arXiv subjects

Holger Schwender

Publications and source records attributed to Holger Schwender.

5 recordsLinked to original sources

arXiv2026

A test for normality based on self-similarity

Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional characteristics such as higher-order moments, others focus on functional aspects such as the distribution function. In this article, we propose an alternative idea by exploiting the self-similarity property of the normal distribution and introduce the Self-Similarity Test for Normality (SSTN). This procedure leverages the structural property that the distribution of a suitably centered and scaled sum of independent and identically distributed random variables with finite variance coincides with the original distribution if and only if that distribution is normal. The SSTN evaluates normality by applying a self-similarity transformation to the standardized empirical characteristic function and examining how the transformed functions change across successive applications. For the normal distribution, repeated applications preserve the functional form of the characteristic function, whereas deviations from normality manifest in systematic changes between consecutive transforms. These changes are aggregated into a test statistic, whose null distribution is obtained by Monte Carlo calibration, using a sample-size-specific calibration for small samples and an approximation of the asymptotic null distribution for larger ones. A comprehensive simulation study shows that the SSTN performs at least competitively and frequently superior to several well-established tests for normality.

stat.ME↗

arXiv2025

A nonparametric statistical method for deconvolving densities in the analysis of proteomic data

In medical research, often, genomic or proteomic data are collected, with measurements frequently subject to uncertainties or errors, making it crucial to accurately separate the signals of the genes or proteins, respectively, from the noise. Such a signal separation is also of interest in skin aging research in which intrinsic aging driven by genetic factors and extrinsic, i.e.\ environmentally induced, aging are investigated by considering, e.g., the proteome of skin fibroblasts. Since extrinsic influences on skin aging can only be measured alongside intrinsic ones, it is essential to isolate the pure extrinsic signal from the combined intrinisic and extrinsic signal. In such situations, deconvolution methods can be employed to estimate the signal's density function from the data. However, existing nonparametric deconvolution approaches often fail when the variance of the mixed distribution is substantially greater than the variance of the target distribution, which is a common issue in genomic and proteomic data. We, therefore, propose a new nonparametric deconvolution method called N-Power Fourier Deconvolution (NPFD) that addresses this issue by employing the $N$-th power of the Fourier transform of transformed densities. This procedure utilizes the Fourier transform inversion theorem and exploits properties of Fourier transforms of density functions to mitigate numerical inaccuracies through exponentiation, leading to accurate and smooth density estimation. An extensive simulation study demonstrates that NPFD effectively handles the variance issues and performs comparably or better than existing deconvolution methods in most scenarios. Moreover, applications to real medical data, particularly to proteomic data from fibroblasts affected by intrinsic and extrinsic aging, show how NPFD can be employed to estimate the pure extrinsic density.

stat.ME↗

arXiv2022

Measuring covariate balance in weighted propensity score analyses by the weighted z-difference

Propensity score (PS) methods have been increasingly used in recent years when assessing treatment effects in nonrandomized studies. In terms of statistical methods, a number of new PS weighting methods were developed, and it was shown that they can outperform PS matching in efficiency of treatment effect estimation in different simulation settings. For assessing balance of covariates in treatment groups, PS weighting methods commonly use the weighted standardized difference, despite some deficiencies of this measure like, for example, the distribution of the weighted standardized difference depending on the sample size and on the distribution of weights. We introduce the weighted z-difference as a balance measure in PS weighting analyses and demonstrate its usage in a simulation study and by applying it to an example from cardiac surgery. The weighted z-difference is computationally simple and can be calculated for continuous, binary, ordinal and nominal covariates. By using Q-Q-plots we can compare the balance of PS weighted samples immediately to the balance in perfectly matched PS samples and to the expected balance in a randomized trial.

stat.ME↗

arXiv2022

Confound-leakage: Confound Removal in Machine Learning Leads to Leakage

Machine learning (ML) approaches to data analysis are now widely adopted in many fields including epidemiology and medicine. To apply these approaches, confounds must first be removed as is commonly done by featurewise removal of their variance by linear regression before applying ML. Here, we show this common approach to confound removal biases ML models, leading to misleading results. Specifically, this common deconfounding approach can leak information such that what are null or moderate effects become amplified to near-perfect prediction when nonlinear ML approaches are subsequently applied. We identify and evaluate possible mechanisms for such confound-leakage and provide practical guidance to mitigate its negative impact. We demonstrate the real-world importance of confound-leakage by analyzing a clinical dataset where accuracy is overestimated for predicting attention deficit hyperactivity disorder (ADHD) with depression as a confound. Our results have wide-reaching implications for implementation and deployment of ML workflows and beg caution against naïve use of standard confound removal approaches.

cs.LG↗

arXiv2017

Hierarchical clustering of DNA k-mer counts in RNA-seq fastq files reveals batch effects

Batch effects, artificial sources of variation due to experimental design, are a widespread phenomenon in high throughput data. Therefore, mechanisms for detection of batch effects are needed requiring comparison of multiple samples. We apply hierarchical clustering (HC) on DNA k-mer counts of multiple RNA-seq derived Fastq files. Ideally, HC generated trees reflect experimental treatment groups and thus may indicate experimental effects, but clustering of preparation groups indicates the presence of batch effects. In order to provide a simple applicable tool we implemented sequential analysis of Fastq reads with low memory usage in an R package (seqTools) available on Bioconductor. DNA k-mer counts were analysed on 61 Fastq files containing RNA-seq data from two cell types (dermal fibroblasts and Jurkat cells) sequenced on 8 different Illumina Flowcells. Results: Pairwise comparison of all Flowcells with hierarchical clustering revealed strong Flowcell based tree separation in 6 (21 %) and detectable Flowcell based clustering in 17 (60.7 %) of 28 Flowcell comparisons. In our samples, batch effects were also present in reads mapped to the human genome. Filtering reads for high quality (Phred >30) did not remove the batch effects. Conclusions: Hierarchical clustering of DNA k-mer counts provides a quality criterion and an unspecific diagnostic tool for RNA-seq experiments.

q-bio.GN↗