Abstract: Importance sampling is recognized as a potentially powerful method for reducing simulation runtimes when estimating the bit error rate (BER) of communications systems using Monte Carlo simulation. Analytically, minimizing the variance of the importance sampling (IS) estimator with respect to the biasing parameters has typically yielded solutions for systems for which the BER could be found analytically. A technique for finding an asymptotically optimal set of biasing parameter values, in the sense that as the resolution of the search and the number of runs used both approach infinity, the algorithm converges to the true optimum, is proposed. The algorithm determines the amount of biasing that minimizes a statistical measure of the variance of the BER estimate and exploits a theoretically justifiable relationship, for small sample sizes, between the BER estimate and the amount of biasing. The translation biasing scheme is considered, although the algorithm is applicable to other parametric IS techniques. Only mild assumptions are required of the noise distribution and system. Experimentally, improvement factors ranging from two to eight orders of magnitude are obtained for a number of distributions for both linear and nonlinear systems with memory. >

Abstract: It is known that the least squares cross-validation bandwidth is asymptotically optimal in the case of kernel-based density and hazard rate estimation in the settings of both complete and randomly right-censored samples. From a practical point of view, it is important to know at what rate the cross-validation bandwidth converges to the optimal. In this paper we answer this question in a general setup which unifies all four possible cases.

Abstract: We propose an asymptotically optimal multiversion B-tree. In our setting, insertions and deletions of data items are allowed only for the present version, whereas range queries and exact match queries are allowed for any version, present or past. The technique we present for transforming a (usual single version) B-tree into a multiversion B-tree is more general: it applies to a number of spatial and non-spatial hierarchical external access structures with certain properties directly, and it can be modified for others. For the B-tree and several other hierarchical external access structures, multiversion capabilities come at no extra cost, neither for storage space nor for runtime, asymptotically in the worst case. The analysis of the behavior of the multiversion B-tree shows that the constant loss of efficiency is low enough to make our suggestion not only a theoretical, but also a practical one.

Abstract: Let ξ1,ξ2,... be random variables which arise as the additive component of a Markov additive process and let Sn =ξ1 + ξ2 + … + ξ n ,n⩾1. Fix M > 0 and let TM be the first index n so that Sn > M (TM = ∞ if Sn ⩽ M for all n). We consider the estimation of the probability ℙ(TM < ∞) by using Monte Carlo simulation and especially importance sampling techniques. Allowing a wide class of possible simulation kernels and using a large deviations criterion for asymptotic efficiency we prove a theorem which exposes a unique asymptotically optimal (M →∞) simulation kernel. The result is applied to a ruin problem.

Abstract: The Distributed Consensus problem involves n processors each of which holds an initial binary value. At most t of the processors may be faulty and ignore any protocol (even behaving maliciously), yet it is required that the non-faulty processors eventually agree on a value that was initially held by one of them. In this paper we focus on consensus in networks whose degree is bounded, following the work of Dwork, Peleg, Pippenger and Upfal [8]. In such a context, complete consensus among all the correct processors is not possible and some exceptions must be allowed. We first show how to achieve consensus in the butterfly network using O(t + log n loglog n) one-bit parallel transmission steps, while tolerating the asymptotically optimal number of faulty processors (O(n/log n)) and having the asymptotically minimal number of exceptions (O(t log t)). This result considerably improves on the running time of existing butterfly consensus protocols [2, 8]. In particular, it replaces the running time of O(n log n loglog n) of [2] with an asymptotically optimal one. As in [8], we can then decrease the number of exceptions to O(t) by using additional links, while maintaining the same running time. The protocol is derived from a consensus protocol for completely connected networks that is interesting in its own right: it achieves Distributed Consensus with optimal number of processors, asymptotically optimal total bit transfer and nearly optimal number of rounds.

Abstract: The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly specified cointegrated Gaussian system, this can be done in a very convenient way. Combining the results of this paper with available general maximum likelihood estimation theories readily shows that the maximum likelihood estimator is asymptotically optimal with a mixed normal limiting distribution. The usefulness of this approach is demonstrated by analyzing a regression model with autoregressive moving average errors and strictly exogenous regressors which may be either integrated of order one, asymptotically stationary, or nonstochastic and bounded.

Abstract: In this paper, the inverse method of nonlinear systems with a nonlinearity is presented, and adaptive control algorithm of this type of nonlinear systems is established. This control algorithm is also suitable for the unstable and (or) inverse unstable systems, achieves virtually asymptotically optimal control and may ensure the closed-loop systems to be globally convergent and stable by choosing weighted polynomials. The simulation results show that the algorithm can overcome the affection of nonlinearity of the systems and may improve control performance. >

Abstract: The problem of performing a global combine (summation) operation on distributed memory computers using a two-dimensional mesh interconnect with wormhole routing is considered. We present algorithms that are asymptotically optimal for short vectors (O(log(p)) for p processing nodes) and for long vecstors (O(n) for n data elements per node), as well as hybrid algorithms that are superior for intermediate n. The algorithms are analyzed using detailed performance models that include the effects of link conflicts and other characteristics of the underlying communication system. The models are validated using experimental data from the Intel Touchstone DELTA computer. We show that while no one algorithm is optimal, each of the presented algorithms is superior under some circumstances.

Abstract: For a change in the mean value parameters of a normal linear model,a class of detecting methods is proposed,which are asymptotically optimal in an appropriate sense. If there exists no nuisance parameters,the Cusum procedure is included in this class.

Abstract: This paper presents an asymptotic analysis of controlled diffusions couled by a parameter process. The oscillation rate of the parameter process is assumed to be very large. This gives rise to a limiting problem in which the stochastic parameter process can be replaced by its averaged value. A control for the original problem can be constructed from the optimal control of the limiting problem in a way which guarantees its asymptotic optimality. It is shown that the value function of the original problem converges to the value function of the limiting problem. The convergence rate of the value function and the error estimate of the constructed asymptotically optimal control are obtained. Finally, the results are applied to an adaptive control problem.

Abstract: We develop necessary and sufficient conditions for importance sampling measures to yield estimates with bounded relative error. We use these conditions to examine the properties of existing methods for estimating failure probabilities in highly reliable systems. We then propose a new approach which we show has bounded relative error and is asymptotically optimal.

Abstract: This paper obtains some extensions of Gilliland and Hannan's results on equivariance and the compound decision problem. Consider a compound decision problem with restricted component risk and component distributions in a norm compact set of mutually absolutely continuous probability measures. Then the method of proof of a theorem of Gilliland and Hannan translates the results of Mashayekhi on symmetrization of product measures into uniform convergence to zero of the excess of the simple envelop over the equivariant envelope. Our envelope results strengthen, among other things, the results of Datta who obtained admissible asymptotically optimal solutions to the compound estimation problem for a large subclass of the real one parameter exponential family under squared error loss. Sufficient conditions for asymptotic optimality of "delete bootstrap" rules are given and, for squared error loss estimation of continuous functions and for finite action space problems with continuous loss functions, the problem of treating the asymptotic excess compound risk of Bayes compound rules is reduced to the question of $L_1$-consistency of certain mixtures. Examples of estimates satisfying the above consistency condition are provided.

Abstract: The authors apply the nonparametric kernel predictor to the time-series prediction problem. Because nonparametric prediction makes few assumptions about the underlying time series, it is useful when modeling uncertainties are pervasive, such as when the time series is non-Gaussian. It is shown that the nonparametric kernel predictor is asymptotically optimal for bounded, mixing time series. Numerical experiments were also performed. For the nonlinear autoregressive process, the kernel predictor is shown to outperform greatly the linear predictor; for the Henon time series, the estimated predictor closely resembles the Henon map. >

Abstract: An algorithm for the constrained problem of estimating the regression coefficients is presented. The algorithm is based on the idea of direct averaging of the observations in order to estimate the search direction. It is shown that if the true parameter belongs to the permitted set, then the algorithm delivers asymptotically optimal estimates of the parameter. Finite convergence of the method is proved when the true parameter lies outside the permitted set. >

Abstract: Let fn(x) denote a kernel density estimator of the density f(x) based on the m.l.e. of the distribution function F associated with the density f(x). Let Ŝ x(x) be the m.l.e. of the survival function S x based on the right censored data and the proportional hazards model of random censorship. The estimate fn(x) depends on the window size,h In this paper it is shown that the least-squares cross-validation method of bandwidth selection is asymptotically optimal under the proportional hazards model of random censorship. This extends the results of Stone (1984) to the proportional hazards model of random censorship.

Abstract: A theory and specific methods for performing optimal transform coding of multispectral images are developed. The theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary Gaussian random processes. Therefore, the methods may be applied to any multilayer data set which meets this assumption. It is demonstrated that a coding scheme consisting of a frequency transform within each layer followed by a separate KL (Karhunen-Loeve) transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large. Two simplifications of this method are also asymptotically optimal if the data can be assumed to satisfy additional constraints. The proposed coding techniques are then implemented using subband filtering methods, and the various algorithms are tested on multispectral images to determine their relative performance characteristics. For the real multispectral images tested, the RSM (real subbands with multiple KL transforms) algorithm gives the best coding performance, with a computational cost only slightly higher than that of the RSS (real subbands with single KL transform) method. >

Abstract: If the quadrature rule Q is applied to the function f, then the error can in many situations be bounded by ps(Q)IIf(S) I I , where p,(Q) is independent of f We obtain the asymptotics of these numbers for the Gaussian method QG (n = 1, 2, ) with very general weight functions and show that p5(QG) is (asymptotically) an upper bound for p5(Q), if Q is any quadrature rule with the same degree as QG

Abstract: The purpose of this paper is to give a new statistical approach to the change diagnosis (detection/isolation) problem. The change detection problem has received extensive research attention. On the contrary, change isolation is mainly an unsolved problem. We consider a stochastic dynamical system with aburpt changes and investigate the multihypothesis extension of Lorden's results. We introduce a joint criterion of optimality for the detection/isolation problem and then design a change detection/isolation algorithm. We also investigate the statistical properties of this algorithm. We prove a lower bound for the criterion in a class of sequential change detection/isolation algorithms. It is shown that the proposed algorithm is asymptotically optimal in this class. The theoretical results are applied to the case of additive changes in linear stochastic models.

Abstract: The problem of coherent multiuser detection is considered for the K-user asynchronous Gaussian Code-Division multiple Access (CDMA) channel. The maximum likelihood sequence detector (MLSD) is asymptotically optimal in that it achieves the highest error exponent of the bit error probability for each user. However, the MLSD can only be implemented by a dynamic programming algorithm whose complexity depends exponentially on K. In order to mitigate the complexity of this scheme, a class of group detection strategies is derived based on optimal statistical inferential procedures. Each member of this class of detectors corresponds to a L group partition of the K users, and consists of a bank of L group detectors, one for demodulating the information symbols of users in each group. Each group detector is a reduced state sequence detector with the dominant complexity determined by the computation of the solution of a combinatorial optimization problem via a forward dynamic programming algorithm. This algorithm has a complexity that is exponential in the number of users in the corresponding group. The overall complexity is determined by the size of the largest group which is a design parameter that can be chosen to be only as large as complexity considerations allow. The performance analysis of the group detection scheme is obtained by deriving asymptotically tight upper and lower bounds on the bit error probability, thereby characterizing its multiuser asymptotic efficiency.