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local linear regression for Function Learning: An Analysis Based on Sample Discrepancy

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2014年第11期25卷 2086-2098页

作者： Cervellera, Cristiano Maccio, Danilo CNR Inst Intelligent Syst Automat I-16149 Genoa Italy

local linear regression models, a kind of nonparametric structures that locally perform a linear estimation of the target function, are analyzed in the context of empirical risk minimization (ERM) for function learning. The analysis is carried out with emphasis on geometric properties of the available data. In particular, the discrepancy of the observation points used both to build the local regression models and compute the empirical risk is considered. This allows to treat indifferently the case in which the samples come from a random external source and the one in which the input space can be freely explored. Both consistency of the ERM procedure and approximating capabilities of the estimator are analyzed, proving conditions to ensure convergence. Since the theoretical analysis shows that the estimation improves as the discrepancy of the observation points becomes smaller, low-discrepancy sequences, a family of sampling methods commonly employed for efficient numerical integration, are also analyzed. Simulation results involving two different examples of function learning are provided.

关键词： Discrepancy efficient sampling local linear regression low-discrepancy sequences (LDS)

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Statistical inference in the partial linear models with the double smoothing local linear regression method

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2014年 146卷 102-112页

作者： He, Hua Tang, Wan Zuo, Guoxin Univ Rochester Dept Biostat & Computat Biol Rochester NY 14627 USA Cent China Normal Univ Sch Math & Stat Wuhan Peoples R China

Statistical inference about a partial linear model includes two parts, one linear and the other nonparametric. The double smoothing method proposed by He and Huang (2009) is a progressive local smoothing method for nonparametric curve estimation. In this paper, we discuss its extension to partial linear models, accompanied with difference-based estimation method for the linear part. Asymptotic theory of the proposed method is developed. The results of simulation studies and real data examples demonstrate that our approach is effective even for data with moderate sample sizes. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Difference-based estimation Double smoothing local linear regression Partial linear model

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local linear regression for Non Grid Spatiotemporal Models with Autoregressive Errors

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2013年第23期42卷 4259-4275页

作者： Wang, Hongxia Wang, Jinde Southeast Univ Dept Math Nanjing 211189 Jiangsu Peoples R China Nanjing Univ Dept Math Nanjing 210008 Jiangsu Peoples R China

In various environmental studies, spatiotemporal correlated data are involved, so there has been increasing demand of proposing spatiotemporal estimation methods that capture spatiotemporal correlation so as to improve the accuracy of estimation. In this article, we construct estimators for non grid spatiotemporal models with autoregressive errors. It is proved that the estimators are asymptotic normality. Simulation results also show the estimators perform well.

关键词： Autoregressive errors local linear regression Non grid spatiotemporal model

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Hyperspectral estimation of soil organic matter content using grey relational local regression model

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GREY SYSTEMS-THEORY AND APPLICATION 2021年第4期11卷 707-722页

作者： Cao, Xuesong Li, Xican Ren, Wenjing Wu, Yanan Liu, Jieya Shandong Agr Univ Sch Informat Sci & Engn Tai An Shandong Peoples R China

Purpose - This study aims to improve the accuracy of hyperspectral estimation of soil organic matter content. Design/methodology/approach - Based on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model. Findings - The results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82;the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R-2 = 0.924, and the average relative error is 6.608%. Originality/value - The paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

关键词： Soil organic matter Hyperspectral remote sensing grey relational local linear regression

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Nonparametric model-assisted estimation from randomized response survey data

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Mostafa, Sayed A. North Carolina A&T State Univ Dept Math & Stat Greensboro NC 27411 USA

The randomized response technique offers an effective way for reducing potential bias resulting from nonresponse and untruthful responses when asking questions about sensitive behaviors or beliefs. The technique is also used for conducting statistical disclosure control of public use data files released by statistical agencies such as the U.S. Census Bureau. In both cases, the technique works by randomizing the actual survey responses using some known randomization model. In the case of asking sensitive survey questions, the randomization of responses is done by the survey respondents and only the randomized responses are collected, whereas in the case of disclosure control, the survey agency implements the randomization of responses after collecting the survey data and prior to releasing it for public use. This paper considers estimating the finite population mean from a survey where randomized responses are available for the study variable along with complete non-randomized auxiliary information. We define and study a class of nonparametric model-assisted estimators that make efficient use of the available auxiliary information and account for the complex survey design. The asymptotic properties of the proposed estimators are derived and a bootstrap variance estimator is presented. The finite sample performance of the proposed estimators is studied via extensive simulations accounting for a wide range of forms for the relationship between the study variable and auxiliary variable. The empirical results support the theoretical analyses and suggest that our proposed estimators are superior to existing estimators in most cases. Furthermore, the proposed methods are illustrated using real data from the 2015 U.S. consumer expenditure survey.

关键词： Complex surveys local linear regression Model-assisted estimation Randomized response model

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linear and nonlinear signal detection and estimation in high-dimensional nonparametric regression under weak sparsity

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BERNOULLI 2024年第1期30卷 636-665页

作者： Cheung, Kin yap Lee, Stephen m. s. Xu, Xiaoya Univ Hong Kong Dept Stat & Actuarial Sci Pokfulam Hong Kong Peoples R China

The partially linear model provides an effective tool to combat the curse of dimensionality in nonparametric regression. Its applicability is, however, compromised by the need for correct distinction between linear and nonlinear components. Existing solutions are restricted to low dimensions or regression functions endowed with special structures. This paper considers a general nonparametric regression framework under which signal strength is embedded in a continuous spectrum scaled by asymptotic orders. Under a weak sparsity condition which allows for the presence of many weak, non-detectable, signals, a novel penalised regression procedure is proposed for detection and estimation of strong linear and nonlinear signals under high dimensions. The procedure applies bandwidth regularisation and SCAD penalisation to select nonlinear and linear signals, respectively, under a partially linear model setting. Theoretical results are established for its consistency in detecting strong signals and its error rate in estimating the regression function. Numerical examples are presented to illustrate its performance.

关键词： High dimensions local linear regression partially linear model SCAD variable selection weak sparsity

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An early indicator for anomalous stock market performance

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QUANTITATIVE FINANCE 2024年第1期24卷 105-118页

作者： Fritz, Marlon Gries, Thomas Wiechers, Lukas Hsch Darmstadt Fachbereich Gesellschaftswissenschaften Schofferstr 3 D-64295 Darmstadt Germany Paderborn Univ Dept Econ Warburger Str 100 D-33098 Paderborn Germany

We propose an indicator for detecting anomalous stock market valuation in real time such that market participants receive timely signals so as to be able to take stabilizing action. Unlike existing approaches, our anomaly indicator introduces three methodological novelties. First, we use an endogenous, purely data-driven, nonparametric trend identification method to separate long-term market movements from more short-term ones. Second, we apply SETAR models that allow for asymmetric expansions and contractions around the long-term trend and find systematic stock price cycles. Third, we implement these findings in our indicator and conduct real-time market forecasts, which have so far been neglected in the literature. Applications of our indicator using monthly S&P 500 stock data from 1970 to the end of 2022 show that short-term anomalous market movements can be identified in real time up to one year ahead. We predict all major anomalies, including the 1987 Bubble and the initial phase of the Financial Crisis that began in 2007. In total, our anomaly indicator identifies more than 80% of all - even minor - anomalous episodes. Thus, smoothing market exaggerations through early signaling seems possible.

关键词： Financial indicator local linear regression Nonparametric trend Stock price cycle Stock pricing Valuation ratio C14 C22 E44 G01

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Time-varying additive model with autoregressive errors for locally stationary time series

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第11期52卷 3848-3878页

作者： Li, Jiyanglin Li, Tao Shanghai Univ Finance & Econ Sch Stat & Management Shanghai Peoples R China

In this article, we study the time-varying additive model with time-varying autoregression (tvAR) error in the locally stationary context, and propose the two-step estimation for it. B-spline method, which is computation efficient, is adopted to obtain the initial estimator of trend function and additive components. And then the structure of autoregression error is estimated by ULASSO, the consistency and asymptotical normality are proved. At last, with the initial estimator and the estimated error structure, the improved estimator of trend function and additive components is derived by local linear smoothing, and its asymptotic normality and oracle property are proved. Simulation studies validate the properties of the proposed estimators. A real data application illustrates the proposed model is applicable and more appropriate than the classical additive model in the presence of locally stationary regressors.

关键词： time-varying autoregressive locally stationary B-spline local linear regression

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Drivers of mortality: risk factors and inequality

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY 2024年第4期187卷 989-1012页

作者： Cairns, Andrew J. G. Kleinow, Torsten Wen, Jie Heriot Watt Univ Maxwell Inst Math Sci Edinburgh EH14 4AS Scotland Heriot Watt Univ Dept Actuarial Math & Stat Edinburgh EH14 4AS Scotland Univ Amsterdam Fac Econ & Business Res Ctr Longev Risk Amsterdam Netherlands Lloyds Banking Grp London England

This paper takes a detailed look at socio-economic variation in mortality across England. Generic metrics such as the index of multiple deprivation (IMD) can be effective at the aggregate level of national deciles, but we demonstrate that they perform much less well at the regional, urban-rural, and neighbourhood level. We use local linear regression to develop a new, customized index for neighbourhood mortality that addresses the mortality-specific shortcomings of the IMD based on socio-economic and related, non-spatial predictive variables. We find that old-age income deprivation and employment deprivation are key determinants of mortality, but also that urban-rural class and the presence of care homes in a neighbourhood have an important role to play in assessing underlying mortality rates relative to national mortality. Residual spatial/regional variation in mortality is found to be much less significant than socio-economic variation and much lower than the residual regional variation that results from the use of the IMD.

关键词： age and deprivation standardized mortality rate local linear regression lower layer super output area mortality inequality regional mortality variation

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Double smoothing local linear estimation in nonlinear time series

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第5期52卷 1385-1399页

作者： Prasangika, K. D. Tang, Wan Yao, Zeng Zuo, Guoxin Univ Ruhuna Dept Math Matara Sri Lanka Tulane Univ Dept Biostat & Data Sci New Orleans LA 70118 USA Cent China Normal Univ Sch Math & Stat Wuhan Peoples R China

We generalize the double smoothing local linear regression method to nonparametric regression of time series. Under a strong mixing condition for the dependence of the time series, we show that after another round of smoothing based on the local linear regression estimates, the double smoothing local linear estimate will have reduced asymptotic bias, while keeping the variance at the same asymptotic order. The asymptotic bias reduces from the order of h(2) for the local linear estimates to h(4) for the double smoothing local linear estimates, where h is the bandwidth. Hence the double smoothing local linear method produces more optimal estimates in terms of mean squared error. Simulation studies and real time series data analysis confirm the advantages of the double smoothing method compared to the local linear method.

关键词： Non parametric regression local linear regression double smoothing local linear regression time series asymptotic properties

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