On Multivariate Density Estimates Based on Orthogonal Expansions

Kernel Methods for Estimating the Utilization Distribution in Home‐Range Studies

“…However, histogram estimates are very subjective because one has to choose (1) the origin, (2) the cell size, and (3) the orientation of the axes. To avoid these problems and the inefficient use of data, Anderson used the Fourier transform method to estimate the UD (see Tarter and Kronmal 1970). Essentially, the method estimates the density by a series of sines and cosines of different frequencies.…”

A New Test For and Class of Transformations To Normality

“…This estimator has been found in the univariate special case to be more efficient than the previous estimators and has the advantage of enabling a researcher to base the estimation of R(z) upon conditional dist)ributions estimat#ed from a moderate sized bivariate sample. Tarter and Kronmal (1970) primarily dealt with the estimation of population densities. The following estimate of the cumulative can be obtained by applying t,he methods used by Kronmal and Tarter (1968, Section 4) to the univariate special case of the density estimator given by Tarter and Kronmal (1970) While this in no way proves the optimality of the pair (fm , P,), it does suggest that these estimators might be well suited for the estimation of both the density and cumulative components of R(z).…”

“…It is suggested however that Formula (3.9) should be replaced by the more elaborate procedures of Siddiqui (1960) and Block and Gastwirth (1968) or Tarter and Kronmal (1970) when the sample size is moderate to large, i.e. n 2 40.…”

Parallel recursive Bayesian estimation on multicore computational platforms using orthogonal basis functions

“…Orthogonal bases have been used for a long time in statistics to estimate PDFs with general distributions [9], [10], [11]. Using orthogonal expansions, it is possible to estimate the PDFs with a substantially lower number of variables than e.g.…”