Consider sequences of statistics Tn(Pni P) of a sample of size ? and the underlying distribution. We analyze a simple data-based procedure proposed by Bickel, G?tze and van Zwet (personal… Expand

We study the asymptotic behavior and limit distributions for sums Sn =bn-1 ∑i=1n ξi,where ξi, i ≥ 1, are i.i.d. random convex compact (cc) sets in a given separable Banach space B and summation is… Expand

Let (Xi)i≥1 be an i.i.d. sequence of random elements in the Banach space B, Sn≔X1+⋅⋅⋅+Xn and ξn be the random polygonal line with vertices (k/n,Sk), k=0,1,...,n. Put ρ(h)=hαL(1/h), 0≤h≤1 with 0<α≤1/2… Expand

Let B be a real separable Banach space with norm || · || = || · || B . Suppose that X, X 1, X 2, … ∈ B are independent and identically distributed (i.i.d.) random elements (r.e.’s) taking values in… Expand

Intraday economic time series are treated as random continuous functions projected onto low dimensional subspace and both B-splines and Fourier bases are considered for data smoothing.Expand

AbstractLet(Xi) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence
$$P\left\{ {\sum\limits_{k = 1}^n {X_k } > \sqrt n r}… Expand

In this paper, we study long memory phenomenon of functional time series. We consider an operator fractional Brownian motion with values in a Hilbert space defined via operator-valued Hurst… Expand