Independent and stationary sequences of random variables

By I. Ibragimov, I. V. Linnik, J. Kingman. 1971

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Citations in the corpus

A general asymptotic scheme for inference under order restrictions (2006, background): “2 in [29] it follows that κ2 exists and that (34) holds, if Assumption A9 is satisfied.”
CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES (2008, background): “fact is an important element of the ideas and techniques of the proof of the CLT for (1.2) (Nn[ϕ]−E{Nn[ϕ]})/(Var{Nn[ϕ]})1/2, viewed as a result of addition of large numbers of small terms (see, e.g., [14], Chapter 18). On the other hand, since the variance of linear statistics of eigenvalues of many”
Applications of distance correlation to time series (2016, methodology): “ we focus on the X-sequence; the proof for the (X;Y)-sequence is analogous and therefore omitted. The convergence of the nite-dimensional distributions of p n(’n X ’ X) follows from Theorem 18.5.2 in Ibragimov and Linnik (1971) combined with the Cramer-Wold device. We need to show tightness of the n”
Martingale approximations for sums of stationary processes (2004, background): “This condition is needed to avoid degeneracy since otherwise there exists a stationary sequence Yn such that g(Xn) = Yn − Yn−1 [Theorem 18.2.2, Ibragimov and Linnik (1971)].”
Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence (2005, unknown): “Phillips, 1987b) that is known to apply in the unit root case. Linkages to the limit theory for the serial correlation coefficient in the stationary case (where α = 0) are established. The paper is organised as follows. Section 2 briefly summarizes the limit theory obtained in PM for autoregressive ”
Central limit theorem for Markov processes with spectral gap in the Wasserstein metric (2011, background): “In this context the results of [18, 22, 36] and [34] should be mentioned.”
Probabilistic Properties of Stochastic Volatility Models (2009, methodology): “holds for some δ > 0, one can apply a classical central limit theorem, see Ibragimov and Linnik [23].”