Multiresolution Analysis Adapted to Irregularly Spaced Data

Multiresolution Analysis Adapted to Irregularly Spaced Data

This paper investigates the mathematical background of multiresolution analysis in the specific context where the signal is represented by irregularly sampled data at known locations. The study is related to the construction of nested piecewise polynomial multiresolution spaces represented by their corresponding orthonormal bases. Using simple spline basis orthonormalization procedures involves...

A test for stationarity for irregularly spaced spatial data

Abstract The analysis of spatial data is based on a set of assumptions, which in practice need to be checked. A commonly used assumption is that the spatial random field is second order stationary. In this paper, a test for spatial stationarity for irregularly sampled data is proposed. The test is based on a transformation of the data (a type of Fourier transform), where the correlations betwee...

Bayesian smoothing of irregularly-spaced data using Fourier basis functions

The spectral representation of Gaussian processes via the Fourier basis provides a computationally efficient specification of spatial surfaces and nonparametric regression functions in various statistical models. I describe the representation in detail and introduce the spectralGP R library for computations. Because of the large number of basis coefficients, some form of shrinkage is necessary;...

Econometric Modeling of Multivariate Irregularly-Spaced High-Frequency Data

The recent advent of high frequency data provides researchers with transaction by transaction level data. Examples include scanner data from grocery stores or financial transactions data. These new data sets allow researchers to take an unprecedented look at the underlying economic structure of the markets. Often the hypothesis of interest is in the context of multivariate time series data. Ana...

Estimating fractal dimension of natural terrain from irregularly spaced data