Boundary-adaptive kernel density estimation: the case of (near) uniform density

We consider nonparametric kernel estimation of density functions in the bounded-support setting having known support $ [a,b] $ [ a , b ] using a boundary-adaptive kernel function and data-driven bandwidth selection, where a and b are finite and known prior to estimation. We observe, theoretically an...

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Bibliographic Details
Published in:Journal of nonparametric statistics 2024-01, Vol.36 (1), p.146-164
Main Authors: Racine, Jeffrey S., Li, Qi, Wang, Qiaoyu
Format: Article
Language:English
Subjects:
boundary
Density
Kernel functions
Nonparametric
Nonparametric statistics
smoothing
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Summary:We consider nonparametric kernel estimation of density functions in the bounded-support setting having known support $ [a,b] $ [ a , b ] using a boundary-adaptive kernel function and data-driven bandwidth selection, where a and b are finite and known prior to estimation. We observe, theoretically and in finite sample settings, that when bounds are known a priori this kernel approach is capable of outperforming even correctly specified parametric models, in the case of the uniform distribution. We demonstrate that this result has implications for modelling a range of densities other than the uniform case. Furthermore, when bounds $ [a,b] $ [ a , b ] are unknown and the empirical support (i.e. $ [\min (x_i),\max (x_i)] $ [ min ( x i ) , max ( x i ) ] ) is used in their place, similar behaviour surfaces.
ISSN:1048-5252
1029-0311
DOI:10.1080/10485252.2023.2250011