Lp-NORM CONSISTENCIES OF NONPARAMETRIC ESTIMATES OF REGRESSION, HETEROSKEDASTICITY AND VARIANCE OF REGRESSION ESTIMATE WHEN DISTRIBUTION OF REGRESSOR IS KNOWN

Radhey S. Singh

No 263067, Department of Economics Discussion Papers from University of Canterbury - New Zealand

Abstract: When dealing with heteroskedastic models Y = μ(X) + c in econometrics and other disciplines, situations often arise (especially with structural models) where the probability distribution of the ((Rd-valued) regressor vector X is known, but postulations about the functional form of the regression μ(x), the heteroskedasticity a'2(x) = var(c I X=x) and the distribution of the disturbance term c are made. These three postulations generally lead to misspecification of • the models. This paper, based on a data set on (Y,X), considers nonparametric kernel estimators μ(x), c3.2(x) and c/(μ(x)), respectively, of the regression μ(x), the heteroskedasticity 2(x) and the asymptotic variances V(i.i(x)) of the regressi cr on estimate ii(x) for situations where only the probability distribution of X, say A is known. For an arbitrary subset A in the interior of the support of A and for 1 p < co, we establish convergences to zero, as the data set gets large, of the L -norms 11μ-μIIP = E I μ(x)-μ(x) I PdX(x) (with A a Rd for p = A •.. 1), 116.-2-cr2IIP (with A a Rd for p = 1) and II'()-V(μ)11P under certain moment conditions on Y but with no assumptions on the joint distribution of (Y,X) or the continuity of μ(x), o'2(x) or the density of X.

Keywords: Agricultural Finance; Financial Economics (search for similar items in EconPapers)
Pages: 26
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Persistent link: https://EconPapers.repec.org/RePEc:ags:canzdp:263067

DOI: 10.22004/ag.econ.263067

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