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In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…
This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…
Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with…
Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but…
Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast…
A general non-Gaussian semiparametric model is adopted to characterize the measurement vectors, i.e.\ the \textit{snapshots}, collected by a linear array. Moreover, the recently derived \textit{robust semiparametric efficient} $R$-estimator…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
Most physical data sets contain a stochastic contribution produced by measurement noise or other random sources along with the signal. Usually, neither the signal nor the noise are accurately known prior to the measurement so that both have…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters…
A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
Autocovariance of the error term in a time series model plays a key role in the estimation and inference for the model that it belongs to. Typically, some arbitrary parametric structure is assumed upon the error to simplify the estimation,…
The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to suggest that the underlying data generating mechanism has changed. This work is concerned with open-end,…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…