Exploring copulas for the imputation of complex dependent data

Lascio, F. Marta L. Di; Giannerini, Simone; Reale, Alessandra

doi:10.1007/s10260-014-0287-2

Cited by 15 publications

(18 citation statements)

References 12 publications

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“…When examined data are correlated through time (i.e., structured times series), missing records can be restored by combining the distribution restoration method with the copulabased imputation method, but this involves the use of a correlated time series measured by another sensor (inter-sensor correlation) with complete records to serve as a collaborative time series. An means of restoring missing time series of strain monitoring data by combining distribution restoration and the copula-based imputation method [28]. The distribution restoration method is mainly applied to monitoring data that can be described by random variables.…”

Section: Description Of Problem and Basic Assumptionsmentioning

confidence: 99%

LQD-RKHS-based distribution-to-distribution regression methodology for restoring the probability distributions of missing SHM data

Chen

Bao

et al. 2019

Mechanical Systems and Signal Processing

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Data loss is a critical problem in structural health monitoring (SHM). Probability distributions play a highly important role in many applications. Improving the quality of distribution estimations made using incomplete samples is highly important. Missing samples can be compensated for by applying conventional missing data restoration methods; however, ensuring that restored samples roughly follow underlying distributions of true missing data remains a challenge. Another strategy involves directly restoring the probability density function (PDF) for a sensor when samples are missing by leveraging distribution information from another sensor with complete data using distribution regression techniques; existing methods include the conventional distribution-to-distribution regression (DDR) and distribution-to-warping function regression (DWR) methods. Due to constraints on PDFs and warping functions, the regression functions of both methods are estimated from the Nadaraya-Watson kernel estimator with relatively low degrees of precision. This article proposes a new indirect distribution-to-distribution regression method in the context of functional data analysis for restoring distributions of missing SHM data. PDFs are transformed to ordinary functions residing in a Hilbert space via the newly proposed log-quantile-density (LQD) transformation; the regression for distributions is realized in the transformed space via a functional regression model constructed based on the theory of Reproducing Kernel Hilbert Space (RKHS),corresponding result is subsequently mapped back to the density space through the inverse LQD transformation. Test results using field monitoring data indicate that the new method significantly outperforms conventional methods in general cases; however, in extrapolation cases, the new method is inferior to the distribution-to-warping function regression method.

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Section: Description Of Problem and Basic Assumptionsmentioning

confidence: 99%

LQD-RKHS-based distribution-to-distribution regression methodology for restoring the probability distributions of missing SHM data

Chen

Bao

et al. 2019

Mechanical Systems and Signal Processing

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“…With continuous variables, MICE assumes normality of the variables. We use here the original untransformed data (same reason as for AME). Copula IMPutation (COIMP) (Di Lascio and Giannerini, ; Di Lascio et al , ) COIMP is a copula‐based method to impute multivariate missing data. Four steps of the method are as follows: (i) non‐parametric estimation of the margins through local polynomial likelihood and parametric estimation of the copula model through maximum likelihood on the available data; (ii) derivation of the joint distribution; (iii) derivation of the conditional distribution of the missing values, conditioned on the observed values; and (iv) imputation by generating from the conditional distribution of the previous step with the Hit or Miss Monte Carlo method.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…The paper enlarges the copula families considered by Käärik & Käärik () and Di Lascio et al () by using vine copulas. The proposed JM strategy is inspired by the work of Aas et al () and can be applied to impute continuous multivariate data that are missing completely at random (MCAR).…”

Section: Introductionmentioning

confidence: 96%

“…The well‐known families of joint distributions usually require that the marginal distributions belong to the same family. To overcome this lack of flexibility, Käärik & Käärik () and Di Lascio et al () use multivariate copulas selected among a limited set of parametric families to model the joint distribution. They draw imputed values from the conditional distribution of the missing values, conditioned by the observed values.…”

Section: Introductionmentioning

confidence: 99%

“…They draw imputed values from the conditional distribution of the missing values, conditioned by the observed values. R package CoImp (Di Lascio & Giannerini, ) implements the copula‐based imputation of Di Lascio et al (). Other authors (Ding & Song, ) propose an EM algorithm in Gaussian copula with missing data.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vine Copulas for Imputation of Monotone Non‐response

Hasler

Craiu

Rivest

2018

Int Statistical Rev

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Monotone patterns of non-response may occur in longitudinal studies. When the measured variables are dependent, it is beneficial to use their joint statistical model to impute the missing values. We propose to use vine copulas to factorise the density of the observed variables into a cascade of bivariate copulas that yield a flexible model of their joint distribution. The structure of the vine depends on the non-response pattern. We propose a method to select the model, to estimate the parameters of the bivariate copulas of the selected model and to impute using the constructed model. The imputed values are drawn from the conditional distribution of the missing values, given the observed data. We discuss the generalisation of our results to more global non-response patterns.

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General Considerations on Univariate Methods: Single and Multiple Imputation

Templ

2023

Statistics and Computing

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Exploring copulas for the imputation of complex dependent data

Cited by 15 publications

References 12 publications

LQD-RKHS-based distribution-to-distribution regression methodology for restoring the probability distributions of missing SHM data

LQD-RKHS-based distribution-to-distribution regression methodology for restoring the probability distributions of missing SHM data

Vine Copulas for Imputation of Monotone Non‐response

General Considerations on Univariate Methods: Single and Multiple Imputation

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