Regularization in statistics

This paper is a selective review of the regularization methods scattered in statistics literature. We introduce a general conceptual approach to regularization and fit most existing methods into it. We have tried to focus on the importance of regularization when dealing with today's high-dimensional objects: data and models. A wide range of examples are discussed, including nonparametric regression, boosting, covariance matrix estimation, principal component estimation, subsampling.     

On Walsh code assignment

We consider the problem of orthogonal variable spreading Walsh code assignments. The aim is to provide assignments that can avoid both complicated signaling from the BS to the users and blind rate and code detection amongst a great number of possible codes. The assignments considered here use partitioning of all users into several pools. Each pool can use its own codes, which are different for different pools. Each user has only a few codes assigned to it within the pool. We state the problem as a combinatorial one expressed in terms of a binary n × k matrix M where n is the number of users and k is the number of Walsh codes in the pool. A solution to the problem is given as a construction of a matrix M which has the assignment property defined in the paper. Two constructions of such M are presented under different conditions on n and k. The first construction is optimal in the sense that it gives the minimal number of Walsh codes — assigned to each user for given n and k. The optimality follows from a proved necessary condition for the existence ofM with the assignment property. In addition, we propose a simple algorithm of optimal assignment for the first construction.     

Self-similar processes in communications networks

This paper reviews and discusses the known definitions and properties of second-order self-similar discrete-time processes and supplements them with some more general conditions of self-similarity. A model for ATM cell traffic is presented and self-similarity conditions of this model are found. This study is motivated by observations that traffic in many real communication networks is self-similar in nature     

Packet multiple access for channel with binary feedback, capture, and multiple reception

This paper considers the multiple access of mobile users to a common wireless channel. The channel is slotted and the binary feedback (empty slot/nonempty slot) is sent to all accessing users. If a slot was not empty and only one user transmitted in it, the transmission is considered successful. Only the user, which had the successful transmission, receives information about its success. In the Introduction, the paper gives a review of known multiple-access algorithms for such a channel. Then our algorithm is constructed that has none of the weaknesses of the algorithms discussed in the Introduction. The algorithm is stable, in contrast to the ALOHA algorithm. It can work in a channel with capture and multiple reception. Without them, the algorithm has a throughput of 0.2891. It is shown how capture and multiple reception can increase the algorithm throughput to 0.6548 and decrease the packet delay for some fading models. The average packet delay and variance are found for two fading models. The models are Rayleigh fading with incoherent and coherent combining of joint interference power. The accessing traffic is Poisson.     

Estimation of matrices with row sparsity

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of an unknown matrix is sparse. We establish minimax optimal rates of convergence for estimating matrices with row sparsity. A major focus in the present paper is on the derivation of lower bounds.     

On a model and capacity of MIMO channels

A model of a MIMO fading channel is considered which does not assume that the discrete-time axis is divided into long intervals with a constant channel. It assumes only that there are ℓ possible states (or subchannels) of the channels, and at each moment both the transmitter and receiver know the channel state. The average input power in the subchannels can be different and not equal to the average input power over the full time axis. We obtain a lower bound for the capacity of the considered vector channel. Also, we consider a vector channel with one transmitting and two or more receiving antennas. We obtain optimum distributions of the average power over the subchannels and lower bounds for the channel capacity.     

Thresholding algorithms, maxisets and well-concentrated bases

The aim of this paper is to synthetically analyse the performances of thresholding and wavelet estimation methods. In this connection, it is useful to describe the maximal sets where these methods attain a special rate of convergence. We relate these “maxisets” to other problems naturally arising in the context of non parametric estimation, as approximation theory or information reduction. A second part of the paper is devoted to isolate two very special properties especially shared by wavelet bases, which allow them to behave almost as in an Hilbertian context even for L _p risks.     

Probability of Heavy Traffic Period in Third Generation CDMA Mobile Communication

The paper considers a problem of deriving the multidimensional distribution of a segment of a long-range dependent traffic in the third generation mobile communication network. An exact expression for the probability is found when a self-similar process from [8] models the traffic. The probability of heavy-traffic period, the outage probability, and the level-crossing probability are found. It is shown that the level crossing probability depends on the average call length only. Further, this probability for traffic with dependent samples is lower than for traffic with independent samples. Also, it is shown that there is a linear dependence between the average heavy traffic interval and the average call length.     

Optimal and robust kernel algorithms for passive stochasticapproximation

The problem of estimating a root of an equation f(x )=0 is considered in the situation where the values of f( x) are measured with random errors at random points and the choice of these points cannot be controlled. Nonlinear modification of the recursive Hardle-Nixdorf method is studied. Almost sure and mean square convergence is proved, and the rate of convergence is estimated. The optimal choice of parameters and of a kernel is presented; it is shown that for the optimal procedure the lower bound for the accuracy of arbitrary methods of solving the problem is attained