Related papers: Beyond the Valley of the Covariance Function
This study addresses the often-overlooked issue of measurability at intermediate points when applying Taylor's theorems to random functions and random vectors (e.g., likelihood functions with respect to estimators) in statistics. Classical…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…
We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not…
This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos…
This is a remark on a recent post by P. Denton, S. Parke, T. Tao, X. Zhang, Eigenvectors from eigenvalues, arXiv:1908.03795v1
Discussion of ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]
Discussion of ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]
Discussion of ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]
Discussion of ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]
A new characterization of the multivariate so-called "quasi-Gaussian distribution" (the authors dared to coin a new term) by means of independence their Cartesian and polar coordinates proposed. The authors try to show that these…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
For a given $p$-variable mean $M \colon I^p \to I$ ($I$ is a subinterval of $\mathbb{R}$), following (Horwitz, 2002) and (Lawson and Lim, 2008), we can define (under certain assumption) its $(p+1)$-variable $\beta$-invariant extension as…
The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Ref.19 is extended to the case of the multisymplectic…
We answer to question Nr. 55 [Are there pictorial examples that distinguish covariant and contravariant vectors ?] posed by D. Neuenschwander, Am. J. Phys. 65 (1), 11 (1997)
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On a characterization of critical points of the scalar curvature functional (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 211-217 (2000), Zbl.…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…