Nonparametric Comparison of Multiple Regression Curves in Scale-Space

Park, Cheolwoo; Hannig, Jan; Kang, Kwan Hyoung

doi:10.1080/10618600.2013.822816

Cited by 18 publications

(6 citation statements)

References 41 publications

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“…SiZer provides us with more information about the locations of the differences among the regression curves if they do exist. Park et al [46] developed an ANOVA-type test statistic and conducted it in scale space for testing the equality of more than two regression curves.…”

Section: Construction Of Sizer-rs Map For Comparing Multiple Regressimentioning

confidence: 99%

Model Testing Based on Regression Spline

Li¹

2018

Topics in Splines and Applications

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Tests based on regression spline are developed in this chapter for testing nonparametric functions in nonparametric, partial linear and varying-coefficient models, respectively. These models are more flexible than linear regression model. However, one important problem is if it is really necessary to use such complex models which contain nonparametric functions. For this purpose, p-values for testing the linearity and constancy of the nonparametric functions are established based on regression spline and fiducial method. In the application of spline-based method, the determination of knots is difficult but plays an important role in inferring regression curve. In order to infer the nonparametric regression at different smoothing levels (scales) and locations, multi-scale smoothing methods based on regression spline are developed to test the structures of the regression curve and compare multiple regression curves. It could sidestep the determination of knots; meanwhile, it could give a more reliable result in using the spline-based method.

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Section: Construction Of Sizer-rs Map For Comparing Multiple Regressimentioning

confidence: 99%

Model Testing Based on Regression Spline

Li¹

2018

Topics in Splines and Applications

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“…Recently, an ANOVA type approach for comparing multiple curves observed at arbitrary values of the dependent variable was developed in Park et al. (). The advantage of this method over the ones that rely on residuals is that, in the spirit of original SiZer, one obtains information also about the potential local scale dependent differences of the underlying curves themselves.…”

Section: Sizer and Its Descendantsmentioning

confidence: 99%

Statistical Scale Space Methods

Holmström

Pasanen

2016

Int Statistical Rev

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The goal of statistical scale space analysis is to extract scale-dependent features from noisy data. The data could be for example an observed time series or digital image in which case features in either different temporal or spatial scales would be sought. Since the 1990s, a number of statistical approaches to scale space analysis have been developed, most of them using smoothing to capture scales in the data, but other interpretations of scale have also been proposed. We review the various statistical scale space methods proposed and mention some of their applications.

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“…In a different line of approach, motivated by the scale-space view from computer vision literature, [4] proposed a graphical device called SiZer to explore structures, such as peaks and valleys, in regression curves. SiZer analysis has been used in comparing two or more regression curves (see, e.g., [30], [29]). [15] proposed a graphical device, based on the derivative and inverse of the derivative of the regression function, to compare the two regression functions up to shift in the horizontal and/or vertical axis.…”

Section: Introductionmentioning

confidence: 99%

A Review: Malware Analysis Work at IIT Kanpur

Kumar

Gupta

Gaurav

et al. 2020

Cyber Security in India

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We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher dimensional topological features such as connected components and holes (cycles or loops) in the data. In other words, persistent homology is a multiscale version of homology that characterizes sets based on the connected components and holes. We use super-level sets of functions to extract geometric features via persistent homology. In particular, we explore structures in regression curves via the persistent homology of super-level sets of a function, where the function of interest is -the first derivative of the regression function.In the course of this study, we extend an existing procedure of estimating the persistent homology for the first derivative of a regression function and establish its consistency. Moreover, as an application of the proposed methodology, we demonstrate that the persistent homology 1

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Nonparametric Comparison of Multiple Regression Curves in Scale-Space

Cited by 18 publications

References 41 publications

Model Testing Based on Regression Spline

Model Testing Based on Regression Spline

Statistical Scale Space Methods

A Review: Malware Analysis Work at IIT Kanpur

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