Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions

By Xiaohong Chen, Timothy M. Christensen. 2014

167 citations recorded by the source corpus.

We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e. sup-norm) convergence rate (n/logn)−p/(2p+d) of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2+(d/p))th absolute moment for d/p<2. We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.

Subfields: Applied Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5887ce8b4ae719af24188a42e426718989083cde

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Citations in the corpus

Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “2 deliver Bernstein-type inequalities or sums and `∞-norms of random matrices formed from β-mixing sequences, extending the result of Chen and Christensen (2015) from the case of a weakly dependent series to panel setting.”
Nonparametric stochastic discount factor decomposition (2014, methodology): “istic sequence of vectors v K2RK with kv Kk= 1. Proof of Lemma D.5. For part (a) we use a truncation argument in conjunction with an exponential inequality for weakly dependent random matrices due to Chen and Christensen (2014). Let fT n: n1gbe a sequence of positive constants to be dened subsequent”
Nonlinearity and Flight‐to‐Safety in the Risk‐Return Trade‐Off for Stocks and Bonds (2019, unknown): “16 In particular, we show the slope of the Treasury yield curve as measured by TERM, the Cochrane and Piazzesi (2005) CP factor, the BAA-AAA credit spread (DEF), the dividend yield (DY) of the S&P500, the CAY factor by Lettau and Ludvigson (2001), the variance risk premium (VRP) of Bollerslev et al.”
Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations (2013, unknown): “d has been used for diverging-dimensions parametric models (He and Shao 2000) and nonparametrics (Newey 1997, Huang 2003, Cattaneo and Farrell 2013, Belloni, Chernozhukov, Chetverikov, and Kato 2015, Chen and Christensen 2015). The eigenvalue assumptions employed in those works are conceptually the ”
Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2015, background): “Xn i=1 (ub i u i)2bK(W i)bK(W i)0 ! G 1=2 b ‘2 O p(( (2+)= b;K p (logK)=n)=(1+)) + kbh h 0k 1 O p(1) + kbh h 0k21 O p(1) where the rst term may easily be deduced from the proof of Lemma 3.1 of Chen and Christensen (2014), the second then follows because 2u i(bu i u i) 2(1 + u2 i )kbh h 0k 1, and th”