![Sample our Economics, Finance,Business & Industry journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5931/TOC-Subject-Sample-2021-Economics-Finance-Business-Industry.jpg"})
ABSTRACT
The paper investigates various nonparametric models including regression, conditional distribution, conditional density and conditional hazard function, when the covariates are infinite dimensional. The main contribution is to prove uniform in bandwidth asymptotic results for kernel estimators of these functional operators. Then, the application issues, involving data-driven bandwidth selection, are discussed.
Acknowledgments
The authors would like to thank gratefully the Editors and the Reviewers of an earlier version of this manuscript. Their pertinent comments and suggestions have greatly participate in improving the presentation of our work.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. Let be a sequence of real random variables. We say that
converges almost-completely (a.co.) towards zero if for all
,
. The rate of convergence is of order
(with
and we write
if there exists
such that
.
2. A semi-metric d satisfies the same properties as a metric excepted that may hold for some
.
3. A class of functions is said to be a pointwise measurable class if there exists a countable subclass
such that, for any function
, there exists a sequence of functions
in
such that:
.
4. An envelope function G for a class of functions is any measurable function such that:
, for all z.