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Statistical inference for a single-index varying coefficient model with measurement errors in all covariates

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2022年第5期92卷 1047-1061页

作者： Huang, Zhensheng Jiang, Zhiqiang Li, Jing Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China

In this paper, a single-index varying coefficient model with measurement errors in all covariates is investigated. We propose a new approach to estimate the link function g(.) and the index parameter beta, which combines the simulation-extrapolation (SIMEX) technique with local linear regression and estimating equation. Under some regularity conditions, large sample properties of the proposed estimators are established. Simulation studies and an application are presented to evaluate the proposed method.

关键词： Bias-corrected estimate local linear regression measurement errors SIMEX technique single-index varying coefficient model

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Prediction in locally Stationary Time Series

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JOURNAL OF BUSINESS & ECONOMIC STATISTICS 2022年第1期40卷 370-381页

作者： Dette, Holger Wu, Weichi Ruhr Univ Bochum Fak Math Bochum Germany Tsinghua Univ Dept Ind Engn Ctr Stat Beijing 10084 Peoples R China

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in nonstationary time series. In contrast to the currently available methods for this problem the predictor developed here does not rely on fitting an autoregressive model and does not require a vanishing trend. The finite sample properties of the new methodology are illustrated by means of a simulation study and a financial indices *** this article are available online.

关键词： High-dimensional autocovariance local linear regression locally stationary time series Matrices Prediction

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local regression Ranking for Saliency Detection

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2020年 29卷 1536-1547页

作者： Zhang, Ying-Ying Zhang, Shuo Zhang, Ping Song, Hai-Zhen Zhang, Xin-Gang Nanyang Normal Univ Phys Elect Engn Coll Nanyang 473061 Peoples R China Beijing Jiaotong Univ Sch Comp & Informat Technol Beijing 100191 Peoples R China Nanyang Normal Univ Comp & Informat Technol Coll Nanyang 473061 Peoples R China

Saliency detection is an important and challenging research topic due to the variety and complex of the background and saliency regions. In this paper, we present a novel unsupervised saliency detection approach by exploiting a learning-based ranking framework. First, the local linear regression model is adopted to simulate the local manifold structure of every image element, which is approximately linear. Using the background queries from the boundary prior, we construct a unified objective function to globally minimize all the errors of the local models for the whole image element points. The Laplacian matrix is learned via optimizing the unified objective function. Low-level image features as well as high-level semantic information extracted from deep neural networks are used for the Laplacian matrix learning. Based on the learnt Laplacian matrix, the saliency of the image element is measured as the relevance ranking to the background queries. The foreground queries are obtained from the background-based saliency and the relevance ranking to the foreground queries is calculated in the same way as the background-based saliency. Second, we calculate an enhanced similarity matrix by fusing two different-level deep feature metrics through cross diffusion. A propagation algorithm uses this enhanced similarity matrix to better exploit the intrinsic relevance of similar regions and improve the saliency ranking results effectively. Results on four benchmark datasets with pixel-wise accurate labelling demonstrate that the proposed unsupervised method shows better performance compared with the newest state-of-the-art methods and is competitive with deep learning-based methods.

关键词： Learning-based ranking saliency detection local linear regression global calibration metric fusion saliency propagation

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Semi-functional partial linear spatial autoregressive model

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第24期50卷 5941-5954页

作者： Li, Yunxia Ying, Caiyun Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou 310018 Peoples R China

This paper proposes a semi-functional partial linear spatial autoregressive (SAR) model, in which we allow one of the explanatory variables to be a functional variable, while the dependent variable is scalar. We aim to enable the spatial econometric models to be applied to various areas where data types can be functional data. Based on quasi-maximum likelihood estimation (QMLE) method and local linear regression method, we construct a two-stage estimator to estimate the parameters and nonparametric component. The convergence rate of the estimator of nonparametric component is given. Furthermore, Monte Carlo simulations are performed to investigate our two-stage estimator's finite sample performance.

关键词： Functional variables SAR local linear regression QMLE

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A New Functional Estimation Procedure for Varying Coefficient Models

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第5期50卷 1117-1133页

作者： Yan, Xingyu Pu, Xiaolong Xun, Xiaolei Zhou, Yingchun East China Normal Univ Sch Stat Key Lab Adv Theory & Applicat Stat & Data Sci MOE Shanghai Peoples R China Fudan Univ Sch Data Sci 220 Handan Rd Shanghai 200433 Peoples R China

There has been substantial research interest in developing various estimation procedures for varying coefficient models. Most methods in the literature require specifying a working covariance structure. In case of a misspecified structure, estimation of the varying coefficient function may be deficient. Taking advantage of functional principal component analysis, we propose a new functional estimation procedure for varying coefficient models which does not need a working covariance structure. Weak convergence property for the proposed estimators has been established. Based on the simulation studies, the proposed procedure works better than the naive local linear regression with working independence error structure by Zhu et al. and Cholesky decomposition method by Lin et al. We apply our method to analyze the growth data of newborn infants in a real medical study and produce interpretable results.

关键词： Varying coefficient models within-subject correlation functional principal component analysis local linear regression

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Estimating trends and the current climate mean in a changing climate

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CLIMATE SERVICES 2024年 33卷

作者： Scherrer, Simon C. de Valk, Cees Begert, Michael Gubler, Stefanie Kotlarski, Sven Croci-Maspoli, Mischa Fed Off Meteorol & Climatol MeteoSwiss Zurich Switzerland Royal Netherlands Meteorol Inst KNMI De Bilt Netherlands Swiss Acad Sci SCNAT Bern Switzerland

Describing the climate evolution using trend lines and estimating the current climate mean (CCM) on the local scale is an important climate service. For an increasing number of variables, accelerating climate change disqualifies the use of traditional climatological normals and long-term linear trends as CCM estimators. Although several alternatives are available and already in use, there are few comprehensive assessments of the different approaches let alone a consensus for recommending a particular method. Here we evaluate frequently used approaches that use past climate data to estimate the CCM applying several transparent criteria. The performance is assessed in a perfect model framework for the strongly changing Swiss mean temperature 1864-2099 with the centered 30-year mean as CCM benchmark. Short-term linear trends, cubic splines and local linear regression with optimized parameters all provide unbiased CCM estimates for a broad range of climate evolutions and independent of trend magnitudes. To enable broad usability, additional criteria are considered such as a wide applicability to a large number of climate variables and simplicity in terms of use, settings and communication. In the overall assessment, local linear regression emerges as a particularly promising method to describe nonlinear climate trends and to determine the CCM. The criteria-based assessment approach has proven very useful in choosing a method as objectively as possible. We present ideas for modern climate services to complement the toolbox of climate monitoring and encourage the community to develop recommendations at the international level to increase the coherence, objectivity and robustness of climate monitoring products.

关键词： Climate monitoring Current climate mean Trends Climate change local linear regression Criteria-based assessment

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Statistical inferences for single-index models with measurement errors

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JOURNAL OF APPLIED STATISTICS 2021年第6期48卷 1033-1052页

作者： Huang, Zhensheng Lou, Wen Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China

An important factor in house prices is its location. However, measurement errors arise frequently in the process of observing variables such as the latitude and longitude of the house. The single-index models with measurement errors are used to study the relationship between house location and house price. We obtain the estimators by a SIMEX method based on the local linear method and the estimating equation. To test the significance of the index coefficient and the linearity of the link function, we establish the generalized likelihood ratio (GLR) tests for the models. We demonstrate that the asymptotic null distributions of the established GLR tests follow -distributions which are independent of nuisance parameters or functions. Finally, two simulated examples and a real estate valuation data set are given to illustrate the effect of GLR tests.

关键词： Single-index model measurement errors local linear regression SIMEX generalized likelihood ratio test

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Curvature-Oriented Splitting for Multivariate Model Trees

Curvature-Oriented Splitting for Multivariate Model Trees

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IEEE Symposium Series on Computational Intelligence (IEEE SSCI)

作者： Schone, Marvin Kohlhase, Martin Bielefeld Univ Appl Sci Ctr Appl Data Sci Gutersloh Gutersloh Germany

ISBN: (纸本)9781728190488

Model trees typically partition the input space by axis-orthogonal splits into local regions for local regression. Due to these splits, properties of the function to be approximated can only be taken into account to a limited extent, which increases the bias of model trees. To minimize this bias, multivariate model trees with axis-oblique splits can be used. However, existing methods to build axis-oblique splits are either not applicable, ineffective, or limited to certain data distributions and properties of the approximated function. In this work, we present a novel method for axis-oblique splitting that overcomes these drawbacks by using the average direction of non-linearity of the function. This direction is estimated by extending the dimensionality reduction method refined Outer Product of Gradients. Moreover, we present a tree construction algorithm in which our method is integrated, and evaluate the resulting multivariate model tree COMT on synthetic data in an experimental study. In this study, we compare COMT and our split method in terms of prediction accuracy with common regression models and a proven method to identify axis-oblique split directions called Principal Hessian Directions. We also analyze the improvements in bias and variance by our axis-oblique splitting over conventional (univariate) model trees and multivariate regression trees. On the used data, COMT outperforms the competitors in terms of prediction accuracy, and our split method significantly reduces bias and variance.

关键词： local linear regression multivariate model trees regression trees axis-oblique splitting outer product of gradients

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Nonparametric estimation of population average dose-response curves using entropy balancing weights for continuous exposures

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HEALTH SERVICES AND OUTCOMES RESEARCH METHODOLOGY 2021年第1期21卷 69-110页

作者： Vegetabile, Brian G. Griffin, Beth Ann Coffman, Donna L. Cefalu, Matthew Robbins, Michael W. McCaffrey, Daniel F. RAND Corp Santa Monica CA 90401 USA RAND Corp Pittsburgh PA USA Temple Univ Philadelphia PA 19122 USA Educ Testing Serv Princeton NJ 08541 USA

Weighted estimators are commonly used for estimating exposure effects in observational settings to establish causal relations. These estimators have a long history of development when the exposure of interest is binary and where the weights are typically functions of an estimated propensity score. Recent developments in optimization-based estimators for constructing weights in binary exposure settings, such as those based on entropy balancing, have shown more promise in estimating treatment effects than those methods that focus on the direct estimation of the propensity score using likelihood-based methods. This paper explores recent developments of entropy balancing methods to continuous exposure settings and the estimation of population dose-response curves using nonparametric estimation combined with entropy balancing weights, focusing on factors that would be important to applied researchers in medical or health services research. The methods developed here are applied to data from a study assessing the effect of non-randomized components of an evidence-based substance use treatment program on emotional and substance use clinical outcomes.

关键词： Causal inference Weighted estimation local linear regression Mental health Substance abuse

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Nonparametric and Semiparametric Approaches to Functional Data Modeling

Nonparametric and Semiparametric Approaches to Functional Da...

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作者： Huang, Wentian Cornell University

学位级别：Ph.D., Doctor of Philosophy

We propose original nonparametric and semiparametric approaches to model the relationship between a pair of variables (X, Y), where X ∈ L2 (T) is a square-integrable random function over a compact interval T, and Y ∈ R. Modeling of functional data greatly extends the nonparameteric approaches that have been widely used in the multivariate setting for both classifications and regressions. However, such approaches can be problematic due to the infinite-dimensional nature of functional data and the so-called curse-of-dimensionality. Fortunately, functional data often lie in a low-dimensional subspace. Therefore, one can project the data onto a subspace of dimensionJ, e.g., the firstJprincipal components, whereJis a tuning parameter, and the model performance is sensitive to the choice ofJ. Our work develops methods controlling the cut-off basising the copula structure to model dependency between theJprojected scores. Furthermore, for functional local linear models, a class of multidimensional data-adaptive ridge penalties is built, and an algorithm of empirically estimating the first-order derivatives is developed. The methods prove to have strong prediction performance and dimension reduction strength when compared to other popular approaches through comprehensive simulation scenarios and real-data examples. We also point out the methods’ effective bandwidth size control, indicating their strength in finite-sample variance reduction. The estimators’ asymptotic performances are also discussed whenJ→ ∞ as n → ∞.

关键词： Asymptotic theory Functional data local linear regression Nonparametric statistics

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