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RECURSIVE IDENTIFICATION OF WIENER-HAMMERSTEIN SYSTEMS

SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2012年第5期50卷 2621-2658页

作者： Mu, Bi-Qiang Chen, Han-Fu Chinese Acad Sci Key Lab Syst & Control Inst Syst Sci AMSS Beijing 100190 Peoples R China

Identification of the Wiener-Hammerstein system consisting of a linear subsystem in a cascade with a static nonlinearity f(.) followed by another linear subsystem with internal noises is considered. On the basis of input and noisy output the impulse responses of the two linear subsystems are estimated by stochastic approximation (SA) algorithms, and the nonlinear function is also estimated by SA algorithms but with kernel functions. The system input is taken to be a sequence of independent and identically distributed (iid) Gaussian random variables u(k) is an element of N(0, v(2)) with v > 0. For convergence of the proposed algorithms, the properties of martingale difference sequences (mds) and alpha-mixings play an important role. The estimates for coefficients of the linear subsystems as well as for values of the nonlinear function are proved to converge to the true values with probability one. Three numerical examples with nonlinearities possessing different properties are given, justifying the theoretical analysis.

关键词： Wiener Hammerstein system stochastic approximation recursive estimates alpha-mixing nonparametric method strong consistency

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On the Number of State Variables in Options Pricing

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MANAGEMENT SCIENCE 2010年第11期56卷 2058-2075页

作者： Li, Gang Zhang, Chu Hong Kong Baptist Univ Kowloon Tong Hong Kong Peoples R China Hong Kong Univ Sci & Technol Kowloon Hong Kong Peoples R China

In this paper, we investigate the methodological issue of determining the number of state variables required for options pricing. After showing the inadequacy of the principal component analysis approach, which is commonly used in the literature, we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and maturities as proxies for the transformed state variables. The methodology is applied to the prices of S&P 500 index options from the period 1996-2005. We find that, in addition to the index value itself, two state variables, approximated by the first two nonlinear principal components, are adequate for pricing the index options and fitting the data in both time series and cross sections.

关键词： options pricing state variables nonparametric method nonlinear principal component analysis

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A robust nonparametric framework for reconstruction of stochastic differential equation models

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2016年 450卷 294-304页

作者： Rajabzadeh, Yalda Rezaie, Amir Hossein Amindavar, Hamidreza Amirkabir Univ Technol Dept Elect Engn Tehran Iran

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler-Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Stochastic differential equation Parameter estimation nonparametric method Stationary process

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Estimating the area under a receiver operating characteristic (ROC) curve: Parametric and nonparametric ways

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SIGNAL PROCESSING 2013年第11期93卷 3111-3123页

作者： Xu, Weichao Dai, Jisheng Hung, Y. S. Wang, Qinruo Guangdong Univ Technol Sch Automat Dept Automat Control Guangzhou Higher Educ Mega Ctr Guangzhou 510006 Guangdong Peoples R China Jiangsu Univ Sch Elect & Informat Engn Zhenjiang 212013 Jiangsu Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China

Receiver operating characteristic (ROC) analysis has become a standard tool to tackle the two-sample problems in many scientific and engineering fields. The area under the curve (AUC) plays a leading role as a figure of merit to characterize the performances of diagnostic systems in medicine, binary classifiers in machine learning, and energy detectors in signal processing. Aiming at addressing some open problems of estimating the AUC, in this paper we deal with the AUC estimation problems in both parametric and nonparametric ways based on the equivalence between the AUC and Mann-Whitney U statistic (MWUS). In parametric ways, we derive the exact analytical expressions of the mean and variance of AUC for samples drawn from some important distributions that are frequently encountered in signal processing;whereas in nonparametric ways, we develop a rank-based algorithm which can estimate the variance of AUC unbiasedly and speedily. Monte Carlo simulations verify both our theoretical and algorithmic findings in this work. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Area under the curve (AUC) Mann-Whitney U statistic (MWUS) nonparametric method Parametric method Ranks Receiver operating characteristic (ROC)

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Testing treatment-covariate interaction in a nonparametric analysis of covariance model

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COMMUNICATIONS IN STATISTICS-THEORY AND methodS 2007年第6期36卷 1153-1171页

作者： Chen, Wonsun Bathke, Arne Univ Kentucky Dept Stat Lexington KY 40506 USA Clin Res Ctr Minist Hlth Biostat Consult Sdn Bhd Kuala Lumpur Malaysia

We consider a recently introduced nonparametric model for Analysis of Covariance and derive an asymptotic test for interaction between covariate and treatment. Furthermore, we suggest data depth techniques to obtain joint confidence regions for the covariate effects in this model. The finite sample behavior of the asymptotic method is evaluated in simulations. Application of the procedures is illustrated using an epileptic seizures and chemotherapy data set.

关键词： analysis of covariance confidence region data depth nonparametric method ordinal data

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KINETIC INVESTIGATION OF PENTOXIFYLLINE BASED ON nonparametric LINEAR REGRESSION OF DERIVATIVE AND CONVOLUTED DERIVATIVE CHROMATOGRAPHIC AND SPECTROPHOTOMETRIC RESPONSES

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JOURNAL OF LIQUID CHROMATOGRAPHY & RELATED TECHNOLOGIES 2014年第4期37卷 475-497页

作者： Korany, Mohamed A. Haggag, Rim S. Ragab, Marwa A. A. Elmallah, Osama A. Univ Alexandria Fac Pharm Dept Pharmaceut Analyt Chem Alexandria 21521 Egypt Pharco B Int Co Pharmaceut Alexandria Egypt

A novel application of chemometrics to the chromatographic peak responses in the kinetic investigation of Pentoxiphylline was introduced using nonparametric linear regression method as the statistical method of analysis. The kinetic study of Pentoxiphylline was conducted under two different stress conditions using DAD-HPLC. The chemometric methods were applied to the HPLC and spectrophotometric data of the kinetic study of Pentoxiphylline. First and second derivative treatment of chromatographic and spectrophotometric response data were followed by convolution of the resulting derivative curves using 8-points sin x(i) polynomials (discrete Fourier functions). The study also presents a comparison between parametric and non-parametric regression methods of analysis. Moreover, application of Arrhenius equation to the determination of the half life of Pentoxiphylline in alkaline condition was studied before and after the chemometric treatment of the data. The results obtained indicated that chemometric treatment of data with the application of non-parametric method enhances the linearity parameters obtained during the kinetic investigation. These linearity parameters were further used to estimate the degradation rate constant (K) and half life of the drug at room temperature which is very important for the estimation of the stability of the drug on shelf with accuracy and with minimum experimental work and errors.

关键词： Arrhenius equation chemometrics DAD-HPLC kinetic study nonparametric method pentoxifylline

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Regularized Policy Iteration with nonparametric Function Spaces

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JOURNAL OF MACHINE LEARNING RESEARCH 2016年第1期17卷 4809-4874页

作者： Farahmand, Amir-Massoud Ghavamzadeh, Mohammad Szepesvari, Csaba Mannor, Shie MERL 201 Broadway8th Floor Cambridge MA 02139 USA Adobe Res 321 Pk Ave San Jose CA 95110 USA Univ Alberta Dept Comp Sci Edmonton AB T6G 2E8 Canada Technion Dept Elect Engn IL-32000 Haifa Israel

We study two regularization-based approximate policy iteration algorithms, namely REG-LSPI and REG-BRM, to solve reinforcement learning and planning problems in discounted Markov Decision Processes with large state and finite action spaces. The core of these algorithms are the regularized extensions of the Least-Squares Temporal Difference (LSTD) learning and Bellman Residual Minimization (BRM), which are used in the algorithms' policy evaluation steps. Regularization provides a convenient way to control the complexity of the function space to which the estimated value function belongs and as a result enables us to work with rich nonparametric function spaces. We derive efficient implementations of our methods when the function space is a reproducing kernel Hilbert space. We analyze the statistical properties of REG-LSPI and provide an upper bound on the policy evaluation error and the performance loss of the policy returned by this method. Our bound shows the dependence of the loss on the number of samples, the capacity of the function space, and some intrinsic properties of the underlying Markov Decision Process. The dependence of the policy evaluation bound on the number of samples is minimax optimal. This is the first work that provides such a strong guarantee for a nonparametric approximate policy iteration algorithm.(1)

关键词： reinforcement learning approximate policy iteration regularization nonparametric method finite-sample analysis

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SPHERE - A CONTOURING PROGRAM FOR SPHERICAL DATA

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COMPUTERS & GEOSCIENCES 1985年第6期11卷 725-766页

作者： DIGGLE, PJ FISHER, NI CSIRO DIV MATH & STATLINDFIELDNSW 2070AUSTRALIA

This paper describes a method for displaying a sample of spherical data, by computing an “optimally” smoothed estimate of the underlying distribution and making a stereographic projection of the contours of this estimate. An interactive FORTRAN program which applies this method is supplied and described and examples given of its use.

关键词： Axial data Cross-validation Density estimation nonparametric method Spherical data Vectorial data

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Analysis of class separation and combination of class-dependent features for handwriting recognition

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1999年第10期21卷 1089-1094页

作者： Oh, IS Lee, JS Suen, CY Woosuk Univ Dept Comp Engn Wanju Kun 565701 Chonbuk South Korea Concordia Univ Ctr Pattern Recognit & Machine Intelligence Montreal PQ H3G 1M8 Canada

In this paper, we propose a new approach to combine multiple features in handwriting recognition based on two ideas: feature selection-based combination and class-dependent features. A nonparametric method is used for feature evaluation, and the first part of this paper is devoted to the evaluation of features in terms of their class separation and recognition capabilities. In the second part, multiple feature vectors are combined to produce a new feature vector. Based on the fact that a feature has different discriminating powers for different classes, a new scheme of selecting and combining class-dependent features is proposed. In this scheme, a class is considered to have its own optimal feature vector for discriminating itself from the other classes. Using an architecture of modular neural networks as the classifier, a series of experiments were conducted on unconstrained handwritten numerals. The results indicate that the selected features are effective in separating pattern classes and the new feature vector derived from a combination of two types of such features further improves the recognition rate.

关键词： handwriting recognition class separation nonparametric method class-dependent feature combination modular neural network

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Identification of atypical (rare) elements-a conditional, distribution-free approach

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2018年第3期35卷 923-937页

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Kowalski, Piotr A. Lukasik, Szymon Polish Acad Sci Syst Res Inst Ctr Informat Technol Data Anal Methods Warsaw Poland AGH Univ Sci & Technol Fac Phys & Appl Comp Sci Div Informat Technol & Syst Res Krakow Poland Catholic Univ Lublin Fac Math Comp Sci & Landscape Inst Math & Comp Sci Lublin Poland

The discovery of atypical elements has become one of the most important challenges in data analysis and exploration. At the same time it is not an easy matter with difficult conditions, and not even strictly defined. This article presents a ready-to-use procedure for identifying atypical elements in the sense of rarely occurring. The issue is considered in a conditional approach, where describing and conditioning variables can be multidimensional continuous with the second type also potentially categorical. The application of nonparametric concepts frees the investigated procedure from distributions of describing and conditioning variables. Ease of interpretation and completeness of the presented material lend themselves to the use of the worked out method in a wide range of tasks in various applications of data analysis in science and practice.

关键词： atypical element rare element outlier atypical element identification conditional approach nonparametric method distribution-free method numerical algorithm

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