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Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Palarea Albaladejo, Javier
MartÃn FernÃ¡ndez, Josep Antoni Olea, Ricardo A. 

Bootstrap resampling is an attractive, computationallyintensive approach for estimating population parameters and their associated uncertainties. Values below detection limitâ€”also referred to as nondetectsâ€”frequently arise particularly when dealing with multivariate geochemical concentrations, making the estimation of distributional parametersâ€”mean, median, percentilesâ€”a difficult challenge. The bootstrap method can be used repeatedly for analyzing resampled versions of the original data set. This way it is possible to estimate univariate distributional parameters while also capturing the additional uncertainty due to missing information. Within this approach, a method must be chosen to substitute nondetects with appropriate values given the compositional nature of the data. This idea was first introduced by Olea (2008) in the previous CoDaWorkâ€™08 meeting. Making use of the isometric logratio transformation and analyzing one variable at a time, he proposed a univariate bootstrap procedure where the distributional parameters of geochemical components were modeled from bootstrap resamples considering different criteria to impute nondetects. After conducting a sensitivity analysis on both proportion of nondetects and sample size, the study concluded that when drawing randomly a value from the extrapolated tail below the detection limit of the distribution best fitting the complete dataâ€”usually the lognormal distribution for geochemical dataâ€”the bootstrap estimates turned out to be more accurate than those obtained using simple imputation methods. Rather than analyzing each variable separately, here we make a step further to get the most of the covariance structure of the data set, extending the univariate approach for replacing nondetects to a multivariate setting. As a test bench, a number of data sets containing nondetects are artificially generated from real geochemical data and used to evaluate the performance of different replacement methods within the bootstrap process. First results show improved results when nondetects are replaced by random values drawn from a conditional truncated additive logistic model  
http://hdl.handle.net/2072/299056  
eng  
Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tots els drets reservats  
EstadÃstica matemÃ tica  Congressos
Mathematical statistics  Congresses AnÃ lisi multivariable  Congressos Multivariate analysis  Congresses EstimaciÃ³ de parÃ metres  Congressos Parameter estimation  Congresses 

Nondetect Bootstrap Method for Estimating Distributional Parameters of Compositional Samples Revisited: a Multivariate Approach  
info:eurepo/semantics/conferenceObject  
Recercat 