zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Local regression and likelihood. (English) Zbl 0929.62046
Statistics and Computing. New York, NY: Springer. xiii, 290 p. DM 129.00; öS 942.00; sFr 117.50; £ 49.50; $ 64.95 (1999).
Suppose a dataset consists of $n$ pairs of observations $(x_1,Y_1),\ (x_2,Y_2),\ldots,(x_n,Y_n)$, where $x$ is a (nonrandom) predictor variable (real or vector valued) and $Y$ is a (random) response variable related to the predictor variable. The problem is to predict $Y$ for a fixed value $x$ which may not belong to the set $\{x_1,x_2,\ldots,x_n\}$. It is obvious that a kind of interpolation (or perhaps extrapolation) between the points $x_1,x_2,\ldots,x_n$ is needed, and that those of the points which are nearer to $x$ should play a greater role. If a model of the form $Y=\mu(x)+\varepsilon$ with a deterministic function $\mu$ and random error $\varepsilon$ is assumed, the problem is known as that of local regression. Ch. 2 of the book gives details. For a model of the form “$Y$ has a probability density function $f(y,\mu(x,\theta))$” with given form of $f$ and $\mu(x,\theta)$, a local maximum likelihood estimate for the parameter $\theta$ may be conctructed. The Local Likelihood Model is discussed in Ch. 4. Similarly one can formulate the problem of local density estimation (Ch. 5), local Survival and Failure Time Analysis (Ch. 6), and so on. The book gives us a complete and uptodate review of the state of the art. Practical applications and computer software (LOCFIT) are presented in detail.

62G08Nonparametric regression
62-02Research monographs (statistics)
62F10Point estimation
62J99Linear statistical inference
62J02General nonlinear regression
65C60Computational problems in statistics
Full Text: DOI