Emmanuel Guerre

Data-Driven Rate-Optimal Specification Testing in Regression Models

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/sqrt(n). Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.

Uniform Bias Study and Bahadur Representation for Local Polynomial Estimators of the Conditional Quantile Function

This paper investigates the bias and the weak Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the quantile level, the covariates and the smoothing parameter. The order of the local polynomial estimator can be higher than the differentiability order of the conditional quantile function. Applications of the results deal with global optimal consistency rates of the local polynomial quantile estimator, performance of random bandwidths and estimation of the conditional quantile density function. The latter allows to obtain a simple estimator of the conditional quantile function of the private values in a first price sealed bids auctions under the independent private values paradigm and risk neutrality.

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

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.

A Data-Driven Nonparametric Specification Test For Dynamic Regression Models

The paper introduces a new nonparametric specification test for dynamic regression models. The test combines chi-square statistics based on Fourier series regression. A data-driven choice of the regression order, which uses the square root of the number of Fourier coefficients, is proposed. The benefits of the new test are (1) the selection procedure produces explicit and chi-square critical values that give a finite-sample size close to the nominal size; (2) the test is adaptive rate-optimal and detects local alternatives converging to the null with a rate that can be made arbitrarily close to the parametric rate. Simulation experiments illustrate the practical relevance of the new test.The first author acknowledges financial support from the Fonds QuA©bA©cois de la Recherche sur la SociA©tA© et la Culture (FQRSC). The second author acknowledges financial support from LSTA.

A Study of a Semiparametric Binary Choice Model with Integrated Covariates

This paper studies a semiparametric nonstationary binary choice model. Imposing a spherical normalization constraint on the parameter for identification purpose, we find that the MSE and SMSE are at least sqrt(n)-consistent. Comparing this rate to the parametric MLE’s convergence rate, we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000)’s parametric MLE converges at a rate of n^(3/4) and its limiting distribution is a mixed normal. Finally, we show briefy how to apply our estimation method to a nonstationary single index model.

A Note on the Nonstationary Binary Choice Logit Model

This paper derives the rate and the asymptotic distribution of the MLE of the parameter of a logit model with a nonstationary covariate when the true parameter is zero. The limit distribution of the t-statistic is also given.

Robust adaptive rate-optimal testing for the white noise hypothesis

A new test is proposed for the weak white noise null hypothesis. The test is based on a new automatic selection of the order for a Box–Pierce (1970) test statistic or the test statistic of Hong (1996). The heteroskedasticity and autocorrelation-consistent (HAC) critical values from Lee (2007) are used, allowing for estimation of the error term. The data-driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o(n−1/2) provided there are sufficiently many of such coefficients. A simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative.

Geometric versus arithmetic random walk. The case of trended variables

The asymptotic behavior of the empirical means and variances for the geometric and arithmetic random walks are studied, when the underlying random walk is trended. Thus the effect of misspecifications can be described, and two tests are proposed. The first test uses a classical approach in model selection and is based on the comparison of estimated quasi likelihoods. The second one is obtained by estimating some nuisance parameters in a Neyman-Pearson test. Some bounds for the power functions are given, which suggest that the second test may be very powerful and better than the first one