotic theory predictions and compares our estimator with some recently proposed alternative estimation procedures.
A class of improved parametrically guided nonparametric regression estimators (with S. Mishra and A. Ullah), Econometric Reviews, 27, 542-573, 2008. (working paper version).
Abstract: In this paper we define a class of improved semiparametric estimators for a regression model. The estimators in the class are obtained via a simple two stage procedure. In the first stage, a potentially misspecified parametric model is estimated and in the second stage the parametric estimate is used to guide the derivation of a final semiparametric estimator. Mathematically, the proposed estimators can be thought as the minimization of a suitably defined Cressie-Read discrepancy that can be showed to produce conventional nonparametric estimators, such as the local polynomial estimator, as well as existing two stage multiplicative estimators, such as that proposed by Glad (1998). We show that under fairly mild conditions the estimators in the proposed class are square root (nh) asymptotically normal and explore their finite sample (simulation) behavior.
A smooth conditional quantile frontier estimator (with F. Yao), Journal of Econometrics, 143, 317-333, 2008. (working paper version)
Abstract: Traditional estimators for nonparametric frontier models (DEA, FDH) are very sensitive to extreme values/outliers. Recently, Aragon, Daouia, and Thomas-Agnan (2005) proposed a nonparametric alpha-frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values/outliers. Their proposed estimator is simple to construct but produces a nonsmooth estimated alpha-frontiers even when the underlying technology induces smooth frontiers. In this paper, we propose a new smooth nonparametric conditional quantile estimator for the alpha-frontier model. Our estimator is a kernel based conditional quantile estimator that builds on early work of Azzalini (1981). It is computationally simple, resistant to outliers and extreme values, and smooth. In addition, the estimator is also shown to be consistent and square root- n asymptotically normal under mild regularity conditions. We also show that our estimator's variance is of smaller order than that of the estimator proposed by Aragon et al. A simulation study confirms the asymptotic theory predictions and contrasts our estimator with that of Aragon et al.
Nonparametric frontier estimation via local linear regression (with F. Yao), Journal of Econometrics, 141, 283-319, 2007. (working paper version)
Abstract: In this paper we propose a nonparametric regression frontier model that assumes no specific parametric family of densities for the unobserved stochastic component that represents efficiency in the model. Nonparametric estimation of the regression frontier is obtained using a local linear estimator that is shown to be consistent and $\sqrt{nh_n}$ asymptotically normal under standard assumptions. The estimator we propose envelops the data but is not inherently biased as Free Disposal Hull - FDH or Data Envelopment Analysis - DEA estimators. It is also more robust to extreme values than the aforementioned estimators. A Monte Carlo study is performed to provide preliminary evidence on the estimator's finite sample properties and to compare its performance to a bias corrected FDH estimator.
Finite Sample performance of backfitting, marginal integration and two stage estimators under common bandwidth selection criterion (with K. Yang), Journal of Nonparametric Statistics, 19, 23-62, 2007. (working paper version)
Abstract: In this paper we investigate the finite sample performance of four kernel-based estimators that are currently available for additive nonparametric regression models - the classic backfitting estimator (CBE), the smooth backfitting estimator (SBE), the marginal integration estimator (MIE) and two versions of a two-stage estimator (2SE1, 2SE2), the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this paper. The bandwidths are selected for each estimator by minimizing their respective asymptotic approximation of the mean average squared errors (AMASE). In our simulations, we are particularly concerned with the performance of these estimators under this unified data-driven bandwidth selection method, since in this case both the asymptotic and the finite sample properties of all estimators are currently unavailable. The comparison is based on the estimators' average squared error. Our Monte Carlo results seem to suggest that the CBE is the best performing kernel-based procedure.
A Note on the Use of V and U statistics in Nonparametric Models of Regression (with F. Yao), Annals of the Institute of Statistical Mathematics, 58, 389-406, 2006. (working paper version)
Abstract: We establish the $\sqrt{n}$ asymptotic equivalence of V and U statistics when the statistic's kernel depends on n. Combined with a lemma of Lee (1988) this result provides conditions under which U statistics projections (Hoeffding, 1961) and V statistics are $\sqrt{n}$ asymptotically equivalent. The use of this equivalence in nonparametric regression models is illustrated with several examples; the estimation of conditional variances, skewness, kurtosis and the construction of a nonparametric R-squared measure.
Estimation of value-at-risk and expected shortfall based on nonlinear models of return dynamics and Extreme Value Theory (with F. Yao), Studies in Nonlinear Dynamics and Econometrics, 10, 4, 2006. (working paper version)
Abstract: We propose an estimation procedure for value at risk (VaR) and expected shortfall (TailVaR) for conditional distributions of a time series of returns on a financial asset. Our approach combines a local polynomial estimator of conditional mean and volatility functions in a conditional heterocedastic autoregressive nonlinear (CHARN) model with Extreme Value Theory for estimating quantiles of the conditional distribution. We investigate the finite sample properties of our method and contrast them with alternatives, including the method recently proposed by McNeil and Frey(2000), in an extensive Monte Carlo study. The method we propose outperforms the estimators currently available in the literature.
Recent Working Papers:
Abstract: The introduction of directional distance functions has given researchers an alternative to Shephard distance functions. In this paper we conduct a Monte Carlo study to determine which distance function better approximates models of technology. We conclude that quadratic representations of technology have better economic approximation properties than translog parameterizations.