Abstract
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.
Original language | English (US) |
---|---|
Pages (from-to) | 447-465 |
Number of pages | 19 |
Journal | Journal of Econometrics |
Volume | 188 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1 2015 |
Keywords
- Nonparametric series regression
- Optimal uniform convergence rates
- Random matrices
- Sieve t statistics
- Splines
- Wavelets (Nonlinear) Irregular functionals
- Weak dependence
ASJC Scopus subject areas
- Economics and Econometrics