Strictly monotone and smooth nonparametric regression for two or more variables
Loading...
Date
2005-07-07T12:28:29Z
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In this article a new monotone nonparametric estimate for a regression function of two
or more variables is proposed. The method starts with an unconstrained nonparametric
regression estimate and uses successively one-dimensional isotonization procedures. In the
case of a strictly monotone regression function, it is shown that the new estimate is first
order asymptotic equivalent to the unconstrained estimate, and asymptotic normality of
an appropriate standardization of the estimate is established. Moreover, if the regression
function is not monotone in one of its arguments, the constructed estimate has approximately
the same Lp-norm as the initial unconstrained estimate. The methodology is also illustrated
by means of a simulation study, and two data examples are analyzed.
AMS Subject Classification: 62G05, 62G20
Description
Table of contents
Keywords
Isotonic regression, Multivariate nonparametric regression, Nondecreasing rearrangement, Order restricted inference