Indirect Cross-Validation for Density Estimation

Savchuk, Olga Y.; Hart, Jeffrey D.; Sheather, Simon J.

doi:10.1198/jasa.2010.tm08532

Cited by 42 publications

(54 citation statements)

References 30 publications

(38 reference statements)

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“…In this section we consider indirect cross-validation in its simplest possible version taken from Savchuk et al (2008Savchuk et al ( , 2010. These papers considered a number of variations of indirect cross-validation.…”

Section: Indirect Cross-validated Bandwidth Selection In Kernel Densimentioning

confidence: 99%

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Further theoretical and practical insight to the do-validated bandwidth selector

Mammen

Miranda

Nielsen

et al. 2014

Journal of the Korean Statistical Society

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This is the accepted version of the paper.This version of the publication may differ from the final published version. and that the recent do-validated method seems to provide the most practical alternative among these methods. In this paper we show step by step how classical cross-validation improves in theory, as well as in practice, from indirectness and that do-validated estimators improve in theory, but not in practice, from further indirectness. This paper therefore provides a strong support for the practical and theoretical properties of do-validated bandwidth selection. Do-validation is currently being introduced to survival analysis in a number of contexts and this paper provides evidence that this might be the immediate step forward. Permanent repository link

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Section: Indirect Cross-validated Bandwidth Selection In Kernel Densimentioning

confidence: 99%

“…Indirect cross-validated bandwidth selection has a number of theoretical and practical advantages, see among others Hart and Yi (1998), Hart and Lee (2005), Savchuk et al (2008Savchuk et al ( , 2010. In this paper classical cross-validation is improved through indirectness considering a series of polynomial kernels as indirect kernels.…”

Section: Introductionmentioning

confidence: 99%

Further theoretical and practical insight to the do-validated bandwidth selector

Mammen

Miranda

Nielsen

et al. 2014

Journal of the Korean Statistical Society

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“…Thus, the general indirect cross-validation method starts by formulating a more complex estimation problem to estimate the bandwidth. Then, the resulting bandwidth is rescaled to the original estimation problem (see Martínez-Miranda et al (2009) and Savchuk et al (2010) for more details).…”

Section: Indirect Cross-validationmentioning

confidence: 99%

“…However, cross-validation breaks down in our application based on aggregated data. Indirect cross-validation is known to have a better theoretical and practical performance than cross-validation, and it is known to be more robust when applied to discrete data (see Martínez-Miranda et al (2009), Savchuk et al (2010), Mammen et al (2011) and Gámiz et al (2013) for the related density case. Consequently, in this paper we develop indirect cross-validation for the local linear estimator, which works well when applied to our aggregated data.…”

Section: Introductionmentioning

confidence: 99%

Bandwidth selection in marker dependent kernel hazard estimation

Pérez

Janys

Miranda

et al. 2013

Computational Statistics & Data Analysis

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractPractical estimation procedures for local linear estimation of an unrestricted failure rate when more information is available than just time are developed. This extra information could be a covariate and this covariate could be a time series. Time dependent covariates are sometimes called markers, and failure rates are sometimes called hazards, intensities or mortalities. It is shown through simulations and a practical example that the fully local linear estimation procedure exhibits an excellent practical performance. Two different bandwidth selection procedures are developed. One is an adaptation of classical cross-validation, and the other one is indirect cross-validation. The simulation study concludes that classical cross-validation works well on continuous data while indirect cross-validation performs only marginally better. However, cross-validation breaks down in the practical data application to old-age mortality. Indirect cross-validation is thus shown to be superior when selecting a fully feasible estimation method for marker dependent hazard estimation.

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“…255 Savchuk et al (2010) propose an indirect cross-validation procedure where one chooses a linear combination of two Gaussian kernels as kernel, L. Mammen et al (2011) introduce the do-validation method, which performs indirect cross-validation twice by using two one-sided kernels, L 1 = K L = 2K(·)I(· ≤ 0) and L 2 = K R , as indirect kernels in (3). The do-validation bandwidth is the average of the two resulting bandwidths,…”

mentioning

confidence: 99%

In-sample forecasting with local linear survival densities

et al. 2016

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This is the accepted version of the paper.This version of the publication may differ from the final published version. In this paper, in-sample forecasting is defined as forecasting a structured density to sets where it is unobserved. The structured density consists of one-dimensional in-sample components that identify the density on such sets. We focus on the multiplicative density structure, which has recently been seen as the underlying structure of non-life insurance forecasts. In non-life insurance the in-sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square. Recent approaches estimate two one-dimensional components by projecting an unstructured two-dimensional density estimator onto the space of multiplicatively separable functions. We show that time-reversal reduces the problem to two onedimensional problems, where the one-dimensional data are left-truncated and a one-dimensional survival density estimator is needed. This paper then uses the local linear density smoother with 25 weighted cross-validated and do-validated bandwidth selectors. Full asymptotic theory is provided, with and without time reversal. Finite sample studies and an application to non-life insurance are included. Permanent repository link

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Indirect Cross-Validation for Density Estimation

Cited by 42 publications

References 30 publications

Further theoretical and practical insight to the do-validated bandwidth selector

Further theoretical and practical insight to the do-validated bandwidth selector

Bandwidth selection in marker dependent kernel hazard estimation

In-sample forecasting with local linear survival densities

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