Directional Mixture Models and Optimal Estimation of the Mixing Density
نویسندگان
چکیده
The authors develop consistent nonparametric estimation techniques for the directional mixing density. Classical spherical harmonics are used to adapt Euclidean techniques to this directional environment. Minimax rates of convergence are obtained for rotationally invariant densities verifying various smoothness conditions. It is found that the difference in smoothness between the Laplace, the Gaussian and the von Mises-Fisher distributions, lead to contrasting inferential conclusions.
منابع مشابه
Robust estimation of mixing measures in finite mixture models
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we empirically believe our data are generated from and use these kernels to fit our models. Nevertheless, as long as the chosen kernel and the true kernel are diffe...
متن کاملGlobal Properties of Kernel Estimators for Mixing Densities in Discrete Exponential Family Models
This paper concerns the global performance of modifications of the kernel estimators considered in Zhang (1995) for a mixing density function g based on a sample from f(x) = ∫ f(x|θ)g(θ)dθ under weighted L-loss, 1 ≤ p ≤ ∞, where f(x|θ) is a known exponential family of density functions with respect to the counting measure on the set of nonnegative integers. Fourier methods are used to derive up...
متن کاملUncertainty Estimation in Stream Bed Sediment Fingerprinting Based on Mixing Model
Uncertainty associated with mixing models is often substantial, but has not yet been fully incorporated in models. The objective of this study is to develop and apply a Bayesian-mixing model that estimates probability distributions of source contributions to a mixture associated with multiple sources for assessing the uncertainty estimation in sediment fingerprinting in Zidasht catchment, Iran....
متن کاملOn the Minimax Optimality of Block Thresholded Wavelets Estimators for ?-Mixing Process
We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...
متن کاملAn Estimation of Required Rotational Torque to Operate Horizontal Directional Drilling Using Rock Engineering Systems
Horizontal directional drilling (HDD) is widely used in soil and rock engineering. In a variety of conditions, it is necessary to estimate the torque required for performing the reaming operation. Nevertheless, there is not presently a convenient method to accomplish this task. In this paper, to overcome this difficulty based on the basic concepts of rock engineering systems (RES), a model for ...
متن کامل