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We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
To derive the auto-covariance function from a sampled and time-limited signal or the cross-covariance function from two such signals, the mean values must be estimated and removed from the signals. If no a priori information about the…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
Shallow quantum circuits are believed to be the most promising candidates for achieving early practical quantum advantage - this has motivated the development of a broad range of error mitigation techniques whose performance generally…
Given data with label noise (i.e., incorrect data), deep neural networks would gradually memorize the label noise and impair model performance. To relieve this issue, curriculum learning is proposed to improve model performance and…
Due to the nature of pure-tone audiometry test, hearing loss data often has a complicated correlation structure. Generalized estimating equation (GEE) is commonly used to investigate the association between exposures and hearing loss,…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article we present two new…
Existing works in optimal filtering for linear Gaussian systems with arbitrary unknown inputs assume perfect knowledge of the noise covariances in the filter design. This is impractical and raises the question of whether and under what…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically…
We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…
We propose an estimation procedure for covariation in wide compositional data sets. For compositions, widely-used logratio variables are interdependent due to a common reference. Logratio uncorrelated compositions are linearly independent…
Truncated linear regression is a classical challenge in Statistics, wherein a label, $y = w^T x + \varepsilon$, and its corresponding feature vector, $x \in \mathbb{R}^k$, are only observed if the label falls in some subset $S \subseteq…
This article develops a general detection theory for speech analysis based on time-varying autoregressive models, which themselves generalize the classical linear predictive speech analysis framework. This theory leads to a computationally…
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone…