On Maximum Depth and Related Classifiers

Ghosh, Anil K.; Chaudhuri, Probal

doi:10.1111/j.1467-9469.2005.00423.x

Cited by 98 publications

(83 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They were also applied in industrial quality control by Liu and Singh [1993] and Liu [1995]. Ghosh and Chaudhuri [2005] investigated the use of depth functions in nonparametric discrimination analysis. Mizera and Müller [2004] defined and studied the location-scale depth and gave some statistical applications.…”

Section: Depth Functionmentioning

confidence: 99%

Depth and homogeneity in regional flood frequency analysis

Chebana

Ouarda

2008

Water Resources Research

View full text Add to dashboard Cite

[1] Regional frequency analysis (RFA) consists generally of two steps: (1) delineation of hydrological homogeneous regions and (2) regional estimation. Existing regionalization methods which adopt this two-step approach suffer from two principal drawbacks. First, the restriction of the regional estimation to a particular region by excluding some sites can correspond to a loss of some information. Second, the definition of a region generates a border effect problem. To overcome these problems, a new method is proposed in the present paper. The proposed method is based on three elements: (1) a weight function to treat the border effect problem, (b) a function to evaluate how ''similar'' each site is to the target one, and (c) an iterative procedure to improve estimation results. Element (b) is treated using the statistical notion of depth functions which is introduced to provide a ranking of stations in a multivariate context. Furthermore, the properties of depth functions meet the characteristics sought in RFA. It is shown that the proposed method is flexible and general and that traditional RFA methods represent special cases of the depth-based approach corresponding to particular weight functions. A comparison is carried out with the canonical correlation analysis (CCA) approach. Results indicate that the depth-based approach performs better than does CCA both in terms of relative bias and relative root mean squares error.

show abstract

Section: Depth Functionmentioning

confidence: 99%

Depth and homogeneity in regional flood frequency analysis

Chebana

Ouarda

2008

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…Recently, new notions of depth for finite dimensional data have been proposed and all of them extensively studied (see, for example, [13], [15], [16], [18], [21], [23], [24] and [25]). Depth-based classification has been already analyzed in the literature for multivariate observations in, e.g., [5], [6], [11], [12] and [20]. Recently, the notion of depth has been extended to functional data.…”

Section: Introductionmentioning

confidence: 99%

Depth-based classification for functional data

López‐Pintado¹,

Romo²

2006

DIMACS Series in Discrete Mathematics And Theoretical Computer Science

View full text Add to dashboard Cite

Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods. Madrid, e-mail: juan.romo@uc3m.es. DIMACS Series in Discrete Mathematics and Theoretical Computer ScienceDepth-based classification for functional data Sara López-Pintado and Juan RomoAbstract. Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods.

show abstract

“…Recently, the depth-based approach proposed by Chebana and Ouarda [2008] improved the performance of Canonical Correlation Analysis in the context of regional flood frequency analysis. Depth functions were also investigated in nonparametric discriminant analysis by Ghosh and Chaudhuri [2005]. Mizera and Müller [2004] defined and studied the location-scale depth and gave some statistical applications.…”

Section: Discussionmentioning

confidence: 99%

Depth-based multivariate descriptive statistics with hydrological applications

Chebana

Ouarda

2011

J. Geophys. Res.

View full text Add to dashboard Cite

Hydrological events are often described through various characteristics which are generally correlated. To be realistic, these characteristics are required to be considered jointly. In multivariate hydrological frequency analysis, the focus has been made on modeling multivariate samples using copulas. However, prior to this step, data should be visualized and analyzed in a descriptive manner. This preliminary step is essential for all of the remaining analysis. It allows us to obtain information concerning the location, scale, skewness, and kurtosis of the sample as well as outlier detection. These features are useful to exclude some unusual data, to make different comparisons, and to guide the selection of the appropriate model. In the present paper we introduce methods measuring these features, which are mainly based on the notion of depth function. The application of these techniques is illustrated on two real‐world streamflow data sets from Canada. In the Ashuapmushuan case study, there are no outliers and the bivariate data are likely to be elliptically symmetric and heavy‐tailed. The Magpie case study contains a number of outliers, which are identified to be real observed data. These observations cannot be removed and should be accommodated by considering robust methods for further analysis. The presented depth‐based techniques can be adapted to a variety of hydrological variables.

show abstract

On Maximum Depth and Related Classifiers

Cited by 98 publications

References 45 publications

Depth and homogeneity in regional flood frequency analysis

Depth and homogeneity in regional flood frequency analysis

Depth-based classification for functional data

Depth-based multivariate descriptive statistics with hydrological applications

Contact Info

Product

Resources

About