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We consider n × n random k-circulant matrices with n → ∞ and k = k(n) whose input sequence {al}l≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + δ) moment. We study the asymptotic distribution of the spectral radius, when n = kg + 1. For this, we first derive the tail behaviour of the g fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with appropriate scaling...

Properties of the induced semigroup of an Archimedean copula

Włodzimierz Wysocki (2004)

Applicationes Mathematicae

It is shown that to every Archimedean copula H there corresponds a one-parameter semigroup of transformations of the interval [0,1]. If the elements of the semigroup are diffeomorphisms, then it determines a special function $v_{H}$ called the vector generator. Its knowledge permits finding a pseudoinverse y = h(x) of the additive generator of the Archimedean copula H by solving the differential equation $d y / d x = v_{H} (y) / x$ with initial condition $(d h / d x) (0) = - 1$ . Weak convergence of Archimedean copulas is characterized in terms of vector...

Quantitative asymptotics of graphical projection pursuit.

Meckes, Elizabeth S. (2009)

Electronic Communications in Probability [electronic only]

Quasiasymptotic in $𝒟_{L^{q}}^{'} (ℝ^{n})$ .

Rakić, Dušan (2007)

Novi Sad Journal of Mathematics

Randomized goodness of fit tests

Friedrich Liese, Bing Liu (2011)

Kybernetika

Classical goodness of fit tests are no longer asymptotically distributional free if parameters are estimated. For a parametric model and the maximum likelihood estimator the empirical processes with estimated parameters is asymptotically transformed into a time transformed Brownian bridge by adding an independent Gaussian process that is suitably constructed. This randomization makes the classical tests distributional free. The power under local alternatives is investigated. Computer simulations...