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Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
A nonparametric method is proposed for estimating the quantile spectra and cross-spectra introduced in Li (2012; 2014) as bivariate functions of frequency and quantile level. The method is based on the quantile discrete Fourier transform…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
Nonlinearities in the gravitational evolution, galaxy bias, and redshift-space distortion drive the observed galaxy density fields away from the initial near-Gaussian states. Exploiting such a non-Gaussian galaxy density field requires…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…
Most biological signals are non-Gaussian, reflecting their origins in highly nonlinear physiological systems. A versatile set of techniques for studying non-Gaussian signals relies on the spectral representations of higher moments, known as…
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…
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…
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…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the…
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap…
Recently, several spectra have emerged, designed to encapsulate the distributional characteristics of non-Gaussian stationary processes. This article introduces parametric families of generalized spectra based on the characteristic…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
Multimodal regression estimation methods are introduced for regression models involving circular response and/or covariate. The regression estimators are based on the maximization of the conditional densities of the response variable over…
The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…