Jq. Fan et I. Gijbels, DATA-DRIVEN BANDWIDTH SELECTION IN LOCAL POLYNOMIAL FITTING - VARIABLE BANDWIDTH AND SPATIAL ADAPTATION, Journal of the Royal Statistical Society. Series B: Methodological, 57(2), 1995, pp. 371-394
Citations number
28
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Journal of the Royal Statistical Society. Series B: Methodological
When estimating a mean regression function and its derivatives, locall
y weighted least squares regression has proven to be a very attractive
technique. The present paper focuses on the important issue of how to
select the smoothing parameter or bandwidth. In the case of estimatin
g curves with a complicated structure, a variable bandwidth is desirab
le. Furthermore, the bandwidth should be indicated by the data themsel
ves. Recent developments in nonparametric smoothing techniques inspire
d us to propose such a data-driven bandwidth selection procedure, whic
h can be used to select both constant and variable bandwidths. The ide
a is based on a residual squares criterion along with a good approxima
tion of the bias and variance of the estimator. The procedure can be a
pplied to select bandwidths not only for estimating the regression cur
ve but also for estimating its derivatives. The resulting estimation p
rocedure has the necessary flexibility for capturing complicated shape
s of curves. This is illustrated via a large variety of testing exampl
es, including examples with a large spatial variability. The results a
re also compared with wavelet thresholding techniques, and it seems th
at our results are at least comparable, i.e. local polynomial regressi
on using our data-driven variable bandwidth has spatial adaptation pro
perties that are similar to wavelets.