arXiv subjects

Kevin Wilk

Publications and source records attributed to Kevin Wilk.

4 recordsLinked to original sources

arXiv2026

Transferring supremum-norm rates and weak convergence of covariance kernel estimators to functional principal components

We show that $L_2$-perturbation theory can be used to transfer rates of convergence in the supremum norm as well as weak convergence in the space of continuous functions from covariance kernel estimators to the associated functional principle components (FPCs). As an application we obtain optimal rates of convergence in sup-norm, including minimax-lower bounds, as well as asymptotic normality for estimating the FPCs in a discrete observational model with errors under fixed, synchronous design. The sparse to dense transition which has previously been observed for mean function and covariance kernel estimators also applies to the FPCs. Surprisingly, eigenvalue estimation exhibits a discretization-dominated regime under sparse designs, too. Our results further apply to estimators of cross-covariance and long-run covariance kernels, as well as to covariance kernels of derivative processes. We also present results of numerical experiments in which we use the Nystr\"om method to compute FPCs and eigenvalues, and give an empirical illustration to series of daily temperature curves.

math.ST↗

arXiv2026

Beyond average warming: Two-sample inference for dense-sparse functional data reveals changes in intraday temperature patterns

Modern weather stations in Germany record daily temperatures every 10 minutes, whereas measurements from historical reference periods are often only available at much coarser temporal resolutions, typically hourly. This discrepancy must be accounted for when comparing historical and current daily temperature patterns. Motivated by this problem, we develop two-sample inference procedures for functional data under sampling schemes where one sample is densely observed while the other is relatively sparse. Building on recent ideas from transfer learning for functional data, we derive estimators of the difference of the mean functions that attain optimal convergence rates in the supremum norm. We further establish a functional central limit theorem in the space of continuous functions and develop multiplier bootstrap methods for constructing uniform confidence bands. Extensions to functional time series are also discussed. Applying the proposed methodology to daily temperature curves from German weather stations, analyzed separately by month, reveals that climate change has altered not only average temperatures but also intraday temperature patterns. In particular, for stations such as Berlin, warming from morning to early afternoon exceeds the daily average increase, whereas evening and nighttime temperatures exhibit comparatively smaller increases.

stat.AP↗

arXiv2019

Understanding nebular spectra of Type Ia supernovae

In this study, we present one-dimensional, non-local-thermodynamic-equilibrium, radiative transfer simulations (using CMFGEN) in which we introduce micro-clumping at nebular times into two Type Ia supernova ejecta models. We use one sub-Chandrasekhar (sub-M$_{\rm Ch}$) ejecta with 1.02 M$_\odot$ and one M$_{\rm Ch}$ ejecta model with 1.40 M$_\odot$. We introduce clumping factors $f=$0.33,0.25, and 0.10 which are constant throughout the ejecta and compared to the unclumped $f=1.0$ case. We find that clumping is a natural mechanism to reduce the ionization of the ejecta, reducing emission from [Fe III], [Ar III], and [S III] by a factor of a few. For decreasing values of the clumping factor $f$, the [Ca II] $λλ$7291,7324 doublet became a dominant cooling line for our M$_{\rm Ch}$ model but still weak in our sub-M$_{\rm Ch}$ model. Strong [Ca II] $λλ$7291,7324 indicates non-thermal heating in that region and may constrain explosion modelling. Due to the low abundance of stable nickel, our sub-M$_{\rm Ch}$ model never showed the [Ni II] 1.939 micron diagnostic feature for all clumping values.

astro-ph.SR↗

arXiv2017

Ejecta Mass Diagnostics of Type Ia Supernovae

We present one-dimensional non-local thermodynamic equilibrium time-dependent radiative transfer simulations (using CMFGEN) of two sub-Chandrasekhar (sub-$M_{\rm Ch}$), one $M_{\rm Ch}$ and one super-$M_{\rm Ch}$ Type Ia SN ejecta models. Three originate from $M_{\rm Ch}$ delayed detonation models, and the fourth is a sub-$M_{\rm Ch}$ detonation model. Ejecta masses are 1.02, 1.04, 1.40, and 1.70 M$_\odot$, and all models have 0.62 M$_\odot$ of $^{56}{\rm Ni}$. Sub-$M_{\rm Ch}$ model light curves evolve faster, reaching bolometric maximum 2--3 days earlier and having 3--4 days shorter bolometric half light widths. The models vary by $\sim$12 per cent at maximum bolometric luminosity and by 0.17 mag in $B_{\rm max}$. While $ΔM_{15}(B)$ increases with ejecta mass it only varies by $\sim$5 per cent around 1 mag. Sub-$M_{\rm Ch}$ models are 0.25 mag bluer in $B-R$ at $B_{\rm max}$. Optical spectra share many similarities, but lower mass models exhibit less UV line blanketing during the photospheric phase. At nebular times, significant NIR spectroscopic differences are seen. In particular, emission lines of the Ca II NIR triplet; [S III] $λλ$9068,9530; [Ca II] $λλ$7291,7324; [Ar III] $λλ$7135,7751; and [Ni II] 1.939 $μ$m are stronger in higher mass models. The [Ni II] 1.939 $μ$m line is absent in the sub-$M_{\rm Ch}$ detonation model, and provides a valuable potential tool to distinguish sub-$M_{\rm Ch}$ explosions from $M_{\rm Ch}$ explosions. In general, the nebular phase models are too highly ionized. We attribute this to the neglect of clumping and/or the distribution of intermediate mass and iron group elements. The two sub-$M_{\rm Ch}$ models, while exploded by different mechanisms, can be distinguished in the $J$ and $H$ bands at late times (e.g., $+200$ days).

astro-ph.SR↗