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The stochastic Fourier transform, or SFT for short, is an application that transforms a square integrable random function f(t, ω) to a random function defined by the following series; T𝜖,φf(t,ω):=∑n𝜖nf̂n(ω)φn(t) ${\mathcal T}_{\epsilon , \varphi }f(t,\o ):= {\sum }_{n} \epsilon _{n} \hat {f}_{n}(\o )\varphi _{n}(t)$ where {𝜖n} is an ℓ2-sequence such that 𝜖n ≠ 0, ∀n and f̂n is the...
Given a partition {I1, …, Ik} of {1, …, n}, let (X1, …, Xn) be random vector with each Xi taking values in an arbitrary measurable space (S,S) $(S,\mathcal {S})$ such that their joint law is invariant under finite permutations of the indexes within each class Ij. Then, it is shown that this law has to be a signed mixture of independent laws and identically distributed within each class Ij. We provide...
The Sigma function, which is the sum of the squares of the number of occurrences of every factor, is a criterion of randomness, measuring specially the uniformity of the block distribution. An infinite word whose prefixes attain asymptotically the smallest possible value of it is called Sigma-random. We prove that the Champernowne word is Sigma-random. We also consider less complex words which have...
In this paper we revisit the so-called non-stationary regression models for repeated categorical/multinomial data collected from a large number of independent individuals. The main objective of the study is to obtain consistent and efficient regression estimates after taking the correlations of the repeated multinomial data into account. The existing (1) ‘working’ odds ratios based GEE (generalized...
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and memory, and so fixed rank kriging has been proposed as a solution. The method however still involves operations on large matrices, so we develop an alteration to this...
In this paper, we consider the pretest, shrinkage, and penalty estimation procedures for generalized linear mixed models when it is conjectured that some of the regression parameters are restricted to a linear subspace. We develop the statistical properties of the pretest and shrinkage estimation methods, which include asymptotic distributional biases and risks. We show that the pretest and shrinkage...
We consider in this paper simultaneous Bayesian variable selection and estimation for linear regression models with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that selects a variable if the ratio of the posterior mean of its regression coefficient to the corresponding ordinary least square estimate is greater than a half. The regression...
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