Abstracts
Return to main page: Summer Term 2025
David Rügamer:
Semi-Structured Regression: Current Advances and Challenges
Neural networks enable learning from various data modalities, such as images and text. This concept has been integrated into statistical modeling through semi-structured regression, which additively combines structured predictors with unstructured effects from arbitrary data modalities by embedding the statistical model into the neural network. This approach opens new opportunities for advancing regression models but also poses challenges, such as increased uncertainty, implicit regularization, and complexities in statistical inference. This presentation will introduce semi-structured regression, discuss recent advances, and highlight the challenges of embedding regression models into neural networks.
Damir Filipovic:
Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels
We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications in Finance. We apply it to an extensive panel of monthly US stock excess returns from 1962 to 2021, using macroeconomic and firm-specific covariates as conditioning variables. The estimator effectively captures time-varying cross-sectional dependencies, demonstrating robust statistical and economic performance. We find that idiosyncratic risk explains, on average, more than 75% of the cross-sectional variance.
Ulrike Schneider:
Understanding the Adaptive LASSO in Predictive Regressions
Several articles have looked at LASSO and adaptive LASSO methods in the context of predictive and cointegrating regressions in the econometrics literature in recent years. The results shown in this literature are derived in a so-called fixed-parameter framework which is known to come with certain limitations regarding the interpretability of the results for the actual performance of the estimator.
To better understand the behavior of the adaptive LASSO, we carry out a full analysis of the estimator in a predictive regression model with only one (endogenous) regressor. We provide insights to the model selection properties in connection with the tuning parameter sequence and extract the two different possible regimes, consistent and conservative model selection. For each regime, we look at convergence rates and asymptotic distributions in a so-called moving-parameter framework, and also work out the local-to-zero rates which still can be detected by the estimator. We find that in the consistently tuned case, the existing results from a fixed-parameter framework do not paint a realistic picture as overall convergence and local-to-zero rates are actually slower and limiting distributions differ. The discrepancies are less pronounced when looking at the conservatively tuned case. We finish our analysis with a simulation study examining the distribution of the estimator in finite samples.
Joint work in progress with Karsten Reichold (TU Wien).
Sara Wade:
Understanding Uncertainty in Bayesian Cluster Analysis
The Bayesian approach to clustering is often appreciated for its ability to shed light on uncertainty in the partition structure. However, summarizing the posterior distribution on the partition space can be challenging. In previous work, we proposed to summarize the posterior samples using a single optimal clustering estimate, which minimizes the expected posterior Variation of Information (VI). In instances where the posterior distribution is multimodal, it can be beneficial to summarize the posterior samples using multiple clustering estimates, each corresponding to a different part of the space of partitions that receives substantial posterior mass. In this work, we propose to find such clustering estimates by approximating the posterior distribution in a VI-based Wasserstein distance sense. An interesting byproduct is that this problem can be seen as using the k-mediods algorithm to divide the posterior samples into different groups, each represented by one of the clustering estimates. Using both synthetic and real datasets, we show that our proposal helps to improve the understanding of uncertainty, particularly when the data clusters are not well separated, or when the employed model is misspecified.
Work in progress with Cecilia Balocchi (Edinburgh), building on previous work (see linked papers on main page).
Gonçalo dos Reis:
Simulation of Mean-Field SDEs: Some Recent Results
We review recent results on the simulation of McKean-Vlasov stochastic differential equations (MV-SDEs). The first set of results concerns the simulation of MV-SDEs with super-linear growth in both the spatial and interaction components of the drift, along with a non-constant Lipschitz diffusion coefficient.
The second set of results is far more curious. It examines the weak convergence properties of the Laimkuhler-Matthews methods, a non-Markovian Euler-type scheme with the same computational cost as the standard Euler method, for approximating the stationary distribution of a one-dimensional MV-SDE, specifically a mean-field (overdamped) Langevin equation (MFL). Under a strong convexity assumption, we provide both weak and strong error estimates in finite and infinite time horizons. Through a careful analysis of the variation processes and the Kolmogorov backward equation for the associated particle system, we show that the method attains a weak order of convergence rate of 3/2 in the long-time limit - exceeding the standard Euler method’s weak order of 1.
While we use an interacting particle system (IPS) to approximate the MV-SDE, we show the convergence rate is independent of the dimension of the IPS, and this includes establishing uniform-in-time decay estimates for moments of the IPS, the Kolmogorov backward equation and their derivatives. The theoretical findings are supported by numerical experiments.
Carolin Strobl:
Detecting Parameter Heterogeneity in Psychometric Models by Means of Model-Based Recursive Partitioning with psychotree, stablelearner & Co.
Model-based recursive partitioning is a flexible framework for detecting differences in model parameters between two or more groups of subjects. Its origins lie in machine learning, where its predecessor methods, classification and regression trees, have been introduced around the 1980s. Today, after the statistical flaws of the early algorithms have been overcome, tree-based methods offer a valuable addition to the “statistical toolbox” in various areas of application, including psychology. This talk reviews the rationale of model-based recursive partitioning in general and in particular with regard to psychometric models for paired comparisons and IRT models. It also discusses two issues that are highly relevant for the interpretation of tree-based methods - quantifying stability and incorporating effect size.
Sascha Desmettre:
Equilibrium Control Theory for Kihlstrom-Mirman Preferences in Continuous Time
Introduced in 1974, Kihlstrom-Mirman preferences represent a multi-attribute generalization of the standard (univariate) expected utility theory. The main appeal of this class of utilities is that, by separating the choice of the elasticity of intertemporal substitution and risk aversion, they allow to disentangle attitudes towards time and risk. We discuss in detail how this approach differs from other classes of preferences exhibiting a similar feature (for instance, Epstein-Zin-Weil recursive utility). However, when solving intertemporal choice problems, the peculiar construction of Kihlstrom-Mirman preferences induces dynamic inconsistency - that is, the dynamic programming principle fails to hold. Our main contribution is therefore to address this challenge. In doing so, we provide a formal template to address the time-inconsistency of Kihlstrom-Mirman preferences in Markovian settings by means of equilibrium control theory. As an application, we study a consumption-investment problem for an agent with constant relative risk aversion and constant elasticity of substitution.
Alessandro Casa:
Truncated Pairwise Likelihood for Sparse High-Dimensional Covariance Estimation
The estimation of covariance structure in high-dimensional settings is a critical yet complex task. Pairwise likelihood provides a computationally feasible approximation to the full likelihood by considering bivariate margins, and in models like the multivariate normal, it can retain statistical efficiency. To address the challenge of estimating sparse high-dimensional covariance matrices, we introduce a novel method based on maximizing a /truncated pairwise likelihood/. This approach selectively incorporates only those pairwise likelihood terms that correspond to nonzero covariance entries. The truncation is achieved by minimizing the L2-distance between the score functions of the pairwise and full likelihoods, coupled with an L1-penalty to promote sparsity at the component level. In contrast to parameter-wise regularization, our method directly selects relevant pairwise likelihood objects, thus preserving the unbiasedness of the estimating equations. We theoretically show that our selection procedure is consistent even as the dimensionality increases exponentially, and the resulting estimator converges to the oracle maximum likelihood estimator. The efficacy and robustness of our proposed method are supported by empirical results on synthetic and real-world datasets.
Return to main page: Summer Term 2025