In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the semi-algebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the ...

An asymptotic expansion is developed for the joint density of the sum and maximum of an i.i.d. sequence when the parent distribution is in the domain of extreme value attraction of the Gumbel distribution. Previous results by Chow and Teugels, extended by Anderson and Turkman, show that in this situation, the normalized sum and normalized maximum of the sample converge to independent normal and...

In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semi-algebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic struc...

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian Motion (fBM). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein-Uhlenbeck type process studie...

In wireless communication systems, mobile users adapt to a time varying radio channel by regulating transmitter powers. This power control is intended to provide each user an acceptable connection, as measured by a carrier to interference ratio (CIR), by eliminating unnecessary interference. It is important that a power control algorithm can converge quickly to a xed point at which either all u...

Hall and Welsh (1984) established the best attainable rate of convergence for estimates of a positive extreme value index under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution. As a rst generalization we obtain a surprisingly sharp bound on the estimation err...