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Spectral estimation is a fundamental problem for time series analysis, which is widely applied in economics, speech analysis, seismology, and control systems. The asymptotic convergence theory for classical, non-parametric estimators, is…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In…
In this work, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with wo steps: first, wavelet estimation across all channels and second, refinement of the…
We study the theoretical performance of a combined approach to demodulation and decoding of binary continuous-phase modulated signals under repetition-like codes. This technique is motivated by a need to transmit packetized or framed data…
The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on…
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…
Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Experimental datasets are growing rapidly in size, scope, and detail, but the value of these datasets is limited by unwanted measurement noise. It is therefore tempting to apply analysis techniques that attempt to reduce noise and enhance…