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Title:An adaptive, rate-optimal test of a parametric model against a nonparametric alternative PDF Logo
Authors:Horowitz, Joel L.
Spokoiny, Vladimir G.
Issue Date:1999
Series/Report no.:Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,10
Abstract:We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n-1/2. Some existing tests have non-trivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n-1/2. There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.
Subjects:Hypothesis testing
local alternative
uniform consistency
asymptotic power
JEL:C12
C14
C21
Persistent Identifier of the first edition:urn:nbn:de:kobv:11-10056063
Document Type:Working Paper
Appears in Collections:Discussion Papers, SFB 373, HU Berlin

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