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A valid Edgeworth expansion is established for the limit distribution of density-weighted semiparametric averaged derivative estimates of single index models. The leading term that corrects the normal limit varies in magnitude, depending on the choice of bandwidth and kernel order. In general this term has order larger than the n -½ that prevails in standard parametric problems, but we find circumstances in which it is O(n -½), thereby extending the achievement of an n -½ Berry-Essen bound in Robinson (1995). A valid empirical Edgeworth expansion is also established. We also provide theoretical and empirical Edgeworth expansions for a studentized statistic, where the correction terms are different from those for the unstudentized case. We report a Monte Carlo study of finite sample performance

Topics:
HB Economic Theory

Publisher: Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science

Year: 1999

OAI identifier:
oai:eprints.lse.ac.uk:2132

Provided by:
LSE Research Online

- (1991). 1) E(W12V1V2)13 A for the definitions of and ). The term involving and is analogous to V1 W12 3 4 the correction term in the Edgeworth expansion of studentized ordinary U-statistics (see n &1/2 Helmers
- and (see (4.35), (4.38), and (4.40) of Powell and Stoker (1996)). On the basis of our h0 calculations, though both absolute bias and MSE
- (1989). and for weakly dependent observations by Robinson
- (1971). and Nagar (see e.g. Nagar
- As discussed in Section 4, Theorems 1 and 3 also imply that bias correction should have the
- (1992). based on Theorem 1. For example, for (L, d, h) satisfying III(a), we have (4.1) .
- (1996). choice of bandwidth. In another paper,
- (1995). d{(1uL)K(u)K )(u)}du sup u R d K )(u) < and for the same L as in (iv) and (v), R du l1 1 u ld d K(u)du 1, if l1ld0 0, if 0<l1ld<L 0, if l1ldL . (ix) as .
- for the Tobit model where is bivariate. We took Yi ( Xi
- L c0 c1 c2 c3 c4 4 1.5 -0.5 8 2.185 -2.185 0.4375 -0.02083 10 1.924 -1.347 0.1230 0.00698 -0.000489 empirical Edgeworth expansions. We considered inference on the two elements
- (1999). List of previous papers in this series The Suntory Centre Suntory and Toyota International Centres for Economics and Related Disciplines London School of Economics and Political Science Discussion Paper Houghton Street No.EM/99/373 London,
- (1992). semiparametric estimates might be expected to have a larger Berry-Esseen bound, and correction term of order greater than If so, the semiparametric estimates are inferior to parametric n
- (1986). Since our estimate is of U-statistic form, our work can also be compared with that on Edgeworth expansions of U-statistics in the mathematical statistics literature
- (1995). The Berry-Esseen bound for averaged derivative estimates of semiparametric index models was derived by Robinson
- third column of
- (1986). zero under (ii)). In their study of ordinary U-statistics and symmetric

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