Point-Wise Wavelet Estimation in the Convolution Structure Density Model

2020 ◽  
Vol 26 (6) ◽  
Author(s):  
Youming Liu ◽  
Cong Wu
Bernoulli ◽  
2017 ◽  
Vol 23 (2) ◽  
pp. 884-926 ◽  
Author(s):  
O.V. Lepski ◽  
T. Willer

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1391
Author(s):  
Kaikai Cao ◽  
Xiaochen Zeng

Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal Lp risk estimations over an anisotropic Nikol’skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat.2019, 47, 233–287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.


1992 ◽  
Vol 8 (01) ◽  
pp. 21-35 ◽  
Author(s):  
K. Ullas Karanth ◽  
Melvin E. Sunquist

ABSTRACTWe studied the population structure, density and biomass of seven ungulate and two primate species in the tropical forests of Nagarahole, southern India, using line transect sampling and roadside/platform counts, during 1986–87. The estimated ecological densities of large herbivore species in the study area are: 4.2 muntjac km−2, 50.6 chital km−2, 5.5 sambar km−2, 0.8 four-horned antelope km−2, 9.6 gaur km−2, 4.2 wild pig km−2, 3.3 elephant km−2, 23.8 hanuman langur km−2and 0.6 bonnet macaque km−2. Most ungulates have female-biased adult sex ratios. Among common ungulate species, yearlings and young of the year comprise about a third of the population, suggesting relatively high turn-over rates. Three species (muntjac, sambar and four-horned antelope) are solitary, while others form groups. The study area supports a wild herbivore biomass density of 14,744 kg km−2. Among the three habitat types within the study area, biomass is lower in dry deciduous forests when compared with moist deciduous or teak plantation dominant forests. Using our results, we have examined the factors that may contribute towards maintenance of high ungulate biomass in tropical forests.


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