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Variable bandwidth kernel regression estimation

ESAIM-PROBABILITY AND STATISTICS 2021年第1期25卷 55-86页

作者： Nakarmi, Janet Sang, Hailin Ge, Lin Univ Cent Arkansas Dept Math Conway AR 72035 USA Univ Mississippi Dept Math University MS 38677 USA Mississippi State Univ Div Arts & Sci Meridian MS 39307 USA

In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in Double-struck capital R-2 to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of O(h(n)(4)) under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.

关键词： kernel regression estimation variable bandwidth bias reduction central limit theorem

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Random Noise Suppression of Magnetic Resonance Sounding Data with Intensive Sampling Sparse Reconstruction and kernel regression estimation

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REMOTE SENSING 2019年第15期11卷 1829-1829页

作者： Yao, Xiaokang Zhang, Jianmin Yu, Zhenyang Zhao, Fa Sun, Yong Jilin Univ Coll Instrumentat & Elect Engn Changchun 130061 Jilin Peoples R China Minist Educ China Key Lab Geoexplorat Instruments Changchun 130061 Jilin Peoples R China Jilin Univ Coll Geoexplorat Sci & Technol Changchun 130026 Jilin Peoples R China

The magnetic resonance sounding (MRS) method is a non-invasive, efficient and advanced geophysical method for groundwater detection. However, the MRS signal received by the coil sensor is extremely susceptible to electromagnetic noise interference. In MRS data processing, random noise suppression of noisy MRS data is an important research aspect. We propose an approach for intensive sampling sparse reconstruction (ISSR) and kernel regression estimation (KRE) to suppress random noise. The approach is based on variable frequency sampling, numerical integration and statistical signal processing combined with kernel regression estimation. In order to realize the approach, we proposed three specific sparse reconstructions, namely rectangular sparse reconstruction, trapezoidal sparse reconstruction and Simpson sparse reconstruction. To solve the distortion of peaks and valleys after sparse reconstruction, we introduced the KRE to deal with the processed data by the ISSR. Further, the simulation and field experiments demonstrate that the ISSR-KRE approach is a feasible and effective way to suppress random noise. Besides, we find that rectangular sparse reconstruction and trapezoidal sparse reconstruction are superior to Simpson sparse reconstruction in terms of noise suppression effect, and sampling frequency is positively correlated with signal-to-noise improvement ratio (SNIR). In one case of field experiment, the standard deviation of noisy MRS data was reduced from 1200.80 nV to 570.01 nV by the ISSR-KRE approach. The proposed approach provides theoretical support for random noise suppression and contributes to the development of MRS instrument with low power consumption and high efficiency. In the future, we will integrate the approach into MRS instrument and attempt to utilize them to eliminate harmonic noise from power line.

关键词： magnetic resonance sounding (MRS) random noise suppression sampling record method signal estimation intensive sampling sparse reconstruction kernel regression estimation

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The kernel regression estimation for randomly censored functional stationary ergodic data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第17期46卷 8557-8574页

作者： Ling, Nengxiang Liu, Yang Hefei Univ Technol Sch Math Hefei 230009 Anhui Peoples R China

In this paper, we investigate the asymptotic properties of the kernel estimator for non parametric regression operator when the functional stationary ergodic data with randomly censorship are considered. More precisely, we introduce the kernel-type estimator of the non parametric regression operator with the responses randomly censored and obtain the almost surely convergence with rate as well as the asymptotic normality of the estimator. As an application, the asymptotic (1 - zeta) confidence interval of the regression operator is also presented (0 < zeta< 1). Finally, the simulation study is carried out to show the finite-sample performances of the estimator.

关键词： Asymptotic properties functional stationary ergodic data kernel regression estimation randomly censorship

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Asymptotic normality of the k-NN single index regression estimator for functional weak dependence data*

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2024年第9期53卷 3143-3168页

作者： Mohammedi, Mustapha Bouzebda, Salim Laksaci, Ali Bouanani, Oussama Univ Abdelhamid Ibn Badis Mostaganem Mostaganem Algeria Univ Djillali Liabes Sidi Bel Abbes LSPS Sidi Bel Abbes Algeria Universie Technol Compiegne LMAC Lab Appl Math Compiegne CS 60 319 F-60203 Compiegne France King Khalid Univ Coll Sci Dept Math Abha Saudi Arabia Univ Dr Moulay Tahar Saida LMSSA Saida Algeria

In this article, we consider the k-Nearest Neighbors (k-NN) method in a single index regression model when the explanatory variable is valued in functional space in the setting of the quasi-association dependence condition. The main result of this work is the establishment of the asymptotic distribution for the k-NN kernel single index estimator. These results are established under fairly general conditions on the underlying models. As an application, the asymptotic confidence bands for the regression model based on the single-index model are presented. Some simulation studies are carried out to show the finite sample performances of the k-NN estimator.

关键词： Asymptotic normality k-Nearest Neighbors (k-NN ) kernel regression estimation quasi-associated variables single functional index model weak dependence data

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A conditional distribution function-based measure for independence and K-sample tests in multivariate data

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JOURNAL OF MULTIVARIATE ANALYSIS 2025年 205卷

作者： Wang, Li Zhou, Hongyi Ma, Weidong Yang, Ying Tsinghua Univ Dept Math Sci Beijing Peoples R China Univ Penn Perelman Sch Med Dept Biostat Epidemiol & Informat Philadelphia PA 19104 USA

We introduce a new index to measure the degree of dependence and test for independence between two random vectors. The index is obtained by generalizing the Cram & eacute;r-von Mises distances between the conditional and marginal distribution functions via the projection- averaging technique. If one of the random vectors is categorical with K categories, we propose slicing estimators to estimate our index. We conduct an asymptotic analysis for the slicing estimators, considering both situations where K is fixed and where K is allowed to increase with the sample size. When both random vectors are continuous, we introduce a kernel regression estimator for the proposed index, demonstrating that its asymptotic null distribution follows a normal distribution and conducting a local power analysis for the kernel estimator-based independence test. The proposed tests are studied via simulations, with a real data application presented to illustrate our methods.

关键词： Categorical variable Conditional distribution function kernel regression estimation Projection-averaging Slicing estimator U-statistics

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The k-nearest neighbors method in single index regression model for functional quasi-associated time series data

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REVISTA MATEMATICA COMPLUTENSE 2023年第2期36卷 361-391页

作者： Bouzebda, Salim Laksaci, Ali Mohammedi, Mustapha Univ Technol Compiegne LMAC Lab Appl Math Compiegne CS 60 319 F-60203 Compiegne France King Khalid Univ Coll Sci Dept Math Abha 61413 Saudi Arabia Univ Djillali Liabes Sidi Bel Abbes BP 89 Sidi Bel Abbes 22000 Algeria LSPS Sidi Bel Abbes Algeria Univ Abdelhamid Ibn Badis Mostaganem Mostaganem Algeria

In the present paper, we consider the k-Nearest Neighbors (k-NN) method in the single index regression model in the case of a functional predictor and a scalar response. The main result of this work is the establishment of the almost complete convergence rates for the quasi-associated data. The obtained results rely on the classical functional kernel estimate. Some simulation studies are carried out to show the finite sample performances of the k-NN estimator. Finally, we show how to use the k-NN estimator of the functional single index regression model in the analysis of air quality to illustrate the effectiveness of our methodology.

关键词： Single functional index model k-Nearest Neighbors Functional Hilbert space kernel regression estimation Weak dependence Quasi-associated variables Almost complete convergence rates

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Robust Portfolio Optimization Based on Semi-Parametric ARMA-TGARCH-EVT Model with Mixed Copula Using WCVaR

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COMPUTATIONAL ECONOMICS 2023年第1期61卷 267-294页

作者： Deng, Xue Liang, Ying South China Univ Technol Sch Math Guangzhou 510640 Peoples R China

Portfolio returns generally follow multivariate distribution, whose effectiveness depends not only on the correct estimation of marginal distributions, but also on the accurate capture of the interdependent structure among them. To effectively estimate the marginal distribution and improve the accuracy, we present a hybrid ARMA-TGARCH-EVT model, which considers the leverage effect, thick tail and heteroscedasticity of the financial asset return series. This model utilizes the extreme value theory to process the tail data and uses the kernel regression estimation to process the intermediate data to make the marginal distribution smooth, natural and regular. Furthermore, a novel semi-parametric ARMA-TGARCH-EVT- Copula portfolio model is proposed to achieve the robustness of minimizing worst-case conditional value-at-risk (WCVaR). In the model, a mixed copula set is presented by t-copula and Archimedean copula to cover the wide joint dependence among logarithmic daily returns. To verify the effectiveness and practicality of our proposed model, a static numerical example and a dynamic portfolio based on the historical index data of two stock crash periods are given. The results show that the new model is superior in terms of daily average logarithmic return, cumulative logarithmic return and sharp ratio.

关键词： Copula Robust portfolio TGARCH Extreme value theory (EVT) kernel regression estimation

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Rates of the Strong Uniform Consistency with Rates for Conditional U-Statistics Estimators with General kernels on Manifolds

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MATHEMATICAL METHODS OF STATISTICS 2024年第2期33卷 95-153页

作者： Bouzebda, Salim Taachouche, Nourelhouda Univ Technol Compiegne LMAC Lab Appl Math Compiegne CS 60 319 F-60203 Compiegne France

U-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [103] introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watsonestimates of a regression function. Stute proved their strong pointwise consistency to: r((k))(phi, t):=E[phi(Y-1,...,Y-k)|(X-1,...,X-k)= t]for t=(t(1),...,t(k))is an element of R-dk. In the analysis of modern machine learning algorithms, sometimes we need to manipulate kernel estimation within the nonconventional setting with intricate kernels that might even be irregular and asymmetric. In this general setting, we obtain the strong uniform consistency result for the general kernel on Riemannian manifolds with Riemann integrable kernels for the conditional U-processes. We treat both cases when the class of functions is bounded or unbounded, satisfying some moment conditions. These results are proved under some standard structural conditions on the classes of functions and some mild conditions on the model. Our findings are applied to the regression function, the set indexed conditional U-statistics, the generalized U-statistics, and the discrimination problem. The theoretical results established in this paper are (or will be) key tools for many further developments in manifold data analysis

关键词： kernel regression estimation density estimation empirical processes VC-classes U-process Riemannian manifolds

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Non-Parametric Procedures in Evaluation of Collective Professional Skills of a Human-Operators Shift 9

Non-Parametric Procedures in Evaluation of Collective Profes...

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9th IFAC/IFIP/IFORS/IISE/INFORMS Conference on Manufacturing Modelling, Management and Control (IFAC MIM)

作者： Chernyshov, K. R. VA Trapeznikov Inst Control Sci 65 Profsoyuznaya St Moscow 117997 Russia

The paper is devoted to a methodology oriented to eliciting professional skills of a shift of human-operators of a technological plant by applying system identification techniques. Within the frameworks, the aim is to derive an input/output model that might reflect the actual level of collective professional competences and skills. Deriving the required input/output model is based on applying such a kind of the "proxy", that is indirect, variables as the time. Namely, there is applied the time that is needed to the shift of human-operators to make a decision on the plant process behavior using the information provided by information sources distributed over an information-and-control board, such as, say, group view displays (GVD) or, generically, within a total control room. In turn, these times are proposed to be fixed by use of eye trackers. Obtained in such a manner and calculated by use of data of observation of actual algorithm of collective performance of an experienced human-operator shift, the model characteristics represent a tool for evaluation of human-operators shift experience. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： collective skills and knowledge human-operator shift input/output model kernel regression estimation strongly consistent estimate system identification

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Cover's Algorithm Modified for Nonparametric estimation of a Log-Optimal Portfolio Selection Function

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第8期59卷 4771-4780页

作者： Walk, Harro Univ Stuttgart Fachbereich Math D-70569 Stuttgart Germany

Cover's algorithm yields an iterative portfolio choice for maximizing expected log investment return where the distribution function of the stock market vector is known. In the case that the stock market vectors form a stationary ergodic sequence with unknown distribution, by stochastic approximation and nonparametric regression estimation the algorithm is modified for iterative estimation of a log-optimal portfolio selection function of the last d observed vectors (fixed d is an element of N) on the basis of an observed training sequence of vectors. Under a boundedness and a mild alpha-mixing condition, a strong consistency result is established.

关键词： alpha-mixing Cover's algorithm kernel regression estimation log-optimal portfolio selection function partitions stationary ergodic training sequence stochastic approximation strong consistency

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