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)
Asymptotic properties of kernel estimators based on local medians. (English) Zbl 0675.62031
Summary: The desire to make nonparametric regression robust leads to the problem of conditional median function estimation. Under appropriate regularity conditions, a sequence of local median estimators can be chosen to achieve the optimal rate of convergence $n\sp{-1/(2+d)}$ both pointwise and in the $L\sp q$ $(1\le q<\infty)$ norm restricted to a compact. It can also be chosen to achieve the optimal rate of convergence $(n\sp{- 1}\log n)\sp{1/(2+d)}$ in the $L\sp{\infty}$ norm restricted to a compact. These results also constitute an answer to an open question of {\it C. J. Stone} [ibid. 10, 1040-1053 (1982; Zbl 0511.62048)].

MSC:
62G05Nonparametric estimation
62E20Asymptotic distribution theory in statistics
WorldCat.org
Full Text: DOI