arXiv subjects

Jens Perch Nielsen

Publications and source records attributed to Jens Perch Nielsen.

7 recordsLinked to original sources

arXiv2025

Low quality exposure and point processes with a view to the first phase of a pandemic

In the early days of a pandemic there is no time for complicated data collection. One needs a simple cross-country benchmark approach based on robust data that is easy to understand and easy to collect. The recent pandemic has shown us what early available pandemic data might look like, because statistical data was published every day in standard news outlets in many countries. This paper provides new methodology for the analysis of data where exposure is only vaguely understood and where the very definition of exposure might change over time. The exposure of poor quality is used to analyse and forecast events. Our example of such exposure is daily infections during a pandemic and the events are number of new infected patients in hospitals every day. Examples are given with French Covid-19 data on hospitalized patients and numbers of infected.

stat.ME↗

arXiv2025

Monitoring a developing pandemic with available data

This paper addresses statistical modelling and forecasting of key indicators describing the severity of a developing pandemic, using routinely reported daily counts of infections, hospitalizations, deaths (both in and out of hospital), and recoveries. These observed counts constitute what we term ``available data''. Because such data are typically incomplete or inconsistently reported, we address several novel missing data challenges arising in this context and propose statistically rigorous solutions that enable inference based solely on the available information. The model is formulated dynamically, explicitly incorporating calendar effects to capture systematic temporal variations in the progression of the pandemic. The proposed framework is illustrated using data from France collected during the COVID-19 pandemic. Our approach also establishes a new benchmark for integrating prior information from domain experts directly into the modelling process, thereby enabling a potential new division of labour between statistical estimation and epidemiological knowledge from external experts.

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arXiv2025

Smooth Backfitting for Additive Hazard Rates

Smooth backfitting was first introduced in an additive regression setting via a direct projection alternative to the classic backfitting method by Buja, Hastie and Tibshirani. This paper translates the original smooth backfitting concept to a survival model considering an additively structured hazard. The model allows for censoring and truncation patterns occurring in many applications such as medical studies or actuarial reserving. Our estimators are shown to be a projection of the data into the space of multivariate hazard functions with smooth additive components. Hence, our hazard estimator is the closest nonparametric additive fit even if the actual hazard rate is not additive. This is different to other additive structure estimators where it is not clear what is being estimated if the model is not true. We provide full asymptotic theory for our estimators. We propose an implementation of estimators that show good performance in practice.

math.ST↗

arXiv2020

Smooth backfitting of proportional hazards with multiplicative components

Smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression. Smooth backfitting projects the data down onto the structured space of interest providing a direct link between data and estimator. This paper introduces the ideas of smooth backfitting to survival analysis in a proportional hazard model, where we assume an underlying conditional hazard with multiplicative components. We develop asymptotic theory for the estimator and we use the smooth backfitter in a practical application, where we extend recent advances of in-sample forecasting methodology by allowing more information to be incorporated, while still obeying the structured requirements of in-sample forecasting.

math.ST↗

arXiv2017

Multiplicative local linear hazard estimation and best one-sided cross-validation

This paper develops detailed mathematical statistical theory of a new class of cross-validation techniques of local linear kernel hazards and their multiplicative bias corrections. The new class of cross-validation combines principles of local information and recent advances in indirect cross-validation. A few applications of cross-validating multiplicative kernel hazard estimation do exist in the literature. However, detailed mathematical statistical theory and small sample performance are introduced via this paper and further upgraded to our new class of best one-sided cross-validation. Best one-sided cross-validation turns out to have excellent performance in its practical illustrations, in its small sample performance and in its mathematical statistical theoretical performance.

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arXiv2012

A comparative study of new cross-validated bandwidth selectors for kernel density estimation

Recent contributions to kernel smoothing show that the performance of cross-validated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classical cross-validated bandwidth from a more rough and difficult smoothing problem than the original one and then rescales this indirect bandwidth to become a bandwidth of the original problem. The motivation for this approach comes from the observation that classical crossvalidation tends to work better when the smoothing problem is difficult. In this paper we find that the performance of indirect crossvalidation improves theoretically and practically when the polynomial order of the indirect kernel increases, with the Gaussian kernel as limiting kernel when the polynomial order goes to infinity. These theoretical and practical results support the often proposed choice of the Gaussian kernel as indirect kernel. However, for do-validation our study shows a discrepancy between asymptotic theory and practical performance. As for indirect crossvalidation, in asymptotic theory the performance of indirect do-validation improves with increasing polynomial order of the used indirect kernel. But this theoretical improvements do not carry over to practice and the original do-validation still seems to be our preferred bandwidth selector. We also consider plug-in estimation and combinations of plug-in bandwidths and crossvalidated bandwidths. These latter bandwidths do not outperform the original do-validation estimator either.

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arXiv2011

Nonparametric regression with filtered data

We present a general principle for estimating a regression function nonparametrically, allowing for a wide variety of data filtering, for example, repeated left truncation and right censoring. Both the mean and the median regression cases are considered. The method works by first estimating the conditional hazard function or conditional survivor function and then integrating. We also investigate improved methods that take account of model structure such as independent errors and show that such methods can improve performance when the model structure is true. We establish the pointwise asymptotic normality of our estimators.

math.ST↗