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local linear regression with nonparametrically generated covariates for weakly dependent data

JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2023年 225卷 89-109页

作者： Chu, Ba Carleton Univ Ottawa ON Canada Carleton Univ Dept Econ B 857 Loeb Bldg1125 Colonel Dr Ottawa ON K1S 5B6 Canada

This paper studies the behaviour of the local linear (LL) estimator for regression with nonparametrically generated regressors under weak dependence conditions, effectively extending the main result of Mammen et al. (2012) to the case with strongly mixing (or alpha-mixing) data. Specifically, we establish that the convergence rate in their Theorem 1 carries over to the case with geometrically alpha-mixing data. In contrast, this convergence rate does not necessarily remain the same for polynomially alpha-mixing data. We then apply the obtained uniform stochastic expansion of the second-step LL estimator to derive normal approximations for the LL estimator of a nonparametric censored autore-gressive model and the three-step nonparametric estimator of the risk-return regression in finance. A rule for bandwidth selection in nonparametric regressions with estimated covariates to obtain valid inference is also suggested. We then provide a simulation study and a real data application to illustrate the practical relevance of the proposed approach. Lastly, technically speaking, to establish a uniform bound for the upper tail probability of a summation involving polynomially strong-mixing empirical processes, we propose a new exponential inequality, which plays a pivotal role in the proof of the main theorem and is of independent interest. (c) 2022 Elsevier B.V. All rights reserved.

关键词： local linear regression Strong mixing Empirical processes Generated regressors Exponential inequality Rio's coupling

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Scalar-on-function local linear regression and beyond

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BIOMETRIKA 2022年第2期109卷 439-455页

作者： Ferraty, F. Nagy, S. Univ Toulouse Toulouse Math Inst 118 Route Narbonne F-31062 Toulouse France Charles Univ Prague Fac Math & Phys Sokolovska 83 Prague 18675 Czech Republic

It is common to want to regress a scalar response on a random function. This paper presents results that advocate local linear regression based on a projection as a nonparametric approach to this problem. Our asymptotic results demonstrate that functional local linear regression outperforms its functional local constant counterpart. Beyond the estimation of the regression operator itself, local linear regression is also a useful tool for predicting the functional derivative of the regression operator, a promising mathematical object in its own right. The local linear estimator of the functional derivative is shown to be consistent. For both the estimator of the regression functional and the estimator of its derivative, theoretical properties are detailed. On simulated datasets we illustrate good finite-sample properties of the proposed methods. On a real data example of a single-functional index model, we indicate how the functional derivative of the regression operator provides an original, fast and widely applicable estimation method.

关键词： Asymptotics Functional data Functional derivative of a regression operator Functional index model local linear regression Nearest neighbours method Scalar-on-function regression

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local linear regression estimator on the boundary correction in nonparametric regression estimation

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Journal of Statistical Theory and Applications 2020年第3期19卷 460-471页

作者： Cheruiyot, Langat Reuben Department of Mathematics and Computer Sciences School of Science and Technology University of Kabianga Kericho Kenya

The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind getting a model that fits the data well can be a challenge. There are many situations where parametric estimation is disadvantageous because of the possible misspecification of the model. Under such circumstance, many researchers normally allow the data to suggest a model for itself in the technique that has become so popular in recent years called the nonparametric regression estimation. In this technique the use of kernel estimators is common. This paper explores the famous Nadaraya-Watson estimator and local linear regression estimator on the boundary bias. A global measure of error criterion-asymptotic mean integrated square error (AMISE) has been computed from simulated data at the empirical stage to assess the performance of the two estimators in regression estimation. This study shows that local linear regression estimator has a sterling performance over the standard Nadaraya-Watson estimator. © 2020 The Authors.

关键词： Bias Kernel estimators local linear regression Nonparametric regression estimation Variance

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Carbon Monoxide Sensor Correction based on local linear regression

International Core Journal of Engineering

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International Core Journal of Engineering 2022年第2期8卷 48-54页

作者： Xingyu Cai Xiaowen Sun Ziwen Sun

Drift is one of the most serious impairments afflicting gas sensors. It can be seen as a gradual change in the sensor response over a long period of time when the external conditions are constant. This paper proposes a simple correction method based on local linear regression. Use the original data as a fitting plane to correct the drift of the sensor. Using linear regression and local linear regression to process the original data respectively, it is found that both methods are effective and the local linear regression effect is better.

关键词： Gas Sensors Drift Correction local linear regression

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local linear regression-based unsupervised truth discovery

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INTELLIGENT DATA ANALYSIS 2019年第3期23卷 573-585页

作者： Zhang, Zhiqiang Hu, Yichao Ye, Songtao Nie, Binbin Tian, Sen Natl Meteorol Informat Ctr Beijing 100081 Peoples R China Xiangtan Univ Coll Informat Engn Xiangtan 411105 Hunan Peoples R China Chinese Acad Sci Inst High Energy Phys Div Nucl Technol & Applicat Beijing 100049 Peoples R China

In the era of big data, the data provided by multiple sources for the same entity may result in conflicting information. Because sources with higher reliability degrees provide true information more frequently, the truth can be obtained by estimating the weights or reliability degrees of the sources. Due to hostile websites or faulty sensors, some sources may occasionally provide outliers that deviate significantly from the truth. However, in the majority of existing truth discovery methods, each source should be uniformly assigned a weight at the initial stage. Therefore, the accuracy of truth estimation is degraded by outliers. Several previous studies have proposed kernel density estimation-based truth discovery algorithms to solve the problems caused by outliers. These approaches aim to estimate the probability distribution of observation values to assess the reliability of sources. Unfortunately, the data with outliers that are smoothed by Gaussian kernels may cause more deviations from the truth. Thus, we propose a local linear regression (LLR) method for addressing the problems caused by outliers. The proposed method can effectively estimate the source reliability and the truth of the datasets with outliers. Experiments on two real-world datasets demonstrate that the proposed method yields more accurate results than existing state-of-the-art methods.

关键词： Truth discovery local linear regression kernel density estimation outlier data source reliability

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KNN-based local linear regression for the analysis and simulation of low flow extremes under climatic influence

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CLIMATE DYNAMICS 2017年第9-10期49卷 3493-3511页

作者： Lee, Taesam Ouarda, Taha B. M. J. Yoon, Sunkwon Gyeongsang Natl Univ Dept Civil Engn ERI 501 Jinju Daero Jinju 52828 Gyeongsangnam D South Korea Masdar Inst Sci & Technol Inst Ctr Water Adv Technol & Environm Res iWATER POB 54224 Abu Dhabi U Arab Emirates INRS ETE Natl Inst Sci Res 490 Couronne Quebec City PQ 490 Canada APEC Climate Ctr Climate Res Dept Busan 48058 South Korea

Climate change frequently causes highly nonlinear and irregular behaviors in hydroclimatic systems. The stochastic simulation of hydroclimatic variables reproduces such irregular behaviors and is beneficial for assessing their impact on other regimes. The objective of the current study is to propose a novel method, a k-nearest neighbor (KNN) based on the local linear regression method (KLR), to reproduce nonlinear and heteroscedastic relations in hydroclimatic variables. The proposed model was validated with a nonlinear, heteroscedastic, lag-1 time dependent test function. The validation results of the test function show that the key statistics, nonlinear dependence, and heteroscedascity of the test data are reproduced well by the KLR model. In contrast, a traditional resampling technique, KNN resampling (KNNR), shows some biases with respect to key statistics, such as the variance and lag-1 correlation. Furthermore, the proposed KLR model was used to simulate the annual minimum of the consecutive 7-day average daily mean flow (Min7D) of the Romaine River, Quebec. The observed and extended North Atlantic Oscillation (NAO) index is incorporated into the model. The case study results of the observed period illustrate that the KLR model sufficiently reproduced key statistics and the nonlinear heteroscedasticity relation. For the future period, a lower mean is observed, which indicates that drier conditions other than normal might be expected in the next decade in the Romaine River. Overall, it is concluded that the KLR model can be a good alternative for simulating irregular and nonlinear behaviors in hydroclimatic variables.

关键词： Hydropower k-Nearest neighbor local linear regression Min7D flow Nonparametric model Stochastic simulation

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BLIND PROPOSAL QUALITY ASSESSMENT VIA DEEP OBJECTNESS REPRESENTATION AND local linear regression

BLIND PROPOSAL QUALITY ASSESSMENT VIA DEEP OBJECTNESS REPRES...

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IEEE International Conference on Multimedia and Expo (ICME)

作者： Wu, Qingbo Li, Hongliang Meng, Fanman Ngan, King N. Xu, Linfeng Univ Elect Sci & Technol China Chengdu Sichuan Peoples R China Chinese Univ Hong Kong Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9781509060672

The quality of object proposal plays an important role in boosting the performance of many computer vision tasks, such as, object detection and recognition. Due to the absence of manually annotated bounding-box in practice, the quality metric towards blind assessment of object proposal is highly desirable for singling out the optimal proposals. In this paper, we propose a blind proposal quality assessment algorithm based on the Deep Objectness Representation and local linear regression (DORLLR). Inspired by the hierarchy model of the human vision system, a deep convolutional neural network is developed to extract the objectness-aware image feature. Then, the local linear regression method is utilized to map the image feature to a quality score, which tries to evaluate each individual test window based on its k-nearest-neighbors. Experimental results on a large-scale IoU labeled dataset verify that the proposed method significantly outperforms the state-of-the-art blind proposal evaluation metrics.

关键词： Blind proposal quality assessment deep objectness representation local linear regression

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local linear regression for efficient data-driven control

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KNOWLEDGE-BASED SYSTEMS 2016年 98卷 55-67页

作者： Maccio, Danilo CNR Inst Intelligent Syst Automat Via Marini 6 I-16149 Genoa Italy

The problem of data-driven control (DDC) represents an important topic in the area of automation, due to the availability of large amount of data generated by the production processes occurring in industrial plants. The aim of this work is the study of an efficient DDC approach for nonlinear dynamic systems that exploits the data directly coming from the plant. In this framework, the control problem consists in the design of an automatic regulator able to execute a task by using the data collected during the successful operation of the plant, regulated by a reference controller such as a human operator. The proposed synthetic regulator is based on local linear regression models chosen for their simplicity of training and efficiency in incorporating new data generated by the plant. The conditions under which the derived controller converges to the optimal one are analysed in the context of statistical learning theory, which provides an appropriate framework to efficiently address this kind of DDC problem. Simulation results involving a dynamical system are provided to show the properties of the proposed method in an applicative context. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Data-driven control local linear regression Statistical learning theory

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local linear regression on correlated survival data

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JOURNAL OF MULTIVARIATE ANALYSIS 2016年 147卷 285-294页

作者： Jin, Zhezhen He, Wenqing Columbia Univ Dept Biostat New York NY 10032 USA Univ Western Ontario Dept Stat & Actuarial Sci London ON N6A 5B7 Canada

Correlated survival data arise in many contexts, and the regression analysis of such data is often of interest in practice. In this paper, we study a weighted local linear regression method for the analysis of correlated censored data, which is a natural extension of classical nonparametric regression that models directly the effect of covariates on survival time, using an unknown smooth nonparametric function. The estimation and inference are based on local linear regression and a class of unbiased data transformations. The most important feature of the proposed method is to weight local observations with local variance, which is the key to improve the estimation efficiency. We derive the asymptotic properties of the resulting estimator and show that the asymptotic variance of the nonparametric estimator is minimized with the correct specification of correlation structure. We evaluate the performance of the proposed method using simulation studies, and illustrate the proposed method with an analysis of data from the Busselton Health Study. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Asymptotic bias Correlated survival data Kernel function local linear regression Mean squared error Nonparametric curve estimation Unbiased data transformation

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A Wi-Fi Wireless localization Method Based on local linear regression and Position Weighting

A Wi-Fi Wireless Localization Method Based on Local Linear R...

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2016 4th International Conference on Machinery,Materials and Information Technology Applications(ICMMITA 2016)

作者： Yongjun ZHANG Haixu GUO Institute of Information Photonics and Optical Communications Beijing University of Posts and Telecommunications

A kind of Wi-Fi wireless location system has been designed and implemented in this research. The system is based on a combined method of local linear regression and position weighting, which develops the traditional ranging algorithm based on RSSI and improves the positioning accuracy. The result shows that the expectation of positioning error is about 2 meters. The error in 83% of the samples is within 3 meters and less than 6 meters in 98%, which shows that the combined method of local linear regression and distributed position weighting can effectively control error range and improve positioning accuracy. With the popularity of indoor wireless routing and mobile phone hotspot, the system will have a very broad application prospects for indoor localization.

关键词： Wi-Fi RSSI Indoor localization local linear regression Position weighting

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