Fast and compact smoothing on large multidimensional grids

Eilers, Paul H.C.; Currie, Iain D.; Durbán, Maŕıa

doi:10.1016/j.csda.2004.07.008

Cited by 174 publications

(159 citation statements)

References 4 publications

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“…The procedure consists of several different steps: first, the major principal components in the zero- Recently, with the increasing of the use of second-order data, several algorithms have been proposed. One of them is the methodology presented by Eilers, i.e., the asymmetric least-squares method [31], which was recently adapted to multidimensional data [32]. This method consists in the On the other hand, on-line coupling between LC and FT-IR becomes a difficult task: as the mobile phases employed in LC absorb strongly in the mid infrared, their accurate compensation is crucial to obtain characteristic analyte spectra.…”

Section: Background Correctionmentioning

confidence: 99%

Chemometric strategies for enhancing the chromatographic methodologies with second-order data analysis of compounds when peaks are overlapped

Goicoechea

Culzoni

García

et al. 2011

Talanta

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This overview covers the different chemometric strategies linked to chromatographic methodologies that have been used and presented in the recent literature to cope with problems related to incomplete separation, the presence of unexpected components in the sample, matrix effect and changes in the analytical signal due to pre-treatment of sample.Among the different chemometric strategies it focuses on pre-treatment of data to correct background and time shift of chromatographic peaks and the use of second-order algorithms to cope with overlapping peaks from analytes or from analytes and interferences in liquid chromatography coupled to diode array, fast-scanning fluorescence spectroscopy and mass spectrometry detectors.Finally the review presents the strategies used to deal with changes in the analytical response as result of matrix effect in liquid and gas chromatography, as well as the use of standardization strategies to correct modifications in the analytical signal as a consequence of sample pre-treatment in liquid chromatography.

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Section: Background Correctionmentioning

confidence: 99%

Chemometric strategies for enhancing the chromatographic methodologies with second-order data analysis of compounds when peaks are overlapped

Goicoechea

Culzoni

García

et al. 2011

Talanta

View full text Add to dashboard Cite

show abstract

“…We present the array algorithm in a nutshell here; for a more detailed account one should consult Currie et al (2006) or Eilers et al (2006). Assume that the T × A matrix Z = BAB is a model for the expected values of the matrix Y of the same size.…”

Section: Efficient Computation Using Array Regressionmentioning

confidence: 99%

“…The standard approach, using vectorization of the data table and Kronecker products for the tensor product basis, puts heavy demands on memory and computation time. Fortunately we can adapt the array regression algorithms Eilers et al 2006) to our case, gaining at least an order of magnitude if efficiency. Details are presented in Sect.…”

Section: Introductionmentioning

confidence: 99%

Bilinear modulation models for seasonal tables of counts

et al. 2009

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We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Twodimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases.

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“…Then, in this new context, the full regression basis B is defined as the 'row-wise' Kronecker product (denoted by , Eilers et al, 2006) of the marginal B-spline bases B 1 = B(x 1 ) and B 2 = B(x 2 ) of dimensions m × c 1 and m × c 2 , respectively:…”

Section: The Spatial Clmmmentioning

confidence: 99%

Penalized composite link models for aggregated spatial count data: A mixed model approach

et al. 2016

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Mortality data provide valuable information for the study of the spatial distribution of mortality risk, in disciplines such as spatial epidemiology and public health. However, they are frequently available in an aggregated form over irregular geographical units, hindering the visualization of the underlying mortality risk. Also, it can be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked to potential risk factors that are usually measured in a different spatial resolution. In this paper, we propose the use of the penalized composite link model and its mixed model representation. This model considers the nature of mortality rates by incorporating the population size at the finest resolution, and allows the creation of mortality maps at a finer scale, thus reducing the visual bias resulting from the spatial aggregation within original units. We also extend the model by considering individual random effects at the aggregated scale, in order to take into account the overdispersion. We illustrate our novel proposal using two datasets: female deaths by lung cancer in Indiana, USA, and male lip cancer incidence in Scotland counties. We also compare the performance of our proposal with the area-to-point Poisson kriging approach.

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Fast and compact smoothing on large multidimensional grids

Cited by 174 publications

References 4 publications

Chemometric strategies for enhancing the chromatographic methodologies with second-order data analysis of compounds when peaks are overlapped

Chemometric strategies for enhancing the chromatographic methodologies with second-order data analysis of compounds when peaks are overlapped

Bilinear modulation models for seasonal tables of counts

Penalized composite link models for aggregated spatial count data: A mixed model approach

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