Influence function analysis of parameter estimation with generalized t distribution noise model

Abstract

A commonly made assumption of Gaussian noise is an approximation to reality. In this paper, we used the influence function in robust statistics to analyze a parameter estimator that modeled noise with the Generalized t (GT) distribution instead of the usual Gaussian noise. The analysis is extended to the case where the estimator designed with probability density function f(ε) is applied to actual noise with different probability density function gk(ε) at different sampling instance, k, to provide a framework for analysis of outliers. By being a superset encompassing Gaussian, uniform, t, and double exponential distributions, GT distribution has the flexibility to characterize data with non-Gaussian statistical properties. Equations derived are useful in determining the variance of the estimates and the impact of outliers. These equations enable us to compute the sample size needed by the estimator to meet specified variance or to tune the estimator to limit the impact of outliers. The theory is verified through simulations and an experiment on the chemical mechanical polishing of semiconductors. © 2013 American Chemical Society.