arXiv subjects

Michael Vogt

Publications and source records attributed to Michael Vogt.

15 recordsLinked to original sources

arXiv2026

High-Dimensional Panel Data Models with Interactive Fixed Effects: Beyond the Linear Case

Modern economic panel data sets are often high-dimensional: they contain information on a wide variety of control variables whose number may even exceed the sample size. Nevertheless, the literature on econometric methods for high-dimensional panels is quite limited. In this paper, we study high-dimensional panel models with interactive fixed effects where the regression function has an additive structure, i.e., each covariate enters the model via an unknown nonlinear component function. We develop estimation methodology and theory in this additive framework which substantially extends previous work on the high-dimensional linear case by Ruecker et al. (2025). In the theoretical part of the paper, we derive the convergence rate of our estimator for both the small-T and the large-T panel case. The theory is complemented by comprehensive Monte Carlo experiments and an empirical application.

econ.EM↗

arXiv2024

Piecewise Constant Hazard Estimation with the Fused Lasso

In applied time-to-event analysis, a flexible and useful approach is to model the hazard rate as a piecewise constant function of time. However, the change points and values of the piecewise constant hazard are usually unknown and need to be estimated. In this paper, we develop a fully data-driven procedure for piecewise constant hazard estimation. We work in a general counting process framework which nests a wide range of popular models in time-to-event analysis including Cox's proportional hazards model with potentially high-dimensional covariates, competing risks models as well as more general multi-state models. To construct our estimator, we set up a regression model for the increments of the Breslow estimator and then use fused lasso techniques to approximate the piecewise constant signal in this regression model. In the theoretical part of the paper, we derive the convergence rate of our estimator as well as some results on how well the change points of the piecewise constant hazard are approximated by our method. We complement the theory by both simulations and a real data example, illustrating that our results apply in rather general event histories such as multi-state models.

stat.ME↗

arXiv2023

FMCW Radar Height Estimation of Moving Vehicles by Analyzing Multipath Reflections

Target classification is an important task of automotive radar systems. In this work, a concept for estimating the height of vehicles to allow for a differentiation between passenger cars, trucks, and others, is presented and discussed. Fixed installed radar sensors for traffic monitoring in the 77 GHz band are used to track and analyze radar echoes from individual vehicles as they move relative to the radar. Considering multipath propagation, which includes the ground reflection, the height of individual radar targets is estimated by analyzing the periodicity of the resulting amplitude modulation (AM) of the echo signal as a function of the horizontal distance from the radar. Two approaches have been realized to integrate the concept into an automotive FMCW signal processing scheme. Measurements in a test field using a trihedral corner reflector as an idealized target in heights from 0 to 2.5 m suggest, that the concept is suitable for height estimation in an automotive context.

eess.SP↗

arXiv2022

Multiscale Comparison of Nonparametric Trend Curves

We develop new econometric methods for the comparison of nonparametric time trends. In many applications, practitioners are interested in whether the observed time series all have the same time trend. Moreover, they would often like to know which trends are different and in which time intervals they differ. We design a multiscale test to formally approach these questions. Specifically, we develop a test which allows to make rigorous confidence statements about which time trends are different and where (that is, in which time intervals) they differ. Based on our multiscale test, we further develop a clustering algorithm which allows to cluster the observed time series into groups with the same trend. We derive asymptotic theory for our test and clustering methods. The theory is complemented by a simulation study and two applications to GDP growth data and house pricing data.

econ.EM↗

arXiv2022

Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects

We develop new econometric methods for estimation and inference in high-dimensional panel data models with interactive fixed effects. Our approach can be regarded as a non-trivial extension of the very popular common correlated effects (CCE) approach. Roughly speaking, we proceed as follows: We first construct a projection device to eliminate the unobserved factors from the model by applying a dimensionality reduction transform to the matrix of cross-sectionally averaged covariates. The unknown parameters are then estimated by applying lasso techniques to the projected model. For inference purposes, we derive a desparsified version of our lasso-type estimator. While the original CCE approach is restricted to the low-dimensional case where the number of regressors is small and fixed, our methods can deal with both low- and high-dimensional situations where the number of regressors is large and may even exceed the overall sample size. We derive theory for our estimation and inference methods both in the large-T-case, where the time series length T tends to infinity, and in the small-T-case, where T is a fixed natural number. Specifically, we derive the convergence rate of our estimator and show that its desparsified version is asymptotically normal under suitable regularity conditions. The theoretical analysis of the paper is complemented by a simulation study and an empirical application to characteristic based asset pricing.

econ.EM↗

arXiv2022

Estimating the Lasso's Effective Noise

Much of the theory for the lasso in the linear model $Y = X β^* + \varepsilon$ hinges on the quantity $2 \| X^\top \varepsilon \|_{\infty} / n$, which we call the lasso's effective noise. Among other things, the effective noise plays an important role in finite-sample bounds for the lasso, the calibration of the lasso's tuning parameter, and inference on the parameter vector $β^*$. In this paper, we develop a bootstrap-based estimator of the quantiles of the effective noise. The estimator is fully data-driven, that is, does not require any additional tuning parameters. We equip our estimator with finite-sample guarantees and apply it to tuning parameter calibration for the lasso and to high-dimensional inference on the parameter vector $β^*$.

stat.ME↗

arXiv2020

Nonparametric comparison of epidemic time trends: the case of COVID-19

The COVID-19 pandemic is one of the most pressing issues at present. A question which is particularly important for governments and policy makers is the following: Does the virus spread in the same way in different countries? Or are there significant differences in the development of the epidemic? In this paper, we devise new inference methods that allow to detect differences in the development of the COVID-19 epidemic across countries in a statistically rigorous way. In our empirical study, we use the methods to compare the outbreak patterns of the epidemic in a number of European countries.

stat.ME↗

arXiv2019

Multiscale inference and long-run variance estimation in nonparametric regression with time series errors

In this paper, we develop new multiscale methods to test qualitative hypotheses about the regression function m in a nonparametric regression model with fixed design points and time series errors. In time series applications, m represents a nonparametric time trend. Practitioners are often interested in whether the trend m has certain shape properties. For example, they would like to know whether m is constant or whether it is increasing/decreasing in certain time regions. Our multiscale methods allow to test for such shape properties of the trend m. In order to perform the methods, we require an estimator of the long-run variance of the error process. We propose a new difference-based estimator of the long-run error variance for the case that the error terms form an AR(p) process. In the technical part of the paper, we derive asymptotic theory for the proposed multiscale test and the estimator of the long-run error variance. The theory is complemented by a simulation study and an empirical application to climate data.

math.ST↗

arXiv2019

Multiscale clustering of nonparametric regression curves

In a wide range of modern applications, we observe a large number of time series rather than only a single one. It is often natural to suppose that there is some group structure in the observed time series. When each time series is modelled by a nonparametric regression equation, one may in particular assume that the observed time series can be partitioned into a small number of groups whose members share the same nonparametric regression function. We develop a bandwidth-free clustering method to estimate the unknown group structure from the data. More precisely speaking, we construct multiscale estimators of the unknown groups and their unknown number which are free of classical bandwidth or smoothing parameters. In the theoretical part of the paper, we analyze the statistical properties of our estimators. Our theoretical results are derived under general conditions which allow the data to be dependent both in time series direction and across different time series. The technical analysis of the paper is complemented by a simulation study and a real-data application.

math.ST↗

arXiv2018

On the Differences between L2-Boosting and the Lasso

We prove that L2-Boosting lacks a theoretical property which is central to the behaviour of l1-penalized methods such as basis pursuit and the Lasso: Whereas l1-penalized methods are guaranteed to recover the sparse parameter vector in a high-dimensional linear model under an appropriate restricted nullspace property, L2-Boosting is not guaranteed to do so. Hence, L2-Boosting behaves quite differently from l1-penalized methods when it comes to parameter recovery/estimation in high-dimensional linear models.

stat.ML↗

arXiv2017

Clustering with Statistical Error Control

This paper presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on a tuning parameter alpha which is similar to the significance level of a statistical hypothesis test. By choosing alpha, one can control the probability of overestimating the true number of clusters, while the probability of underestimation is asymptotically negligible. In addition, the probability that the estimated clusters differ from the true ones is controlled. In the theoretical part of the paper, formal versions of these statements on statistical error control are derived in a standard model setting with convex clusters. A simulation study and two applications to temperature and gene expression microarray data complement the theoretical analysis.

math.ST↗

arXiv2015

Detecting gradual changes in locally stationary processes

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework. We set up a general procedure which allows us to deal with a wide variety of stochastic properties including the mean, (auto)covariances and higher moments. The theoretical part of the paper establishes the convergence rate of the new estimator. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by two applications to financial return data.

stat.ME↗

arXiv2014

Detecting Gradual Changes in Locally Stationary Processes

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly start to change. In such situations, it is frequently of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong paramet- ric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework. We set up a general procedure which allows to deal with a wide variety of stochastic properties including the mean, (auto)covariances and higher-order moments. The theoretical part of the paper estab- lishes the convergence rate of the new estimator. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by applications to temperature and financial return data.

stat.ME↗

arXiv2013

Nonparametric regression for locally stationary time series

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not suffer from the curse of dimensionality.

math.ST↗

arXiv1999

Chaotic scattering on surfaces and collisional damping of collective modes

The damping of hot giant dipole resonances is investigated. The contribution of surface scattering is compared with the contribution from interparticle collisions. A unified response function is presented which includes surface damping as well as collisional damping. The surface damping enters the response via the Lyapunov exponent and the collisional damping via the relaxation time. The former is calculated for different shape deformations of quadrupole and octupole type. The surface as well as the collisional contribution each reproduce almost the experimental value, therefore we propose a proper weighting between both contributions related to their relative occurrence due to collision frequencies between particles and of particles with the surface. We find that for low and high temperatures the collisional contribution dominates whereas the surface damping is dominant around the temperatures $\sqrt{3}/2π$ of the centroid energy.

astro-ph↗