1Subdirección Salud Pública de Gipuzkoa, CIBER de Epidemiología y Salud Pública (CIBERESP), Donostia, Spain. Investigador postdosctoral. Email: pmcamblor@hotmail.com
2Universidad de Oviedo, Estadística e Investigación Operativa y Didáctica de la Matemática, Asturias, Spain. Catedrático. Email: norbert@uniovi.es
3Universidad de Oviedo, Estadística e Investigación Operativa y Didáctica de la Matemática, Asturias, Spain. Profesora titular. Email: teresa@uniovi.es
In this paper a Chernoff type theorem for the L1 distance between kernel estimators from two independent and identically distributed random samples is developed. The harmonic mean is used to correct the distance for inequal sample sizes case. Moreover, the proved result is used to compute the Bahadur slope of a test based on L1 distance and to compare it with the classical nonparametric Mann-Whitney test by using the Bahadur relative efficiency.
Palabras clave: Kernel estimator, Large deviation, Bahadur slope.
En este trabajo se desarrolla un teorema de tipo Chernoff para la distancia L1 entre estimadores núcleo procedentes de muestras aleatorias independientes e idénticamente distribuidas. Se usa la media armónica para corregir esta distancia en el caso de muestras de distintos tamaños. Además, se usa el resultado demostrado para el cálculo de la pendiente de Bahadur de un test para la comparación de densidades basado en la distancia L1 y se compara con el clásico test de Mann-Whitney a partir de la eficiencia relativa de Bahadur.
Key words: estimador núcleo, grandes muestras, pendiente de Bahadur.
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Referencias
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv32n2a07,
AUTHOR = {Martínez-Camblor, Pablo and Corral, Norberto and López, Teresa},
TITLE = {{Cramér-Chernoff Theorem for L1-norm in Kernel Density Estimator for Two Independent Samples}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2009},
volume = {32},
number = {2},
pages = {289-299}
}