Parameter estimation for orthogonal polynomial moments

Diverging moments and parameter estimation

Heavy tailed distributions which allow for values far from the mean to occur with considerable probability are of increasing importance in various applications as the arsenal of analytical and numerical tools grows. Examples of interest are the Stable and more generally the Pareto distributions for which moments of sufficiently large order diverge. In fact, the asymptotic powerlaws of the distr...

Proper orthogonal decomposition for parameter estimation in oscillating biological networks

Model parameter estimation for mixture density polynomial segment models

In this paper, we propose parameter estimation techniques for mixture density polynomial segment models (MDPSMs) where their trajectories are specified with an arbitrary regression order. MDPSM parameters can be trained in one of three different ways: (1) segment clustering; (2) expectation maximization (EM) training of mean trajectories; and (3) EM training of mean and variance trajectories. T...

Parametric Methods Comparisons for Parameter Estimation of Polynomial Phase Signals

Parameter estimation of polynomial phase signals (PPSs) is of great interest in various practical applications. In this paper, parametric methods for parameter estimation of polynomial phase signals are discussed and compared. The suboptimal maximum likelihood estimation methods, such as the high-order ambiguity function (HAF) and the product HAF (PHAF) are presented. The polynomial time freque...

Polynomial probability distribution estimation using the method of moments

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the...