Related papers: Locally adaptive estimation of evolutionary wavele…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps…
We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the "Local Whittle Wavelet…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
Two adaptive bandwidth selection methods for nonparametric estimators in locally stationary processes are proposed. We investigate a cross validation approach and a method based on contrast minimization and derive asymptotic properties of…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
Sequential latent-variable models with subject-specific random effects provide a flexible framework for modeling temporally structured data with both local latent dynamics and stable between-subject heterogeneity. In such models,…
The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet…
Spatio-temporal forecasting is challenging attributing to the high nonlinearity in temporal dynamics as well as complex location-characterized patterns in spatial domains, especially in fields like weather forecasting. Graph convolutions…
The Davenport spectrum is a modification of the classical Kolmogorov spectrum for the inertial range of turbulence that accounts for non-scaling low frequency behavior. Like the classical fractional Brownian motion vis-\`a-vis the…
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…
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…
The availability of data on economic uncertainty sparked a lot of interest in models that can timely quantify episodes of international spillovers of uncertainty. This challenging task involves trading off estimation accuracy for more…
A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…
We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile…
We present the application of the variational-wavelet approach to the construction and analysis of solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…
We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…