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Some New Asymptotic Theory for Least Squares Series: Pointwise and Uniform Results (2012)
| Content Provider | CiteSeerX |
|---|---|
| Author | Belloni, Alexandre Chernozhukov, Victor Chetverikov, Denis Kato, Kengo |
| 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. These technical tools allow us to contribute to the series literature, specifically the seminal work of Newey (1997), as follows. First, we weaken considerably the condition on the number k of approximating functions used in series estimation from the typical k2/n → 0 to k/n → 0, up to log factors, which was available only for spline series before. |
| File Format | |
| Publisher Date | 2012-01-01 |
| Access Restriction | Open |
| Content Type | Text |
