E. Rafajlowicz, CONSISTENCY OF ORTHOGONAL SERIES DENSITY ESTIMATORS BASED ON GROUPED OBSERVATIONS, IEEE transactions on information theory, 43(1), 1997, pp. 283-285
Citations number
33
Categorie Soggetti
Information Science & Library Science","Engineering, Eletrical & Electronic
In this correspondence we show that nonparametric orthogonal series es
timators of probability densities retain the mean integrated square er
ror (MISE) consistency when observations are grouped to the points of
a uniform grid (prebinned). This kind of grouping is typical for compu
ter rounding errors and may also be useful in data compression, before
calculating estimates, e.g., using the FFT, The main result shows tha
t MISE consistency holds for all square-integrable densities under mil
d conditions on the grid step size.