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Explicit solutions of moment problems, I。
Explicit connections between longitudinal data analysis and kernel machines
Best linear unbiased prediction classification generalized linear mixed models machine learning linear mixed models reproducing kernel Hilbert spaces
2009/9/16
Two areas of research – longitudinal data analysis and kernel machines – have large, but mostly distinct, literatures. This article shows explicitly that both fields have much in common with each othe...
Explicit ecpressions for the variogram of first-order intrinsic autoregressions
Appell’s hypergeometric functions F2 F4 first-order intrinsic autoregression
2009/9/16
Exact and explicit expressions for the variogram of first-order intrinsic autoregressions have not been known. Various asymptotic expansions and approximations have been used to compute the variogram....
Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples
Laplace transform Generalized Gamma Convolutions (GGC) Wiener Gamma representation Stieltjes transform Dirichlet processes
2009/5/18
In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes.
...
Explicit Bounds for the Approximation Error in Benford's Law
Approximation Error Benford's Law
2009/3/19
Benford’s law states that for many random variables X > 0 its leading digit D = D(X) satisfies approximately the equation ℙ(D = d) = log 10(1 + 1∕d) for d = 1,2,…,9. This phenomenon follows from...
Explicit expressions for the variogram of first--order intrinsic autoregressions
Appell’s hypergeometric functions F2 F4 First–order intrinsic autoregression Hypergeometric 3F2 4F3 Variogram
2010/3/18
Exact and explicit expressions for the variogram of first–order
intrinsic autoregressions have not been known. Various asymptotic expansions
and approximations have been used to compute the variogra...
Unsupervised bayesian convex deconvolution based on a field with an explicit partition function
Deconvolution Bayesian statistics regularization convex potentials partition function hyperparametersestimation
2010/3/17
This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function.To the best of our knowledge, this is an original contribution. Moreover, the explicit expression...
Explicit Formula for Constructing Binomial Confidence Interval with Guaranteed Coverage Probability
Confidence Interval Probability Statistics Normal Approximation
2010/4/30
In this paper, we derive an explicit formula for constructing the
confidence interval of binomial parameter with guaranteed coverage probability.
The formula overcomes the limitation of normal appro...
The Explicit Chaotic Representation of the powers of increments of Levy Processes
Chaotic representation property Levy process Power jump process Poisson randommeasure Martingale representation
2010/4/29
An explicit formula for the chaotic representation of the powers of increments, (Xt+t0 − Xt0)n ,of a L´evy process is presented. There are two different chaos expansions of a square integr...