Estimating conditional hazard functions and densities with the highly-adaptive lasso Article Swipe

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Anders Munch , Thomas Alexander Gerds , Mark J. van der Laan , Helene C. W. Rytgaard ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2404.11083

We consider estimation of conditional hazard functions and densities over the class of multivariate càdlàg functions with uniformly bounded sectional variation norm when data are either fully observed or subject to right-censoring. We demonstrate that the empirical risk minimizer is either not well-defined or not consistent for estimation of conditional hazard functions and densities. Under a smoothness assumption about the data-generating distribution, a highly-adaptive lasso estimator based on a particular data-adaptive sieve achieves the same convergence rate as has been shown to hold for the empirical risk minimizer in settings where the latter is well-defined. We use this result to study a highly-adaptive lasso estimator of a conditional hazard function based on right-censored data. We also propose a new conditional density estimator and derive its convergence rate. Finally, we show that the result is of interest also for settings where the empirical risk minimizer is well-defined, because the highly-adaptive lasso depends on a much smaller number of basis function than the empirical risk minimizer.

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Lasso (programming language) Hazard Econometrics Statistics Conditional probability distribution Mathematics Computer science Biology Ecology World Wide Web

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2404.11083
PDF: https://arxiv.org/pdf/2404.11083
OA Status: green
Cited By: 1
Related Works: 10
OpenAlex ID: https://openalex.org/W4394946668

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DOI: https://doi.org/10.48550/arxiv.2404.11083

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Title: Estimating conditional hazard functions and densities with the highly-adaptive lasso

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-04-17

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Authors: Anders Munch, Thomas Alexander Gerds, Mark J. van der Laan, Helene C. W. Rytgaard

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Landing page: https://arxiv.org/abs/2404.11083

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PDF URL: https://arxiv.org/pdf/2404.11083

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Concepts: Lasso (programming language), Hazard, Econometrics, Statistics, Conditional probability distribution, Mathematics, Computer science, Biology, Ecology, World Wide Web

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Cited by: 1

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