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Redescending M-estimators in regression analysis, cluster analysis and image analysis

100%

Müller C.

Discussiones Mathematicae Probability and Statistics

2004

tom 24

nr 1

59-75

We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness properties. However, there is a problem in calculating the redescending M-estimators in regression. While in the location-scale case, for example, the Cauchy estimator has only one local extremum this is not the case in regression. In regression there are several local minima reflecting several substructures in the data. This is the reason that the redescending M-estimators can be used to detect substructures in data, i.e. they can be used in cluster analysis. If the starting point of the iteration to calculate the estimator is coming from the substructure then the closest minimum corresponds to this substructure. This property can be used to construct an edge and corner preserving smoother for noisy images so that there are applications in image analysis as well.

Stochastic multivariable self-tuning tracker for non-gaussian systems

100%

Filipovic V.

International Journal of Applied Mathematics and Computer Science

2005

tom 15

nr 3

351-357

This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker's product is used, which allows us to represent unknown parameters in the form of vectors. For parameter estimation a stochastic approximation algorithm is employed. Using the concept of the stochastic Lyapunov function, global stability and optimality of the feedback system are established.

Ograniczanie wyników

1 Discussiones Mathematicae Probability and Statistics

1 International Journal of Applied Mathematics and Computer Science

1 Filipovic V.

1 Müller C.

1 2005

1 2004

Wyniki wyszukiwania

Redescending M-estimators in regression analysis, cluster analysis and image analysis

Stochastic multivariable self-tuning tracker for non-gaussian systems