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 g k (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.

Filtering of the ARMAX Process with Generalized t-Distribution Noise: The Influence Function Approach

“…Instead of using the IF as an analysis tool to analyze a given estimator, this paper makes use of the IF to synthesize or construct an estimator. The other difference is that, while ref studied the estimation of the parameters in the transfer function, this paper estimates the states or output of the transfer function.…”

“…The IF was used in ref 14 to analyze parameter estimation with GT noise. Instead of using the IF as an analysis tool to analyze a given estimator, this paper makes use of the IF to synthesize or construct an estimator.…”

Indoor Tracking With the Generalized <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math> </inline-formula>-Distribution Noise Model

“…GT was also explored in [28] to help understand the nature of genetic association signal. By being a superset encompassing Gaussian, uniform, t, Cauchy, and double exponential distributions, GT distribution has the flexibility of characterizing noise with Gaussian or non-Gaussian statistical properties [29]. In practice, noise modelling in the GT setting can proceed by likelihood methods analogous to those for the Gaussian distribution.…”

Iterative Algorithms for Data Reconciliation Estimator Using Generalized t-Distribution Noise Model

“…A broader approach is to use the generalized t -distribution (GT, Figure ) noise model as the GT distribution is very flexible in transforming to many other distributions . This approach has been widely adopted in many research areas such as econometrics, data reconciliation problems, , bias estimation for multizone thermal systems, and parameters estimation in semiconductor manufacturing . Moreover, Wang and Romagnoli , have shown that data reconciliation with the GT noise model is very robust against outliers.…”