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First, we analyze the variance of the Cross Validation (CV)-based estimators used for estimating the performance of classification rules. Second, we propose a novel estimator to estimate this variance using the Influence Function (IF)…

We develop a Bayesian framework for the efficient estimation of impulse responses using Local Projections (LPs) with instrumental variables. It accommodates multiple shocks and instruments, accounts for autocorrelation in multi-step…

In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling…

The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…

It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to…

Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…

This paper introduces a novel two-stage estimation and inference procedure for generalized impulse responses (GIRs). GIRs encompass all coefficients in a multi-horizon linear projection model of future outcomes of y on lagged values (Dufour…

We introduce new estimators of the inhomogeneous $K$-function and the pair correlation function of a spatial point process as well as the cross $K$-function and the cross pair correlation function of a bivariate spatial point process under…

We present a continuous-time probabilistic approach for estimating the chirp signal and its instantaneous frequency function when the true forms of these functions are not accessible. Our model represents these functions by non-linearly…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

Derivation of the procedures that can be applied in evaluating two-time correlation function in terms of coherent-state propagator and corresponding Q-function is presented. On the basis that the involved functions are generally exponential…

We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…

We consider a longitudinal data structure consisting of baseline covariates, time-varying treatment variables, intermediate time-dependent covariates, and a possibly time dependent outcome. Previous studies have shown that estimating the…

This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…

Mechanistic interpretability has identified functional subgraphs within large language models (LLMs), known as Transformer Circuits (TCs), that appear to implement specific algorithms. Yet we lack a formal, single-pass way to quantify when…

Modern causal inference methods allow machine learning to be used to weaken parametric modeling assumptions. However, the use of machine learning may result in complications for inference. Doubly-robust cross-fit estimators have been…

Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…

Room impulse response (RIR) estimation naturally arises as a class of inverse problems, including denoising and deconvolution. While recent approaches often rely on supervised learning or learned generative priors, such methods require…

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…