zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Consistent nonparametric multiple regression for dependent heterogeneous processes: the fixed design case. (English) Zbl 0698.62040

Summary: Consider the nonparametric regression model

Y i (n) =g(x i (n) )+ϵ i (n) ,i=1,···,n,

where g is an unknown regression function and assumed to be bounded and real valued on A p , x i (n) ’s are known and fixed design points and ϵ i (n) ’s are assumed to be both dependent and non-identically distributed random variables.

This paper investigates the asymptotic properties of the general nonparametric regression estimator

g n (x)= i=1 n W ni (x)Y i (n) ,

where the weight function W ni (x) is of the form W ni (x)=W ni (x;x 1 (n) ,x 2 (n) ,,x n (n) ). The estimator g n (x) is shown to be weak, mean square error, and universal consistent under very general conditions on the temporal dependence and heterogeneity of ϵ i (n) ’s. Asymptotic distribution of the estimator is also considered.


MSC:
62G05Nonparametric estimation
62E20Asymptotic distribution theory in statistics
60G44Martingales with continuous parameter
60F05Central limit and other weak theorems