Some new asymptotic theory for least squares series: Pointwise and uniform results

A-Tier
Journal: Journal of Econometrics
Year: 2015
Volume: 186
Issue: 2
Pages: 345-366

Authors (4)

Belloni, Alexandre (not in RePEc) Chernozhukov, Victor (Massachusetts Institute of Tec...) Chetverikov, Denis (not in RePEc) Kato, Kengo (not in RePEc)

Score contribution per author:

1.009 = (α=2.02 / 4 authors) × 2.0x A-tier

α: calibrated so average coauthorship-adjusted count equals average raw count

Abstract

In econometric applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements over a pre-specified functional form, especially if they nest some successful parametric economically-motivated forms. Series method offers exactly that by approximating the unknown function based on k basis functions, where k is allowed to grow with the sample size n to balance the trade off between variance and bias. In this work we consider series estimators for the conditional mean in light of four new ingredients: (i) sharp LLNs for matrices derived from the non-commutative Khinchin inequalities, (ii) bounds on the Lebesgue factor that controls the ratio between the L∞ and L2-norms of approximation errors, (iii) maximal inequalities for processes whose entropy integrals diverge at some rate, and (iv) strong approximations to series-type processes.

Technical Details

RePEc Handle
repec:eee:econom:v:186:y:2015:i:2:p:345-366
Journal Field
Econometrics
Author Count
4
Added to Database
2026-01-25