Efficient estimation of generalized additive nonparametric regression models.

We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the Linton and Härdle (1996, Biometrika 83, 529–540) integration-based method and achieve certain oracle bounds. We consider criterion functions based on the Linear exponential family, which includes many important special cases. We also consider the extension to multiple parameter models like the gamma distribution and to models for conditional heteroskedasticity.

Nonparametric inference for unbalance time series data

Estimation of heteroskedasticity and autocorrelation consistent covariance matrices (HACs) is a well established problem in time series. Results have been established under a variety of weak conditions on temporal dependence and heterogeneity that allow one to conduct inference on a variety of statistics, see Newey and West (1987), Hansen (1992), de Jong and Davidson (2000), and Robinson (2004). Indeed there is an extensive literature on automating these procedures starting with Andrews (1991). Alternative methods for conducting inference include the bootstrap for which there is also now a very active research program in time series especially, see Lahiri (2003) for an overview. One convenient method for time series is the subsampling approach of Politis, Romano, andWolf (1999). This method was used by Linton, Maasoumi, andWhang (2003) (henceforth LMW) in the context of testing for stochastic dominance. This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a standard HAC/bootstrap theory applies, but at the expense of throwing away data and perhaps losing effciency. An alternative is to use some sort of imputation method, but this requires additional modelling assumptions, which we would rather avoid.1 We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss effciency and power. Unbalanced data of the type we consider are quite common in financial panel data, see for example Connor and Korajczyk (1993). These data also occur in cross-country studies.

Nonparametric Inference for Unbalanced Time Series Data

This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a standard HAC/Bootstrap theory applies, but at the expense of throwing away data and perhaps losing efficiency. An alternative is to use some sort of imputation method, but this requires additional modelling assumptions, which we would rather avoid. We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss efficiency and power. Unbalanced data of the type we consider are quite common in financial panel data, see, for example, Connor and Korajczyk (1993). These data also occur in cross-country studies.Bootstrap, efficient, HAC estimation, missing data, subsampling.

Nonparametric Censored Regression

The nonparametric censored regression model is y = max[c, m(x) + e], where both the regression function m(x) and the distribution of the error e are unknown, but the fixed censoring point c is known. This paper provides a simple consistent estimator of the derivative of m(x) with respect to each element of x. The convergence rate of this estimator is the same as for the derivatives of an uncensored nonparametric regression. We then estimate the regression function itself by solving the associated partial differential equation system. We show that our estimator of m(x) achieves the same rate of convergence as the usual estimators in uncensored nonparametric regression. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in any linear or partly linear specification for m(x).Semiparametric, nonparametric, censored regression, Tobit, latent variable

Consistent estimation of the risk-return tradeoff in the presence of measurement error

Prominent asset pricing models imply a linear, time-invariant relation between the equity premium and its conditional variance. We propose an approach to estimating this relation that overcomes some of the limitations of the existing literature. First, we do not require any functional form assumptions about the conditional moments. Second, the GMM approach is used to overcome the endogeneity problem inherent in the regression. Third, we correct for the measurement error arising because of using a proxy for the latent variance. The empirical findings reveal significant time-variation in the relation that coincide with structural break dates in the market-wide price-dividend rati

Evaluating hedge fund performance: a stochastic dominance approach

We introduce a general and flexible framework for hedge fund performance evaluation and asset allocation: stochastic dominance (SD) theory. Our approach utilizes statistical tests for stochastic dominance to compare the returns of hedge funds. We form hedge fund portfolios by using SD criteria and examine the out-of-sample performance of these hedge fund portfolios. Compared to performance of portfolios of randomly selected hedge funds and mean-variance e¢ cient hedge funds, our results show that fund selection method based on SD criteria greatly improves the performance of hedge fund portfolio

A smoothed least squares estimator for threshold regression models

We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen (2000) to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold e¤ect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the threshold parameters themselves. We compare our con dence intervals with those of Hansen (2000) in a simulation study and show that our methods outperform his for large values of the threshold. We also include an application to cross-country growth regressions

Estimating Quadratic VariationConsistently in thePresence of Correlated MeasurementError

We propose an econometric model that captures the e¤ects of marketmicrostructure on a latent price process. In particular, we allow for correlationbetween the measurement error and the return process and we allow themeasurement error process to have a diurnal heteroskedasticity. Wepropose a modification of the TSRV estimator of quadratic variation. Weshow that this estimator is consistent, with a rate of convergence thatdepends on the size of the measurement error, but is no worse than n1=6.We investigate in simulation experiments the finite sample performance ofvarious proposed implementations.Endogenous noise, Market Microstructure, Realised Volatility,Semimartingale

Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods

We investigate a class of semiparametric ARCH(8) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the 'news impact' function. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric and nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 daily returns. We find some evidence of asymmetric news impact functions in the data.ARCH, inverse problem, kernel estimation, news impact curve, nonparametric regression, profile likelihood, semiparametric estimation, volatility

Semiparametric Estimation of aCharacteristic-based Factor Model ofCommon Stock Returns

We introduce an alternative version of the Fama-French three-factor model of stockreturns together with a new estimation methodology. We assume that the factorbetas in the model are smooth nonlinear functions of observed securitycharacteristics. We develop an estimation procedure that combines nonparametrickernel methods for constructing mimicking portfolios with parametric nonlinearregression to estimate factor returns and factor betas simultaneously. Themethodology is applied to US common stocks and the empirical findings comparedto those of Fama and French.characteristic-based factor model, arbitrage pricing theory, kernelestimation, nonparametric estimation.