Search results for "Covariance function"
showing 10 items of 22 documents
The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies
2003
We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform …
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
2013
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajectories, sampling scheme, and smoothing bandwidth, we prove a Central Limit theorem in the space of …
SPECTRAL ANALYSIS WITH TAPERED DATA
1983
. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.
Model comparison and selection for stationary space–time models
2007
An intensive simulation study to compare the spatio-temporal prediction performances among various space-time models is presented. The models having separable spatio-temporal covariance functions and nonseparable ones, under various scenarios, are also considered. The computational performance among the various selected models are compared. The issue of how to select an appropriate space-time model by accounting for the tradeoff between goodness-of-fit and model complexity is addressed. Performances of the two commonly used model-selection criteria, Akaike information criterion and Bayesian information criterion are examined. Furthermore, a practical application based on the statistical ana…
Linear Recursive Equations, Covariance Selection, and Path Analysis
1980
Abstract By defining a reducible zero pattern and by using the concept of multiplicative models, we relate linear recursive equations that have been introduced by econometrician Herman Wold (1954) and path analysis as it was proposed by geneticist Sewall Wright (1923) to the statistical theory of covariance selection formulated by Arthur Dempster (1972). We show that a reducible zero pattern is the condition under which parameters as well as least squares estimates in recursive equations are one-to-one transformations of parameters and of maximum likelihood estimates, respectively, in a decomposable covariance selection model. As a consequence, (a) we can give a closed-form expression for t…
Robustifying principal component analysis with spatial sign vectors
2012
Abstract In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods.
Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
2013
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator …
Varying-time random effects models for longitudinal data: unmixing and temporal interpolation of remote-sensing data
2008
Remote sensing is a helpful tool for crop monitoring or vegetation-growth estimation at a country or regional scale. However, satellite images generally have to cope with a compromise between the time frequency of observations and their resolution (i.e. pixel size). When concerned with high temporal resolution, we have to work with information on the basis of kilometric pixels, named mixed pixels, that represent aggregated responses of multiple land cover. Disaggreggation or unmixing is then necessary to downscale from the square kilometer to the local dynamic of each theme (crop, wood, meadows, etc.). Assuming the land use is known, that is to say the proportion of each theme within each m…
A Random Field Approach to Transect Counts of Wildlife Populations
1991
Line transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot-noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.
The Role of Covariance Matrix Forecasting Method in the Performance of Minimum-Variance Portfolios
2014
Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this paper, we evaluate alternative covariance matrix forecasting methods by looking at (1) their forecast accuracy, (2) their ability to track the volatility of the minimum-variance portfolio, and (3) their ability to keep the volatility of the minimum-variance portfolio at a target level. We find large differences between the methods. Our results suggest that shrinkage of the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample covariance ma…