Influence diagnostics in the varying coefficient model with longitudinal data

Bae, Whasoo; Hwang, Soonyoung; Kim, Choongrak

doi:10.1007/s00180-007-0025-4

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…Kim, Lee, and Park (2001) defined Cook's distance in the local polynomial regression, and Fung, Zhu, Wei, and He (2002) and Kim, Park, and Kim (2002) studied influence diagnostics in the semiparametric model. Recently, Bae, Hwang, and Kim (2008) developed diagnostic issues in the varying coefficient model.…”

Section: Introductionmentioning

confidence: 99%

Case influence diagnostics in the lasso regression

Kim

Lee

Yang

et al. 2015

Journal of the Korean Statistical Society

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a b s t r a c tUsing the diagnostic results in the ridge regression model, we propose an approximate version of Cook's distance in the lasso regression model since the analytic expression of the lasso estimator is not available. Also, we express the proposed Cook's distance in terms of basic building blocks such as residuals and leverages. We verify that the proposed statistic successfully detects potentially influential observations on estimators of regression coefficients and on the model selection in the lasso regression model. An illustrative example based on a real dataset is given.

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Section: Introductionmentioning

confidence: 99%

Case influence diagnostics in the lasso regression

Kim

Lee

Yang

et al. 2015

Journal of the Korean Statistical Society

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“…Among other measures, we preferred Cook's distance since it allows robust fitting despite data are being contaminated by outliers (or anomalies). Many diagnostic measures have been introduced other than the seminal work of Cook such as linear regression [33], [34], penalized (ridge) regression [35], sparse regression models like LASSO [36] as parametric models, spline smoothing [37]- [39] and polynomial regression [40] as nonparametric models, and longitudinal regression [41], generalized linear, and Cox proportional hazard models [42]- [44] as semiparametric models.…”

Section: Introductionmentioning

confidence: 99%

Efficient Kernel Cook's Distance for Remote Sensing Anomalous Change Detection

Padrón-Hidalgo¹,

Pérez-Suay²,

Nar³

et al. 2020

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Detecting anomalous changes in remote sensing images is a challenging problem, where many approaches and techniques have been presented so far. We rely on the standard field of multivariate statistics of diagnostic measures, which are concerned about the characterization of distributions, detection of anomalies, extreme events, and changes. One useful tool to detect multivariate anomalies is the celebrated Cook's distance. Instead of assuming a linear relationship, we present a novel kernelized version of the Cook's distance to address anomalous change detection in remote sensing images. Due to the large computational burden involved in the direct kernelization, and the lack of out-of-sample formulas, we introduce and compare both random Fourier features and Nyström implementations to approximate the solution. We study the kernel Cook's distance for anomalous change detection in a chronochrome scheme, where the anomalousness indicator comes from evaluating the statistical leverage of the residuals of regressors between time acquisitions. We illustrate the performance of all algorithms in a representative number of multispectral and very high resolution satellite images involving changes due to droughts, urbanization, wildfires, and floods. Very good results and computational efficiency confirm the validity of the approach.

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“…In the spline smoothing model, Eubank (1985), Kim (1996), and Silverman (1985) suggested versions of Cook's distance, and Kim et al (2001) suggested Cook's distance in the local polynomial regression, and Fung et al (2002) and Kim et al (2002) studied detection of influential observations in the semiparametric model. Bae et al (2008) also studied diagnostic issues in the varying coefficient model.…”

Section: Introductionmentioning

confidence: 99%

Case influence diagnostics for the significance of the linear regression model

Bae

Noh

Kim

2017

CSAM

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In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination R 2 and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in R 2 and F-statistic.

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Influence diagnostics in the varying coefficient model with longitudinal data

Abstract: Deletion diagnostics, Influential observations, Local polynomial estimation, Reference values,

Cited by 5 publications

References 27 publications

Case influence diagnostics in the lasso regression

Case influence diagnostics in the lasso regression

Efficient Kernel Cook's Distance for Remote Sensing Anomalous Change Detection

Case influence diagnostics for the significance of the linear regression model

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