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

Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov and Kengo Kato

Journal of Econometrics, 2015, vol. 186, issue 2, 345-366

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.

Keywords: Least squares series; Strong approximations; Uniform confidence bands (search for similar items in EconPapers)
JEL-codes: C01 C14 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (133)

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Working Paper: Some New Asymptotic Theory for Least Squares Series: Pointwise and Uniform Results (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:186:y:2015:i:2:p:345-366

DOI: 10.1016/j.jeconom.2015.02.014

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