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Linear Regression

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Longhai Li - One of the best experts on this subject based on the ideXlab platform.

  • A new Regression model: modal Linear Regression - eScholarship
    2020
    Co-Authors: Longhai Li
    Abstract:

    A New Regression Model: Modal Linear Regression Weixin Yao and Longhai Li Abstract The mode of a distribution provides an important summary of data and is often es- timated based on some non-parametric kernel density estimator. This article devel- ops a new data analysis tool called modal Linear Regression in order to explore high- dimensional data. Modal Linear Regression models the conditional mode of a response Y given a set of predictors x as a Linear function of x. Modal Linear Regression differs from standard Linear Regression in that standard Linear Regression models the condi- tional mean (as opposed to mode) of Y as a Linear function of x. We propose an Expectation-Maximization algorithm in order to estimate the Regression coefficients of modal Linear Regression. We also provide asymptotic properties for the proposed esti- mator without the symmetric assumption of the error density. Our empirical studies with simulated data and real data demonstrate that the proposed modal Regression gives shorter predictive intervals than mean Linear Regression, median Linear Regression, and MM-estimators. Key Words: Forest fire data; Linear Regression; Modal Regression; Mode. Weixin Yao is Associate Professor, Department of Statistics, Kansas State University, Manhattan, Kansas 66506, U.S.A. Email: wxyao@ksu.edu. Longhai Li is Associate Professor, Department of Math- ematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N5E6, Canada. Email: longhai@math.usask.ca. The research of Longhai Li is supported by fundings from Natural Sciences and Engineering Research Council of Canada, and Canadian Foundation of Innovations.

  • A New Regression Model: Modal Linear Regression.
    Scandinavian Journal of Statistics, 2013
    Co-Authors: Longhai Li
    Abstract:

    type="main" xml:id="sjos12054-abs-0001"> The mode of a distribution provides an important summary of data and is often estimated on the basis of some non-parametric kernel density estimator. This article develops a new data analysis tool called modal Linear Regression in order to explore high-dimensional data. Modal Linear Regression models the conditional mode of a response Y given a set of predictors x as a Linear function of x . Modal Linear Regression differs from standard Linear Regression in that standard Linear Regression models the conditional mean (as opposed to mode) of Y as a Linear function of x . We propose an expectation–maximization algorithm in order to estimate the Regression coefficients of modal Linear Regression. We also provide asymptotic properties for the proposed estimator without the symmetric assumption of the error density. Our empirical studies with simulated data and real data demonstrate that the proposed modal Regression gives shorter predictive intervals than mean Linear Regression, median Linear Regression and MM-estimators.

Keith A Marill - One of the best experts on this subject based on the ideXlab platform.

  • Advanced statistics: Linear Regression, part I: simple Linear Regression.
    Academic emergency medicine : official journal of the Society for Academic Emergency Medicine, 2020
    Co-Authors: Keith A Marill
    Abstract:

    Simple Linear Regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in Linear Regression analysis, the four fundamental assumptions and the mechanics of simple Linear Regression are reviewed. The most common technique used to derive the Regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple Linear Regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple Linear Regression, in which there are multiple predictor variables.

  • Advanced statistics: Linear Regression, part II: multiple Linear Regression.
    Academic Emergency Medicine, 2020
    Co-Authors: Keith A Marill
    Abstract:

    Simple Linear Regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in Linear Regression analysis, the four fundamental assumptions and the mechanics of simple Linear Regression are reviewed. The most common technique used to derive the Regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple Linear Regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple Linear Regression, in which there are multiple predictor variables.

Xiaozhao Fang - One of the best experts on this subject based on the ideXlab platform.

  • Kernel Linear Regression for face recognition
    Neural Computing and Applications, 2014
    Co-Authors: Yuwu Lu, Xiaozhao Fang
    Abstract:

    Linear Regression uses the least square algorithm to solve the solution of Linear Regression equation. Linear Regression classification (LRC) shows good classification performance on face image data. However, when the axes of Linear Regression of class-specific samples have intersections, LRC could not well classify the samples that distribute around intersections. Moreover, the LRC could not perform well at the situation of severe lighting variations. This paper proposes a new classification method, kernel Linear Regression classification (KLRC), based on LRC and the kernel trick. KLRC is a nonLinear extension of LRC and can offset the drawback of LRC. KLRC implicitly maps the data into a high-dimensional kernel space by using the nonLinear mapping determined by a kernel function. Through this mapping, KLRC is able to make the data more Linearly separable and can perform well for face recognition with varying lighting. For comparison, we conduct on three standard databases under some evaluation protocols. The proposed methodology not only outperforms LRC but also takes the better performance than typical kernel methods such as kernel Linear discriminant analysis and kernel principal component analysis.

Xiaogang Su - One of the best experts on this subject based on the ideXlab platform.

  • Linear Regression analysis theory and computing
    2009
    Co-Authors: Xiaogang Su
    Abstract:

    This volume presents in detail the fundamental theories of Linear Regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the methods and techniques described in the book. It covers the fundamental theories in Linear Regression analysis and is extremely useful for future research in this area. The examples of Regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using Linear Regression analysis substantially in their subject fields. Introduction Simple Linear Regression Multiple Linear Regression Detection of Outliers and Influential Observations in Multiple Linear Regression Model Selection Model Diagnostics Extensions of Least Squares Generalized Linear Models Bayesian Linear Regression

Xiebinglei - One of the best experts on this subject based on the ideXlab platform.