# 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)
Nonparametric binary discrimination. Methods for estimating the smoothing para. (Discrimination binaire non paramétrique. Méthodes d’estimation du paramètre de lissage.) (French) Zbl 0972.62510
Summary: The kernel method for estimating the cell probabilities of a multivariate discrete distribution, due to Aitchison and Aitken (1976), depends crucially on an unknown smoothing parameter $\lambda$. Most of the methods for choosing the smoothing parameter are discussed in the context of density estimation. The choice may be based on a pseudo-likelihood or on loss functions for the estimation of the density. In this setting, we show how to apply resampling methods (cross-validation and bootstrap) to estimating the smoothing parameters. If the main interest is not in density estimation but in discrimination, alternative methods for choosing $\lambda$ from the discrimination viewpoint may yield better performance for separation of groups. Methods of this type have been proposed by Tutz (1986, 1989) for discrete kernels and more recently by Hall and Wand (1988). In the same setting, we propose a method, estimating $\lambda$ explicitly, based on minimization of the leaving-one-out estimator of the error rate, without using the iterative method. Moreover, we extend the method of bootstrap to Hall and Wand’s approach in the case of two groups. An example is given to illustrate the practical behaviour of all these methods.
##### MSC:
 62G05 Nonparametric estimation 62H30 Classification and discrimination; cluster analysis (statistics)