Goodness‐of‐fit Tests Based on the Kernel Density Estimator

Ricardo Cao and Gabor Lugosi

Scandinavian Journal of Statistics, 2005, vol. 32, issue 4, 599-616

Abstract: Abstract. Given an i.i.d. sample drawn from a density f on the real line, the problem of testing whether f is in a given class of densities is considered. Testing procedures constructed on the basis of minimizing the L1‐distance between a kernel density estimate and any density in the hypothesized class are investigated. General non‐asymptotic bounds are derived for the power of the test. It is shown that the concentration of the data‐dependent smoothing factor and the ‘size’ of the hypothesized class of densities play a key role in the performance of the test. Consistency and non‐asymptotic performance bounds are established in several special cases, including testing simple hypotheses, translation/scale classes and symmetry. Simulations are also carried out to compare the behaviour of the method with the Kolmogorov‐Smirnov test and an L2 density‐based approach due to Fan [Econ. Theory10 (1994) 316].

Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9469.2005.00471.x

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:32:y:2005:i:4:p:599-616

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().