arXiv subjects

Georg Keilbar

Publications and source records attributed to Georg Keilbar.

6 recordsLinked to original sources

arXiv2026

Embedded Conditional Independence Tests for Large Language Model Generated Text with an Application to German Parliament Speeches

Conditional independence tests (CITs) test for conditional dependence between two random objects $X$ and $Y$ given a third random object $Z$. Existing CITs have limited applicability to high-dimensional data, especially multimodal data like text. However, we show that such tests are of interest for large language model (LLM) outputs, where we test whether an output $X$ generated from a source text $Z$ carries information about an attribute $Y$ beyond $Z$ itself. For this purpose, we propose embedded CITs (eCITs), which embed $X$ and $Z$ and apply an existing CIT to the resulting representations and to $Y$. We show that, provided the embedding of $Z$ is sufficient, i.e. retains the information $Z$ carries about either $Y$ or the representation of $X$, the null hypothesis transfers from $X$ and $Z$ to their representations, so that a CIT valid for the embedded hypothesis is valid for the original one. We further give conditions for equivalence of the two hypotheses, and show that sufficiency weakens to mean sufficiency when the embedded test targets conditional mean independence. We propose a semi-synthetic simulation design to assess type I error (T1E) control and power of the eCITs for given embedding maps on a specific dataset and task, and use it to evaluate them on our application. Applying the eCITs to German Parliament speeches, we find for all combinations of embedding maps considered that the summaries of two LLMs contain information about the speaker's faction and gender beyond the speech they were generated from.

stat.ML↗

arXiv2026

Counterfactual Density Effects and the German East--West Income Gap

We propose a novel framework for conducting causal inference based on counterfactual densities. While the current paradigm of causal inference is mostly focused on estimating average treatment effects (ATEs), which restricts the analysis to the first moment of the outcome variable, our density-based approach is able to detect causal effects based on general distributional characteristics. Following the Oaxaca-Blinder decomposition approach, we consider two types of counterfactual density effects that together explain observed discrepancies between the densities of the treated and control group. First, the distribution effect is the counterfactual effect of changing the conditional density of the control group to that of the treatment group, while keeping the covariates fixed at the treatment group distribution. Second, the covariate effect represents the effect of a hypothetical change in the covariate distribution. Both effects have a causal interpretation under the classical unconfoundedness and overlap assumptions. Methodologically, our approach is based on analyzing the conditional densities as elements of a Bayes Hilbert space, which preserves the non-negativity and integration-to-one constraints. We specify a flexible functional additive regression model estimating the conditional densities. We apply our method to analyze the German East--West income gap, i.e., the observed differences in wages between East Germans and West Germans. While most of the existing studies focus on the average differences and neglect other distributional characteristics, our density-based approach is suited to detect all nuances of the counterfactual distributions, including differences in probability masses at zero.

econ.EM↗

arXiv2025

Online simultaneous inference for quantiles via smoothed stochastic gradient descent

This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the score function with a bandwidth tied to the learning rate, we obtain estimates that are monotone in the quantile level at every iteration, while retaining the memory and computational efficiency required for streaming data. We establish non-asymptotic tail probability bounds for the smoothed estimate with and without Polyak-Ruppert averaging, which are sub-exponential with a multi-regime structure. For the averaged estimate we further derive a Bahadur representation that is uniform in the quantile level and across coordinates, and a resulting Gaussian approximation by the maximum of Brownian bridges, with the dimension $p$ allowed to grow exponentially in the sample size. This yields simultaneous inference across coordinates and quantile levels. As an alternative that avoids estimating the sparsity function, we propose an online multiplier bootstrap that preserves monotonicity, runs in a single pass and is asymptotically valid. Extending the theory to a localized recursion, we obtain online nonparametric conditional quantile estimates with uniform bands over design points and quantile levels. Simulations confirm accurate finite-sample coverage, and we illustrate the method on conditional value-at-risk curves.

stat.ML↗

arXiv2024

Shapley Curves: A Smoothing Perspective

This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level \textit{Shapley curves} to measure the true variable importance, determined by the conditional expectation function and the distribution of covariates. Having defined the estimand, we derive minimax convergence rates and asymptotic normality under general conditions for the two leading estimation strategies. For finite sample inference, we propose a novel version of the wild bootstrap procedure tailored for capturing lower-order terms in the estimation of Shapley curves. Numerical studies confirm our theoretical findings, and an empirical application analyzes the determining factors of vehicle prices.

stat.ML↗

arXiv2023

High-dimensional inference on jumps in nonparametric time series regression models

We study simultaneous inference on jumps in the conditional mean functions of a high-dimensional collection of heterogeneous nonparametric time series, where the number of series may exceed the sample size and the data may exhibit strong cross-sectional dependence. The jump depends on one specific covariate, and we allow the regression function to vary with additional latent variables. We propose two uniform tests: one for the existence of jumps and one for their homogeneity across series. We derive a simple closed-form approximation to the covariance structure of the jump estimators and establish a high-dimensional Gaussian approximation showing that, owing to the localized construction of the statistics, the maximum of the studentized jumps is approximated by the maximum of independent Gaussians. The cross-sectional dependence is thus asymptotically negligible for critical values, even under strong (e.g., factor) dependence, and the approximation requires estimating only the variance for each series. For pronounced cross-sectional dependence, a dependence-aware refinement restores the off-diagonal covariances, improving finite-sample size and power. Simulations show accurate size and reasonable power under both cross-sectional and serial dependence, and two empirical applications reveal significant non-smooth effects.

econ.EM↗

arXiv2022

A projection based approach for interactive fixed effects panel data models

This paper introduces a straightforward sieve-based approach for estimating and conducting inference on regression parameters in panel data models with interactive fixed effects. The method's key assumption is that factor loadings can be decomposed into an unknown smooth function of individual characteristics plus an idiosyncratic error term. Our estimator offers advantages over existing approaches by taking a simple partial least squares form, eliminating the need for iterative procedures or preliminary factor estimation. In deriving the asymptotic properties, we discover that the limiting distribution exhibits a discontinuity that depends on how well our basis functions explain the factor loadings, as measured by the variance of the error factor loadings. This finding reveals that conventional ``plug-in'' methods using the estimated asymptotic covariance can produce excessively conservative coverage probabilities. We demonstrate that uniformly valid non-conservative inference can be achieved through the cross-sectional bootstrap method. Monte Carlo simulations confirm the estimator's strong performance in terms of mean squared error and good coverage results for the bootstrap procedure. We demonstrate the practical relevance of our methodology by analyzing growth rate determinants across OECD countries.

econ.EM↗