Related papers: Factor Analysis for Spectral Estimation
Multi-index models provide a popular framework to investigate the learnability of functions with low-dimensional structure and, also due to their connections with neural networks, they have been object of recent intensive study. In this…
We present a new method for multi-component power spectra estimation in multi-frequency observations of the CMB. Our method is based on matching a model to the cross and auto power spectra of observed maps. All the component power spectra…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into…
Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian…
We consider the problem of estimating the covariance matrix of a random signal observed through unknown translations (modeled by cyclic shifts) and corrupted by noise. Solving this problem allows to discover low-rank structures masked by…
The dynamic range is an important parameter which measures the spread of sound power, and for music signals it is a measure of recording quality. There are various descriptive measures of sound power, none of which has strong statistical…
We consider the origin of noise and distortions in power spectral estimates of randomly sampled data, specifically velocity data measured with a burst-mode laser Doppler anemometer. The analysis guides us to new ways of reducing noise and…
Spectral analysis using overlapping sliding windows is among the most widely used techniques in analyzing non-stationary time series. Although sliding window analysis is convenient to implement, the resulting estimates are sensitive to the…
We present the XFaster analysis package. XFaster is a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. XFaster uses Monte Carlo simulations to compute noise biases…
Source enumeration, the task of estimating the number of sources from the signal received by the array of antennas, is a critical problem in array signal processing. Numerous methods have been proposed to estimate the number of sources…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
The extraction of signals from noise is a common problem in all areas of science and engineering. A particularly useful version is that of forecasting: determining a causal filter that estimates a future value of a hidden process from past…
The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…
Thomson's multitaper method estimates the power spectrum of a signal from $N$ equally spaced samples by averaging $K$ tapered periodograms. Discrete prolate spheroidal sequences (DPSS) are used as tapers since they provide excellent…
We have developed a fast, accurate and generally applicable method for inferring the power spectrum and its uncertainties from maps of the cosmic microwave background (CMB) in the presence of inhomogeneous and correlated noise. For maps…
We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…
This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…
While the Lomb-Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60-year history of developing…
Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very…