Statistical inference and visualization in scale-space for spatially dependent images

Vaughan, A.; Jun, Mikyoung; Park, Cheolwoo

doi:10.1016/j.jkss.2011.07.006

Cited by 9 publications

(5 citation statements)

References 25 publications

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“…The S 3 method was extended to images with spatially correlated noise in Vaughan et al. ). The covariance of the ϵ i , j 's in ( was assumed isotropic and S 3 was applied to analyze numerical climate model outputs.…”

Section: Higher Dimensional Settings and Data On Manifoldsmentioning

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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Section: Higher Dimensional Settings and Data On Manifoldsmentioning

confidence: 99%

Statistical Scale Space Methods

Holmström

Pasanen

2016

Int Statistical Rev

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“…() examined generalized additive models, and Holmstrom and Pasanen () and Vaughan et al . () applied the SiZer idea to images.…”

Section: Introductionmentioning

confidence: 99%

Metrics for SiZer map comparison

Hannig

Lee

Park

2013

Stat

Self Cite

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SiZer is a powerful visualization tool for uncovering real structures masked in noisy data. It produces a two‐dimensional plot, the so‐called SiZer map, to help the data analyst to carry out this task. Since its first proposal, many different extensions and improvements have been developed, including robust SiZer, quantile SiZer, and various SiZers for time series data, just to name a few. Given these many SiZer variants, one important question is, how can one evaluate the quality of a SiZer map produced by any one of these variants? The primary goal of this article aims to answer this question by proposing two metrics for quantifying the discrepancy between any two SiZer maps. With such metrics, one can systematically calculate the distance between a “true” SiZer map and a SiZer map produced by any one of the SiZer variants. Consequently, one can select a “best” SiZer variant for the problem at hand by selecting the variant that produces SiZer maps that are, on average, closest to the “true” SiZer map. Copyright © 2013 John Wiley & Sons Ltd

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“…SiZer for smoothing splines method has been investigated by Marron and Zhang [29]. The other specific SiZer tools include SiZer for additive model [19], comparison of curves [30], time series analysis [31], SiZer for regression quantiles [32], analysis of random signals [33], and spatially dependent images [34], among others. Recently, Zhang and Mei [35] developed a SiZer approach for the varying coefficient models to explore the statistically significant features of the coefficient functions under different bandwidths.…”

Section: Introductionmentioning

confidence: 99%

Robust SiZer Approach for Varying Coefficient Models

Zhang

Mei

Wang

2013

Mathematical Problems in Engineering

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Varying coefficient models have widely been applied to many practical fields for exploring dynamic patterns of the regression relationships. In this study, we propose a robust scenario of SiZer (significant zero crossing of derivatives) inference approach based on the local least absolute deviation fitting procedure and the bootstrap confidence interval to uncover the statistically significant features of the coefficient functions in a varying coefficient model under different smoothing scales. The simulation study shows that the proposed SiZer approach is quite robust to outliers and performs well in finding the significant features of the coefficient functions. Furthermore, a real environmental data set is analyzed to demonstrate the application of the proposed approach.

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Statistical inference and visualization in scale-space for spatially dependent images

Cited by 9 publications

References 25 publications

Statistical Scale Space Methods

Statistical Scale Space Methods

Metrics for SiZer map comparison

Robust SiZer Approach for Varying Coefficient Models

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