Published in: Journal of Quantitative Economics, 1997 Vol. 13, 81-131.
Nonparametric Least Squares Regression and
Testing in E conomic Mode ls1
Adonis Yatchew and Len Bos *
This paper proposes a tractable and consistent estimator of the (possibly multi-equation)
nonparametric regression model. The estimator is based on least squares over sets of functions
bounded in Sobolev norm and is closely related to penalized least squares. We establish consistency
and rate of convergence results as well as asymptotic normality of the (suitably standardized) sum
of squared residuals is established. These results are then used to produce a -consistent,
asymptotically normal estimator in the partial linear model . Conditional moment
tests are provided for a variety of hypotheses including specification, significance, additive and
multiplicative separability, monotonicity, concavity and demand theory. The validity of bootstrap
test procedures is proved.
Keywords: nonparametric regression, semiparametric regression, partial linear model, least
squares, empirical processes, hypothesis testing, conditional moment tests, -
statistics, bootstrap, specification test, significance test, additive separability,
multiplicative separability, homogeneity, monotonicity, concavity, demand theory,
October 23, 1997.
Department of Economics, University of Toronto, firstname.lastname@example.org
Department of Mathematics and Statistics, University of Calgary.