UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

By Efang Kong, Oliver B. Linton, Yingcun Xia. Econometric Theory, 2007

129 citations recorded by the source corpus.

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi, Xi)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/03a5976ee1d1bf98f5057050f18164be369e9b53

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Local quantile regression (2010, background): “Another line of literature considers structural semipara- metric models to cope with the curse of dimensionality, like, partial linear models, Härdle et al. (2012), etc., additive models, Kong et al. (2010), Horowitz and Lee (2005), etc; single index models, Wu et al. (2010), Koenker (2010), etc.”
Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆ (2013, background): “8 For a recent detailed discussion of the applicability of the Bahadur representation to semiparametric inference, and such a result for kernel-based local polynomials, see Kong et al. (2010).”
Intersection bounds: estimation and inference (2009, methodology): “ |Ap|×1 vector 34 such that up(z) = {zu : u ∈ Ap}, Bn(z,j) = O(hp+1 n ) and Rn(z,j) = oP δn (nhd n)1/2 , uniformly in (z,j) ∈ Z × {1,...,J}. The exact form of Bn(z,j) is given in equation (12) of [39]. The result that Bn(z,j) = O(h p+1 n ) uniformly in (z,j) follows from the standard argument base”
Conditional quantile processes based on series or many regressors (2011, background): “[13] Xiaohong Chen and Xiaotong Shen.”
Massachusetts Institute of Technology Department of Economics Working Paper Series Conditional Quantile Processes Based on Series or Many Regressors Conditional Quantile Processes Based on Series or Many Regressors (unknown): “Other very important work includes Chaudhuri [10], and Chaudhuri, Doksum and Samarov [11], Härdle, Ritov, and Song [20], Cattaneo, Crump, and Jansson [8], and Kong, Linton, and Xia [27], among others, but this work focused on local, non-series, methods.”
UNIFORM BIAS STUDY AND BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATORS OF THE CONDITIONAL QUANTILE FUNCTION (2011, background): “Hence Kong et al. (2010) derives a strong uniform Bahadur representation for robust local polynomial M-estimators for dependent observations.”
Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions (2013, unknown): “This is a minor variation of results given in e.g. Masry (1996) or Kong, Linton, and Xia (2010).”
A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION (2012, methodology): “The proof then would involve truncating techniques used in Masry (1996), as well as in Kong et al. (2010).”
CONFIDENCE BANDS IN QUANTILE REGRESSION (2009, methodology): “More generally, for an M-regression function that involves quantile regression as a special case, the uniform Bahadur representation and application to the additive model are studied by Kong, Linton, and Xia (2010).”
TENET: Tail-Event driven NETwork risk (2016, background): “In fact we assume an exponential decaying rate here, which implies the (A.4) in Kong et al. (2010).”