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A new multiple kernel-based regularization method for identification of delay linear dynamic systems

CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2020年第0期199卷 103971-000页

作者： Chen, Xiaolong Mao, Zhizhong Jia, Runda Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Liaoning Peoples R China

Model parameter estimation, model order selection, variable selection and time delay estimation are four important issues that receive increasing interests in dynamic system identification. However, previous work did not solve the four issues simultaneously. Motivated by the multiple kernel-based regularization method (MKRM), this paper proposes a new multiple kernel-based regularization method for joint model parameter estimation, model order selection, variable selection and time delay estimation for delay linear dynamic systems, referred to as the MKRM-D. Then, an efficient iterative reweighted algorithm is derived to solve the resulting difference of convex functions programming (DCP) problem. In addition, by exploiting the structure of the objective function in each iteration of this algorithm, the alternating direction method of multipliers (ADMM) is employed to decompose the centralized problem into a series of independent subproblems with lower variable dimension, which can be solved in a parallel and distributed manner. The performance of the proposed method is demonstrated by numerical experiments using both synthetic and real data.

关键词： Linear system identification Variable selection Time delay estimation Multiple kernel-based regularization iterative reweighting algorithm ADMM

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Convergence behavior of an iterative reweighting algorithm to compute multivariate M-estimates for location and scatter

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2004年第1-2期118卷 115-128页

作者： Arslan, O Cukurova Univ Dept Math TR-01330 Balcali Adana Turkey

The iteratively reweighting algorithm is one of the widely used algorithm to compute the M-estimates for the location and scatter parameters of a multivariate dataset. If the M estimating equations are the maximum likelihood estimating equations from some scale mixture of normal distributions (e.g. from a multivariate t-distribution), the iteratively reweighting algorithm is identified as an EM algorithm and the convergence behavior of which is well established. However, as Tyler (J. Roy. Statist. Soc. Ser. B 59 (1997) 550) pointed out, little is known about the theoretical convergence properties of the iteratively reweighting algorithms if it cannot be identified as an EM algorithm. In this paper, we consider the convergence behavior of the iteratively reweighting algorithm induced from the M estimating equations which cannot be identified as an EM algorithm. We give some general results on the convergence properties and, we show that convergence behavior of a general iteratively reweighting algorithm induced from the M estimating equations is similar to the convergence behavior of an EM algorithm even if it cannot be identified as an EM algorithm. (C) 2002 Elsevier B.V.. All rights reserved.

关键词： iterative reweighting algorithm M estimates robustness EM algorithm

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On the computation and finite sample behavior of the constrained M-estimates for multivariate location and scatter

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2004年第3期33卷 685-701页

作者： Arslan, O St Cloud State Univ Dept Stat St Cloud MN 56301 USA

Constrained M (CM) estimates of multivariate location and scatter [Kent, J. T., Tyler, D. E. (1996). Constrained M-estimation for multivariate location and scatter. Ann. Statist. 24:1346-1370] are defined as the global minimum of an objective function subject to a constraint. These estimates combine the good global robustness properties of the S estimates and the good local robustness properties of the redescending M estimates. The CM estimates are not explicitly defined. Numerical methods have to be used to compute the CM estimates. In this paper, we give an algorithm to compute the CM estimates. Using the algorithm, we give a small simulation study to demonstrate the capability of the algorithm finding the CM estimates, and also to explore the finite sample behavior of the CM estimates. We also use the CM estimators to estimate the location and scatter parameters of some multivariate data sets to see the performance of the CM estimates dealing with the real data sets that may contain outliers.

关键词： CM-estimator M-estimator S-estimator robustness iterative reweighting algorithm

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A note on the maximum likelihood estimators for the location and scatter parameters of a multivariate Cauchy distribution

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 1998年第12期27卷 3007-3014页

作者： Arslan, O Kent, JT Univ Leeds Dept Stat Leeds LS2 9JT W Yorkshire England Cukurova Univ Dept Math Adana Turkey

The likelihood function of a multivariate Cauchy distribution with unknown location and scatter parameters in p dimensions has a unique maximum provided the sample is in general position and is of size n > p + 1 (see Kent and Tyler 1991 and Kent et al., 1994). fn this paper, we show that when n = p + 1, the maximum of the location-scatter Cauchy likelihood function occurs when the parameters lie on a p-dimensional surface.

关键词： Cauchy distribution robustness maximum likelihood estimator EM algorithm iterative reweighting algorithm

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CONVERGENCE BEHAVIOR OF THE EM algorithm FOR THE MULTIVARIATE T-DISTRIBUTION

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 1995年第12期24卷 2981-3000页

作者： ARSLAN, O CONSTABLE, PDL KENT, JT UNIV LEEDS DEPT STATLEEDS LS2 9JTW YORKSHIREENGLAND

iterative reweighting (IR) is a popular method for computing M-estimates of location and scatter in multivariate robust estimation. When the objective function comes from a scale mixture of normal distributions the iterative reweighting algorithm can be identified as an EM algorithm. The purpose of this paper is to show that in the special case of the multivariate t-distribution, substantial improvements to the convergence rate can be obtained by modifying the EM algorithm.

关键词： CONVERGENCE RATE EM algorithm iterative reweighting algorithm MULTIVARIATE T-DISTRIBUTION ROBUSTNESS

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DOMAINS OF CONVERGENCE FOR THE EM algorithm - A CAUTIONARY TALE IN A LOCATION ESTIMATION PROBLEM

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STATISTICS AND COMPUTING 1993年第3期3卷 103-108页

作者： ARSLAN, O CONSTABLE, PDL KENT, JT UNIV LEEDS DEPT STATLEEDS LS2 9JTW YORKSHIREENGLAND

The EM algorithm is a popular method for maximizing a likelihood in the presence of incomplete data. When the likelihood has multiple local maxima, the parameter space can be partitioned into domains of convergence, one for each local maximum. In this paper we investigate these domains for the location family generated by the t-distribution. We show that, perhaps somewhat surprisingly, these domains need not be connected sets. As an extreme case we give an example of a domain which consists of an infinite union of disjoint open intervals. Thus the convergence behaviour of the EM algorithm can be quite sensitive to the starting point.

关键词： iterative reweighting algorithm ROBUSTNESS T-DISTRIBUTION UPDATING FUNCTION

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