Piecewise linear density estimation for sampled data

Details Piecewise linear density estimation for sampled data Piecewise linear density estimation for sampled data

2007-09-28

arxiv.org/abs/0709.4543v3

Mathematics

Statistics Theory

23 pages

Scientific paper

Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency polygons can reach the same optimal $L_{2}$-rates as in the independent and identically distributed case. Moreover, thanks to a suitable "high frequency" sampling design, these rates are derived together with a minimized time of observation depending on the regularity of sample paths.

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