Browsing by Author "Acosta Salazar, Jonathan Daniel"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Comparing two spatial variables with the probability of agreement
    (2024) Acosta Salazar, Jonathan Daniel; Vallejos, Ronny; Ellison, Aaron M.; Osorio, Felipe; de Castro, Mário
    Computing the agree ment betwee n 2 con tinuous sequences is of grea t interest in statistics when comparing 2 instruments or one instrument with a gold standard. The probability of agree ment quantifies the similarity between 2 variables of interest, and it is useful for determining what constitutes a practically important difference. In this article, we introduce a generalization of the PA for the treatment of spatial vari ables. Our proposal makes the PA dependent on the spatial lag. We establish the conditions for which the PA decays as a function of the distance lag for isotropic stationary and nonstationary spatial processes . Estimtion is addr essed through a first-order appr oxima tion that guarantees the asymp totic normality of the sample version of the PA. The sensitivity of the PA with respect to the covariance parame ters is studied for finite sample size. The new method is described and illustrated with real data involving autumnal changes in the green chromatic coordinate ( G cc ) , an index of “greeness ”that captures the phenological stage of tree leaves, is associ ated with carbon flux from econsys tems, and is estimated from repeated images of forest canopies.
  • Thumbnail Image
    Item
    Correlation integral for stationary gaussian time series
    (2023) Acosta Salazar, Jonathan Daniel; Vallejos, Ronny O.; Gómez, John
    The correlation integral of a time series is a normalized coefficient that represents the number of close pairs of points of the series lying in phase space. It has been widely studied in a number of disciplines such as phisycs, mechanical engineering, bioengineering, among others, allowing the estimation of the dimension of an attractor in a chaotic regimen. The computation of the dimension of an attractor allows to distinguish deterministic behavior in stochastic processes with a weak structure on the noise. In this paper, we establish a power law for the limiting expected value of the correlation integral for Gaussian stationary time series. Examples with linear and nonlinear time series are used to illustrate the result.
  • Thumbnail Image
    Item
    The effective sample size for multivariate spatial processes with an application to soil contamination
    (2021) Vallejo, Ronny; Acosta Salazar, Jonathan Daniel
    Effective sample size accounts for the equivalent number of independent observations contained in a sample of correlated data. This notion has been widely studied in the context of univariate spatial variables. In that case, the effective sample size determines the reduction in the sample size due to the existing spatial correlation. In this paper, we generalize the methodology for multivariate spatial variables to provide a common effective sample size when all variables have been measured at the same locations. Together with the definition, we provide examples to investigate what an effective sample size looks like. An application for a soil contamination data set is considered. To reduce the dimensions of the process, clustering techniques are applied to obtain three bivariate vectors that are modeled using coregionalization models. Because the sample size of the data set is moderate and the locations are very unevenly distributed in the study area, the spatial analysis is challenging and interesting. We find that due to the presence of spatial autocorrelation, the sample size can be reduced by 38.53%, avoiding the duplication of information. Recommendations for Resource Managers: Before carrying out a sample survey with georeferenced data, it is essential to consider the impact of spatial correlation on sample size calculations. When the nature of the problem requires multivariate characteristics analysis, we provide a methodology to evaluate the effective sample size from a multivariate perspective. If the sample size is large, the effective sample size allows us to define the size of the subsample that should be used to preserve the theoretical properties of the estimation of the mean.