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Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.


Papers
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Journal ArticleDOI
TL;DR: In this article, a natural extension of the conventional accelerated failure time model for survival data is presented to formulate the effects of covariates on the mean function of the counting process for recurrent events.
Abstract: SUMMARY We present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events. A class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model. In addition, a Nelson-Aalen-type estimator for the mean function of the counting process is constructed, which is consistent and, properly normalised, converges weakly to a zeromean Gaussian process. We assess the finite-sample properties of the proposed estimators and the associated inference procedures through Monte Carlo simulation and provide an application to a well-known bladder cancer study.

165 citations

Journal ArticleDOI
TL;DR: In this article, Dudley-Fernique et al. discuss the problems of the processus p-stables fortement stationnaires, 1
Abstract: On etend le probleme de Dudley-Fernique aux processus p-stables fortement stationnaires, 1

165 citations

ReportDOI
TL;DR: In this paper, the authors give explicit comparisons of expectations of smooth functions and distribution functions of maxima of Gaussian random vectors without any restriction on the covariance matrices, and establish an anti-concentration inequality for the maximum of a Gaussian vector, which derives a useful upper bound on the Levy concentration function for the Gaussian maximum.
Abstract: Slepian and Sudakov–Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give explicit comparisons of expectations of smooth functions and distribution functions of maxima of Gaussian random vectors without any restriction on the covariance matrices. We also establish an anti-concentration inequality for the maximum of a Gaussian random vector, which derives a useful upper bound on the Levy concentration function for the Gaussian maximum. The bound is dimension-free and applies to vectors with arbitrary covariance matrices. This anti-concentration inequality plays a crucial role in establishing bounds on the Kolmogorov distance between maxima of Gaussian random vectors. These results have immediate applications in mathematical statistics. As an example of application, we establish a conditional multiplier central limit theorem for maxima of sums of independent random vectors where the dimension of the vectors is possibly much larger than the sample size.

164 citations

Journal ArticleDOI
TL;DR: In this paper, the variograms of data simulated from stationary Gaussian processes were used to estimate variograms from actual metal concentrations in topsoil in the Swiss Jura, and the variogram was used for kriging.
Abstract: Summary Variograms of soil properties are usually obtained by estimating the variogram for distinct lag classes by the method-of-moments and fitting an appropriate model to the estimates. An alternative is to fit a model by maximum likelihood to data on the assumption that they are a realization of a multivariate Gaussian process. This paper compares the two using both simulation and real data. The method-of-moments and maximum likelihood were used to estimate the variograms of data simulated from stationary Gaussian processes. In one example, where the simulated field was sampled at different intensities, maximum likelihood estimation was consistently more efficient than the method-of-moments, but this result was not general and the relative performance of the methods depends on the form of the variogram. Where the nugget variance was relatively small and the correlation range of the data was large the method-of-moments was at an advantage and likewise in the presence of data from a contaminating distribution. When fields were simulated with positive skew this affected the results of both the method-of-moments and maximum likelihood. The two methods were used to estimate variograms from actual metal concentrations in topsoil in the Swiss Jura, and the variograms were used for kriging. Both estimators were susceptible to sampling problems which resulted in over- or underestimation of the variance of three of the metals by kriging. For four other metals the results for kriging using the variogram obtained by maximum likelihood were consistently closer to the theoretical expectation than the results for kriging with the variogram obtained by the method-of-moments, although the differences between the results using the two approaches were not significantly different from each other or from expectation. Soil scientists should use both procedures in their analysis and compare the results.

164 citations

Journal ArticleDOI
Arak M. Mathai1
TL;DR: A general real matrix-variate probability model is introduced in this paper, which covers almost all real matrixvariate densities used in multivariate statistical analysis, such as Student t, F, Cauchy density, etc.

163 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023502
20221,181
20211,132
20201,220
20191,119
2018978