Functional outlier detection by a local depth with application to NO x levels

Sguera, Carlo; Galeano, Pedro; Lillo, Rosa E.

doi:10.1007/s00477-015-1096-3

Cited by 30 publications

(28 citation statements)

References 21 publications

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“…Hence, the bootstrap procedure can be called conservative. This finding is also supported by Sguera et al 19 Still, a few exceptions can be found for the h-modal depth; see (d). (c) When assuming Gaussian error and inverse or logistic link, regardless of the true error distribution, it turns out that MBD outperforms the other depths.…”

Section: Main Findingssupporting

confidence: 85%

“…Thereby, we gain

{\hat{μ}}_{i} (t) = h [{\hat{β}}_{0} (t) + \sum_{j = 1}^{k} x_{i, j} {\hat{β}}_{j} (t)] = h [{\hat{η}}_{i} (t)], i = 1, \dots, n,

as fitted observations and estimated deviance residuals

{\overset{ϵ}{true}}_{i} (t) = sign (y_{i} (t) - {\overset{μ}{true}}_{i} (t)) \sqrt{d_{i} (t)},

where d i ( t ) denotes the contribution of the i th component to the deviance. Other residual types like Pearson or working residuals have certain drawbacks, see Wood, Chap. 2].…”

Section: Methodsmentioning

confidence: 99%

“…where d i .t/ denotes the contribution of the ith component to the deviance. Other residual types like Pearson or working residuals have certain drawbacks, see Wood 19, Chap. 2 .…”

Section: Methodsmentioning

confidence: 99%

“…This finding is also supported by Sguera et al . Still, a few exceptions can be found for the h ‐modal depth; see (d). When assuming Gaussian error and inverse or logistic link, regardless of the true error distribution, it turns out that MBD outperforms the other depths. In any other case, h ‐modal depth outperforms the remaining depths. h ‐modal depth tends to identify too many false positives (incorrectly classified non‐outliers).…”

Section: Simulation Studymentioning

confidence: 99%

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Residual Analysis in Generalized Function‐on‐Scalar Regression for an HVOF Spraying Process

Kuhnt

Rehage

Becker-Emden

et al. 2016

Quality & Reliability Eng

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The coating of materials plays an important role in various fields of engineering. Essential properties such as wear protection can be improved by a suitable coating technique. One of these techniques is high‐velocity oxygen‐fuel spraying. A drawback of high‐velocity oxygen‐fuel spraying is that it lacks reproducibility due to effects which are hard to measure directly. However, coating powder particles are observable over time during their flight towards the material and contain valuable information about the state of the process. Because of their smooth nature, measures of temperature and velocity can be assumed as target variables in generalized function‐on‐scalar regression. We propose methods to perform residual analysis in this framework aiming at the detection of individual residual functions which deviate from the majority of residuals. These methods help to detect anomalies in the process and hence improve the estimators. Functional target variables result in functional residuals whose analysis is barely explored. One reason might be that ordinary residual plots should be inspected at each observed point in time. We circumvent this infeasible procedure by the use of functional depths that help to identify unusual residuals and thereby gain deeper insight of the data‐generating process. In a simulation study, we find that a good depth for detecting trend outliers is the h‐modal depth as long as the link function is chosen correctly. In case of shape outliers rFUNTA pseudo‐depth performs well. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Main Findingssupporting

confidence: 85%

“…Thereby, we gain

{\hat{μ}}_{i} (t) = h [{\hat{β}}_{0} (t) + \sum_{j = 1}^{k} x_{i, j} {\hat{β}}_{j} (t)] = h [{\hat{η}}_{i} (t)], i = 1, \dots, n,

as fitted observations and estimated deviance residuals

{\overset{ϵ}{true}}_{i} (t) = sign (y_{i} (t) - {\overset{μ}{true}}_{i} (t)) \sqrt{d_{i} (t)},

where d i ( t ) denotes the contribution of the i th component to the deviance. Other residual types like Pearson or working residuals have certain drawbacks, see Wood, Chap. 2].…”

Section: Methodsmentioning

confidence: 99%

“…where d i .t/ denotes the contribution of the ith component to the deviance. Other residual types like Pearson or working residuals have certain drawbacks, see Wood 19, Chap. 2 .…”

Section: Methodsmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

See 2 more Smart Citations

Residual Analysis in Generalized Function‐on‐Scalar Regression for an HVOF Spraying Process

Kuhnt

Rehage

Becker-Emden

et al. 2016

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…According to Febrero, Galeano, and Gonzalez-Manteiga (2007) and Shang (2015), a functional outlier is a curve generated by a stochastic process that has a different distribution from that of normal curves. This general definition covers many types of outliers: for example, magnitude, shape, and partial outliers (see Sguera, Galeano, & Lillo, (2016), for more details).…”

Section: Intraday Sandp 500 Indexmentioning

confidence: 99%

Forecasting intraday S&P 500 index returns: A functional time series approach

Shang

2017

Journal of Forecasting

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Financial data often take the form of a collection of curves that can be observed sequentially over time; for example, intraday stock price curves and intraday volatility curves. These curves can be viewed as a time series of functions that can be observed on equally spaced and dense grids. Owing to the so‐called curse of dimensionality, the nature of high‐dimensional data poses challenges from a statistical perspective; however, it also provides opportunities to analyze a rich source of information, so that the dynamic changes of short time intervals can be better understood. In this paper, we consider forecasting a time series of functions and propose a number of statistical methods that can be used to forecast 1‐day‐ahead intraday stock returns. As we sequentially observe new data, we also consider the use of dynamic updating in updating point and interval forecasts for achieving improved accuracy. The forecasting methods were validated through an empirical study of 5‐minute intraday S&P 500 index returns.

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Multivariate functional outlier detection using the fast massive unsupervised outlier detection indices

Ojo

Anta

Genton

et al. 2023

Stat

Self Cite

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We present definitions and properties of the fast massive unsupervised outlier detection (FastMUOD) indices, used for outlier detection (OD) in functional data. FastMUOD detects outliers by computing, for each curve, an amplitude, magnitude, and shape index meant to target the corresponding types of outliers. Some methods adapting FastMUOD to outlier detection in multivariate functional data are then proposed. These include applying FastMUOD on the components of the multivariate data and using random projections. Moreover, these techniques are tested on various simulated and real multivariate functional datasets. Compared with the state of the art in multivariate functional OD, the use of random projections showed the most effective results with similar, and in some cases improved, OD performance. Based on the proportion of random projections that flag each multivariate function as an outlier, we propose a new graphical tool, the magnitude‐shape‐amplitude (MSA) plot, useful for visualizing the magnitude, shape and amplitude outlyingness of multivariate functional data.

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Functional outlier detection by a local depth with application to NO x levels

Cited by 30 publications

References 21 publications

Residual Analysis in Generalized Function‐on‐Scalar Regression for an HVOF Spraying Process

Residual Analysis in Generalized Function‐on‐Scalar Regression for an HVOF Spraying Process

Forecasting intraday S&P 500 index returns: A functional time series approach

Multivariate functional outlier detection using the fast massive unsupervised outlier detection indices

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