An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative

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 fastes...

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Bibliographic Details
Published in:Econometrica 2001-05, Vol.69 (3), p.599-631
Main Authors: Horowitz, Joel L., Spokoiny, Vladimir G.
Format: Article
Language:English
Subjects:
asymptotic power
Consistent estimators
Critical values
Econometrics
Economic models
Economic theory
Estimators
Exact sciences and technology
Hypotheses
Hypothesis testing
local alternative
Mathematics
Minimax
Model testing
Monte Carlo methods
Nonparametric inference
Null hypothesis
Parametric inference
Parametric models
Probability and statistics
Regression analysis
Sampling distributions
Sciences and techniques of general use
Statistical variance
Statistics
Studies
Test methods
uniform consistency
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Summary: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 nontrivial 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.
ISSN:0012-9682
1468-0262
DOI:10.1111/1468-0262.00207