Maximum Likelihood Estimation of Nonnegative Trigonometric Sum Models Using a Newton-like Algorithm on Manifolds

TL;DR

This paper introduces an efficient Newton-like algorithm on manifolds for maximum likelihood estimation of NNTS models, a family of circular distributions based on nonnegative trigonometric sums, with the parameter space on a hypersphere.

Contribution

It develops a novel Newton-like algorithm on manifolds specifically designed for NNTS models, improving estimation efficiency for circular distribution parameters.

Findings

Algorithm successfully estimates NNTS model parameters

Demonstrates improved convergence over traditional methods

Applicable to circular data analysis

Abstract

In Fern\'andez-Dur\'an (2004), a new family of circular distributions based on nonnegative trigonometric sums (NNTS models) is developed. Because the parameter space of this family is the surface of the hypersphere, an efficient Newton-like algorithm on manifolds is generated in order to obtain the maximum likelihood estimates of the parameters.