Relative efficiencies of kernel and local likelihood density estimators
AbstractLocal likelihood methods enjoy advantageous properties, such as good performance in the presence of edge effects, that are rarely found in other approaches to nonparametric density estimation. However, as we argue in this paper, standard kernel methods can have distinct advantages when edge effects are not present. We show that, whereas the integrated variances of the two methods are virtually identical, the integrated squared bias of a conventional kernel estimator is less than that of a local log-linear estimator by as much as a factor of 4. Moreover, the greatest bias improvements offered by kernel methods occur when they are needed most-i.e. when the effect of bias is particularly high. Similar comparisons can also be made when high degree local log-polynomial fits are assessed against high order kernel methods. For example, although (as is well known) high degree local polynomial fits offer potentially infinite efficiency gains relative to their kernel competitors, the converse is also true. Indeed, the asymptotic value of the integrated squared bias of a local log-quadratic estimator can exceed any given constant multiple of that for the competing kernel method. In all cases the densities that suffer problems in the context of local log-likelihood methods can be chosen to be symmetric, either unimodal or bimodal, either infinitely or compactly supported, and to have arbitrarily many derivatives as functions on the real line. They are not pathological. However, our results reveal quantitative differences between global performances of local log-polynomial estimators applied to unimodal or multimodal distributions. Copyright 2002 Royal Statistical Society.
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Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal Of The Royal Statistical Society.
Volume (Year): 64 (2002)
Issue (Month): 3 ()
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- Rodrigues, Clarissa G. & Rios-Neto, Eduardo L G & Pinto, Cristine Campos de Xavier, 2012. "Changes in test scores distribution for students of the fourth grade in Brazil: A relative distribution analysis for the years 1997 to 2005," Textos para discussÃ£o 282, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
- Otneim, Håkon & Karlsen, Hans Arnfinn & Tjøstheim, Dag, 2013. "Bias and bandwidth for local likelihood density estimation," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1382-1387.
- Rodrigues, Clarissa Guimarães & Rios-Neto, Eduardo Luiz Gonçalves & de Xavier Pinto, Cristine Campos, 2013. "Changes in test scores distribution for students of the fourth grade in Brazil: A relative distribution analysis for the years 1997–2005," Economics of Education Review, Elsevier, vol. 34(C), pages 227-242.
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