Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing

Abstract

A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidth, random trimming, and estimated weights. An extension allows for generated regressors, without requiring the calculation of functional derivatives. Example applications are provided for a binary choice model with selection, including a new semiparametric maximum likelihood estimator, and a new directional test for correct specification of the average structural function. An extended Appendix contains general results on uniform rates for kernel estimators, additional applications, and primitive sufficient conditions for high level assumptions.

Semiparametric estimation of moment condition models with weakly dependent data

“…Assumption 5(a) assumes uniform consistency (possibly also with respect to α) of the nonparametric estimator used for h 0 . This is a standard assumption in the semiparametric literature of two-step estimation procedures, see, e.g., Chen et al (2003), Escanciano et al (2014Escanciano et al ( , 2016, Chen et al (2016), andBravo et al (2016). Similarly, Andrews (1995) provides sufficient conditions including the case of estimated random variables for kernel smoothing estimators.…”

“…This case is empirically relevant because it often arises in situations where an estimated variable is used as a proxy for an unobservable variable of interest, such as for example the risk term in finance, and it is also theoretically interesting because with weakly dependent data the characterization of the estimation effect is more complicated. As far as we are aware of, this is the first paper that fully considers the estimation effect in semiparametric generalized estimating equations models with weakly dependent observations (see Mammen et al, 2015 andEscanciano et al, 2014 for the case of just-identified semiparametric estimating equations models with independent and identically distributed (i.i.d.) observations).…”

Minimum Distance Estimation of Search Costs Using Price Distribution

“…We assume the search model described in Section 2 serves as a (very) crude approximation of the true mechanism that generates the prices that we see in the data. 14 We obtain the data from http://www.oddsportal.com/, which is an open website that collects 13 Gambling operators have been able to advertise on TV and radio from 1st of September 2007. Previously the rules for advertising for all types of gambling companies, including casinos and betting shops have been highly regulated.…”

“…Traditional outlets for advertising are through magazines and newspapers, or other means to get public attention such as sponsoring major sporting events. Further information on the background and impact of the Gambling Act 2005 can be found in the review produced by the Committees of Advertising Practice at the request by the Department for Culture, Media and Sport, http://www.cap.org.uk/Newsreports/~/media/Files/CAP/Reports%20and%20surveys/CAP%20and%20BCAP%20Gambling%20Review.ashx 14 We highlight three underlying assumptions of the theoretical model. First, products are homogeneous.…”

Generalized empirical likelihood M testing for semiparametric models with time series data

“…Second, we explicitly consider the case where the estimation of the infinite dimensional parameter might affect the asymptotic properties of the proposed GEL and LM statistics and provide a general formula to characterize it. The characterization is based on the pathwise derivative as in Newey (1994) and relies on a certain A C C E P T E D M A N U S C R I P T linear representation of the infinite dimensional estimator, which is satisfied for example in the important case of nonparametric regression estimators and can also be used when the infinite dimensional parameter can depend on estimated random vectors -the so-called nonparametric generated regressor, see for example Escanciano, Jacho-Chávez, andLewbel (2014, 2016). Finally we propose a test for omitted covariates in a partially linear regression model in which we allow some of the covariates to be endogenous (that is they are correlated with the unobservable errors) and others not to be directly observable but can be consistently estimated.…”