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Nonparametric regression

About: Nonparametric regression is a(n) research topic. Over the lifetime, 7682 publication(s) have been published within this topic receiving 354435 citation(s). more


Journal ArticleDOI: 10.1080/01621459.1979.10481038
William S. Cleveland1Institutions (1)
Abstract: The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology. more

Topics: Scatterplot smoothing (65%), Robust regression (61%), Smoothing (58%) more

9,473 Citations

Journal ArticleDOI: 10.1198/016214501753382273
Jianqing Fan1, Runze Li1Institutions (1)
Abstract: Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized likelihood approaches are proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously. Hence they enable us to construct confidence intervals for estimated parameters. The proposed approaches are distinguished from others in that the penalty functions are symmetric, nonconcave on (0, ∞), and have singularities at the origin to produce sparse solutions. Furthermore, the penalty functions should be bounded by a constant to reduce bias and satisfy certain conditions to yield continuous solutions. A new algorithm is proposed for optimizing penalized likelihood functions. The proposed ideas are widely applicable. They are readily applied to a variety of ... more

Topics: Likelihood function (57%), Penalty method (56%), Lasso (statistics) (53%) more

7,149 Citations

Open accessJournal ArticleDOI: 10.1214/AOS/1176347963
Abstract: A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions. more

6,289 Citations

Journal ArticleDOI: 10.1080/01621459.1988.10478639
Abstract: Locally weighted regression, or loess, is a way of estimating a regression surface through a multivariate smoothing procedure, fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series With local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions, such as polynomials The goal of this article is to show, through applications, how loess can be used for three purposes: data exploration, diagnostic checking of parametric models, and providing a nonparametric regression surface Along the way, the following methodology is introduced: (a) a multivariate smoothing procedure that is an extension of univariate locally weighted regression; (b) statistical procedures that are analogous to those used in the least-squares fitting of parametric functions; (c) several graphical methods that are useful tools for understanding loess estimates and checking the a more

Topics: Local regression (69%), Nonparametric regression (67%), Regression diagnostic (65%) more

4,803 Citations

Open accessBook
01 Jan 1978-
Abstract: Applied nonparametric statistics , Applied nonparametric statistics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی more

Topics: Semiparametric regression (75%), Semiparametric model (74%), Nonparametric statistics (70%) more

4,239 Citations

No. of papers in the topic in previous years

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Topic's top 5 most impactful authors

Oliver Linton

79 papers, 3.4K citations

Holger Dette

65 papers, 1.5K citations

Wolfgang Karl Härdle

55 papers, 9.3K citations

Raymond J. Carroll

50 papers, 6.9K citations

Peter Hall

42 papers, 4K citations

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