Abstract: The local asymptotic normality property is established for a regression model with fractional ARIMA($p, d, q$) errors. This result allows for solving, in an asymptotically optimal way, a variety of inference problems in the long-memory context: hypothesis testing, discriminant analysis, rank-based testing, locally asymptotically minimax andadaptive estimation, etc. The problem of testing linear constraints on the parameters, the discriminant analysis problem, and the construction of locally asymptotically minimax adaptive estimators are treated in some detail.

Abstract: We obtain designs for linear regression models under two main departures from the classical assumptions: (1) the response is taken to be only approximately linear, and (2) the errors are not assumed to be independent, but to instead follow a first-order autoregressive process. These designs have the property that they minimize (a modification of) the maximum integrated mean squared error of the estimated response, with the maximum taken over a class of departures from strict linearity and over all autoregression parameters p, Ipl < 1, of fixed sign. Specific methods of implementation are discussed. We find that an asymptotically optimal procedure for AR(1) models consists of choosing points from that design measure which is optimal for uncorrelated errors, and then implementing them in an appropriate order.

Abstract: Optimal rank-based procedures have been derived for testing arbitrary linear restrictions on the parameters of autoregressive moving average (ARMA) models with unspecified innovation densities. The finite-sample performances of these procedures are investigated here in the context of AR order identification and compared to those of classical (partial correlograms and Lagrange multipliers) methods. The results achieved by rank-based methods are quite comparable, in the Gaussian case, to those achieved by the traditional ones, which, under Gaussian assumptions, are asymptotically optimal. However, under non-Gaussian innovation densities, especially heavy-tailed or nonsymmetric, or when outliers are present, the percentages of correct order selection based on rank methods are strikingly better than those resulting from traditional approaches, even in the case of very short (n = 25) series. These empirical findings confirm the often ignored theoretical fact that the Gaussian case, in the ARMA context...

Abstract: We design asymptotically optimal query strategies for the class of parity functions which contain at most k essential variables. The number of questions asked is at most twice the number asked by an optimal strategy. The strategy presented is even non-adaptive. For fixed k, the number of questions is optimal up to additive constants. Our results improve upon results by Uehara, Tsuchida and Wegener [6].

Abstract: Ordered binary decision diagrams (OBDDs) are nowadays the most common dynamic data structure or representation type for Boolean functions. Among the many areas of application are verification, model checking, and computer aided design. For many functions it is easy to estimate the OBDD size but asymptotically optimal bounds are only known in simple situations. In this paper, methods for proving asymptotically optimal bounds are presented and applied to the solution of some basic problems concerning OBDDs. The largest size increase by a synthesis step of π-OBDDs followed by an optimal reordering is determined as well as the largest ratio of the size of deterministic finite automata and quasi-reduced OBDDs compared to the size of OBDDs. Moreover, the worst case OBDD size of functions with a given number of 1-inputs is investigated.

Abstract: Considers the allocation of a fixed total number of simulation replications among competing design alternatives in order to (i) identify the best simulated design, (ii) intelligently determine the best simulation run lengths for all simulation experiments, and (iii) significantly reduce the total computation cost. An asymptotically optimal allocation rule for maximizing a lower bound of the probability of correct selection is presented. Moreover, we illustrate the efficiency of our method with a series of generic numerical experiments. The simulation cost is significantly reduced with our sequential approach.

Abstract: It is shown that the idea of the successive refinement of interval partitions, which plays the key role in the interval algorithm for random number generation proposed by Han and Hoshi (see ibid., vol.43, p.599-611, 1997) is also applicable to the homophonic coding. An interval algorithm for homophonic coding is introduced which produces an independent and identically distributed (i.i.d.) sequence with probability p. Lower and upper bounds for the expected codeword length are given. Based on this, an interval algorithm for fixed-to-variable homophonic coding is established. The expected codeword length per source letter converges to H(X)/H(p) in probability as the block length tends to infinity, where H(X) is the entropy rate of the source X. The algorithm is asymptotically optimal. An algorithm for fixed-to-fixed homophonic coding is also established. The decoding error probability tends to zero as the block length tends to infinity. Homophonic coding with cost is generally considered. The expected cost of the codeword per source letter converges to c~H(X)/H(p) in probability as the block length tends to infinity, where, c~ denotes the average cost of a source letter. The main contribution of this paper can be regarded as a novel application of Elias' coding technique to homophonic coding. Intrinsic relations among these algorithms, the interval algorithm for random number generation and the arithmetic code are also discussed.

Abstract: Speckman (1988) proposed a kernel smoothing method to estimate the parametric component β in the semiparametric regression model y = x τ β +g(t)+e, and showed that this kernel smoothing estimator is √ n-consistent for a certain deterministic bandwidth choice. However, the important issue of automatic band- width choice in this semiparametric setting has not been examined. This paper studies the asymptotic behavior of the bandwidth choice based on a general band- width selector which covers such well known data-driven methods as GCV and CV. This automatic bandwidth choice is proved to be asymptotically optimal and its asymptotic normality is established. The resulting data-driven kernel smoothing estimator of β is then showed to be still √ n-consistent. A simulation study is per- formed to compare small sample behaviors of various commonly used bandwidth selectors in this semiparametric setting, and a real data example is given.

Abstract: We propose asymptotically optimal algorithms for job shop scheduling. We propose a fluid relaxation for the job shop scheduling problem, in which we replace discrete jobs with the flow of a continuous fluid. We compute an optimal solution of the fluid relaxation in closed form, obtain a lower bound C/sub max/ to the job shop scheduling problem, and construct a feasible schedule from the fluid relaxation with objective value at most C/sub max/+O(/spl radic/C/sub max/), where the constant in the O(/spl middot/) notation is independent of the number of jobs. However, it depends on the processing times of the jobs, thus producing an asymptotically optimal schedule as the total number of jobs tends to infinity. If the initially present jobs increase proportionally, then our algorithm produces a schedule with value at most C/sub max/+O(1). In computational experiments our algorithms produce schedules which are within 1% of optimality even for moderately sized problems.

Abstract: SYNOPTIC ABSTRACTHeteroscedasticity has been a problem in statistics from the start of the field. For example, the Behrens-Fisher Problem (of testing the equality of two normal means when the variances are not known and cannot be assumed equal) has received the attention of Linnik, H. Scheffe, Welch, Chernoff, Chapman, Prokof'yev, Shishkin, B.K. Taneja, and others, and papers on it continue to appear (see Dudewicz and Ahmed (1998) for recent references). A new type of two-stage procedure was put forth by Aoshima, Hyakutake, and Dudewicz (1996) which allows an exact solution, and that solution can be (in some cases) asymptotically optimal. Dudewicz and Ahmed (1998) developed this solution, which is exact, for the Behrens-Fisher Problem, and gave tables needed to achieve level α. In the present paper we: review the previous work (Section 1), state the exact solution (Section 2), give tables needed for level α and power β (Sections 3 & 4), prove asymptotic optimality (Section 5), and give notes and programs ...

Abstract: Consider k (k ≥ 2) populations whose mean θ i and variance σ i 2 are all unknown. For given control values θ0 and σ 0 2 , we are interested in selecting some population whose mean is the largest in the qualified subset in which each mean is larger than or equal to θ0 and whose variance is less than or equal to σ 0 2 . In this paper we focus on the normal populations in details. However, the analogous method can be applied for the cases other than normal in some situations. A Bayes approach is set up and an empirical Bayes procedure is proposed which has been shown to be asymptotically optimal with convergence rate of order O(ln2n/n). A simulation study is carried out for the performance of the proposed procedure and it is found satisfactory.

Abstract: Sequential selection has been solved in linear time by Blum e.a. Running this algorithm on a problem of size N withN >M, the size of the main memory, results in an algorithm that reads and writes O(N) elements, while the number of comparisons is also bounded by O(N). This is asymptotically optimal, but the constants are so large that in practice sorting is faster for most values of M and N. This paper provides the fi rst detailed study of the external selection problem. A randomized algorithm of a conventional type is close to optimal in all respects. Our deterministic algorithm is more or less the same, but fi rst the algorithm builds an index structure of all the elements. This effort is not wasted: the index structure allows the retrieval of elements so that we do not need a second scan through all the data. This index structure can also be used for repeated selections, and can be extended over time. For a problem of size N, the deterministic algorithm reads N + o(N) elements and writes only o(N) elements and is thereby optimal to within lower-order terms.

Abstract: The problem of sequential estimation of the mean, subject to the loss defined as the sum of squared error loss and sampling costs, is considered within the Bayesian framework. It is shown that the sequential procedure, as proposed by Chow and Yu (1981) in classical non-Bayesian sequential estimation, is, in fact, asymptotically Bayes for a large class of prior distributions. The proposed pro- cedure, without using any auxiliary data, is robust in the sense that it does not depend on the distribution of outcome variables and the prior.

Abstract: Two distributed systems are considered for discriminating between two finite-alphabet bivariate memoryless sources and for detecting a known signal in stationary bivariate additive Gaussian noise. Each system comprises two sensors, M-ary local quantizers and a fusion center which makes decisions based on quantized source observations. The problem of asymptotically optimal quantization is considered in detail for the binary (M=2) case. It is shown that optimality is achieved by quantizing a locally computed likelihood ratio wherein one distribution is in general different from the appropriate source marginal. For the problem of detection in Gaussian noise, it is further demonstrated that the optimal distributed system attains the same asymptotic performance as the optimal centralized system for appropriate choice of M.

Abstract: We show two asymptotically optimal probabilistic tree embedding algorithms in hypercubes with constant dilation. These algorithms are slight extension of the random walk algorithm. The first algorithm allows a tree node to have a stay option during each step of a random walk. The second algorithm permits varying length of random walks. Numerical data are given to demonstrate performance improvement.

Abstract: This paper presents an extension of earlier research on hierarchical control of stochastic manufacturing systems with long-run average cost in which a positive inventory deterioration/cancellation rate for each product is assumed. Here we drop the assumption of the positive inventory deterioration/cancellation rate for each product, and give an asymptotic analysis of the manufacturing systems as the rates of change of the machine states approach infinity. We obtain a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. We use a near optimal control of the limiting problem to construct nearly asymptotically optimal open-loop piecewise deterministic controls for the original problem.

Abstract: A reformulation of the Witsenhausen counter-example is considered, where the first station is allowed to transmit its information to the second station through a low noise channel. This is in fact a decentralized stochastic system where the communication uncertainty induces a non-classical information pattern. Assuming a small transmission noise intensity, an asymptotic approach is used in order to find an approximated cost. Then, the necessary conditions for asymptotically optimal strategies are obtained using a variational approach. It is shown that the necessary conditions are satisfied by linear strategies with slightly different coefficients than the noiseless transmission case.

Abstract: In 1979, J.M. Bernardo argued heuristically that in the case of regular product experiments his information theoretic reference prior is equal to Jeffreys' prior. In this context, B.S. Clarke and A.R. Barron showed in 1994, that in the same class of experiments Jeffreys' prior is asymptotically optimal in the sense of Shannon, or, in Bayesian terms, Jeffreys' prior is asymptotically least favorable under Kullback Leibler risk. In the present paper, we prove, based on Clarke and Barron's results, that every sequence of Shannon optimal priors on a sequence of regular iid product experiments converges weakly to Jeffreys' prior. This means that for increasing sample size Kullback Leibler least favorable priors tend to Jeffreys' prior.

Abstract: Scheduling a set of n jobs on a single machine so as to minimize the completion time variance is a well-known NP-hard problem. In this paper, we propose a sequence, which can be constructed in O(n log n) time, as a solution for the problem. Our primary concern is to establish the asymptotical optimality of the sequence within the framework of probabilistic analysis. Our main result is that, when the processing times are randomly and independently drawn from the same uniform distribution, the sequence is asymptotically optimal in the sense that its relative error converges to zero in probability as n increases. Other theoretical results are also derived, including: (i) When the processing times follow a symmetric structure, the problem has 2⌊(n−1)/2⌋ optimal sequences, which include our proposed sequence and other heuristic sequences suggested in the literature; and (ii) when these 2⌊(n−1)/2⌋ sequences are used as approximate solutions for a general problem, our proposed sequence yields the best approximation (in an average sense) while another sequence, which is commonly believed to be a good approximation in the literature, is interestingly the worst. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 373–398, 1999

Abstract: Summary form only given. An alternate approach to representing a data sequence is to associate with each source letter, the list of locations at which it appears in the data sequence. We present a data compression algorithm based on a generalization of this idea. The algorithm parses the data with respect to a static dictionary of phrases and associates with each phrase in the dictionary a list of locations at which the phrase appears in the parsed data. Each list of locations is then run-length encoded. This collection of run-length encoded lists constitutes the compressed representation of the data. We refer to the collection of lists as an inverted index. While in information retrieval systems, the inverted index is an adjunct to the main database used to speed up searching, we regard it here as a self-contained representation of the database itself. Further, our inverted index does not necessarily list every occurrence of a phrase in the data, only every occurrence in the parsing. This allows us to be asymptotically optimal in terms of compression, though at the cost of a loss in searching efficiency. We discuss this trade-off between compression and searching efficiency. We prove that in terms of compression, this algorithm is asymptotically optimal universally over the class of discrete memoryless sources. We also show that pattern matching can be performed efficiently in the compressed domain. Compressing and storing data in this manner may be useful in applications which require frequent searching of a large but mostly static database.

Abstract: To solve the transport problem (hereinafter TP) of linear programming, effective algorithms have been developed (among them the flow algorithms [1-3], the method of potentials [4 ], and the method of residual reduction [3, 4 ]). The efficiency of these algorithms is mainly defined by the number of iterations necessary for solution of the TP. This number depends on specific features of the problem and on the choice of the initial plan. Among flow algorithms of solution of the TP, there are polynomial ones [1, 2], i.e., algorithms having the number of operations (arithmetical operations and operations equivalent to them) limited from above by some polynomial in dimension of the problem. The complexity of the best flow algorithm is equal to O(m2n21og n + mn21og 2 n) operations, where mxn is the dimension (order) of the TP (m ~ n) [1, 2 ]. It is well known [3, 5 ] that the method of potentials is exponential for solution of the TP in the worst case analysis and polynomial in the analysis of computing experiments and the solution of applied problems. The number of iterations in the method of potentials substantially depends on the initial (start) vertex. In most cases, this vertex (support plan) is selected using the minimum-element method (see, e.g., [4 ]), taking into account both the fight-hand sides of the constraints and the coefficients of the objective function of the specific problem. In this connection, the following question is of doubtless interest: How frequently do we encounter an m xn-TP, in which a plan constructed by the minimum-element method is optimal or close to optimal in the value of the objective function? It is natural to analyze this problem in asymptotics (as m -* ,o, n -~ ~). The present paper presents a theoretical substantiation of the closeness of an m xn-TP plan constructed by the minimum-element method to the optimal plan in the sense of relative error of their objective function. Namely, it is proved that as m and n increase, the portion of TPs in which the minimum-element method constructs an asymptotically optimal plan tends to 1 among all problems. Similar studies were made earlier for different extremal problems on graphs (the travelling salesman problem [6, 7 ], the problem on spanning trees and chains [8, 9 ], the problem on perfect matchings [8-10 ] and the k-median [11 ], and the problem on coveting of a graph by chains (stars) [12-14 ]) and the general problem of linear [ 15 ] and integer linear [16, 17 ] programming.

Abstract: In a network of asynchronous processors, the cost to send a message can differ significantly from one communication link to another. In such a setting, it is desirable to factor the cost of links into the cost of distributed computation. Assume that associated with each link is a positive weight representing the cost of sending one message along the link, and the cost of an algorithm executed on a weighted network is the sum of the costs of all messages sent during its execution. We determine the asymptotic complexity of distributed leader election on a weighted unidirectional asynchronous ring assuming this notion of cost, by exhibiting a simple algorithm and a matching lower bound for the problem for any collection of edge weights. As a consequence, we see that algorithms designed for unweighted rings are not in general efficient for the weighted case.

Abstract: Consider the one-way analysis of variance (ANOVA) model Yij=μ+αi+∈ij,i=1,…,a; j = 1,…,b, ∈ij～N(0, σ2) By using the kernel estimation of multivariate density function and its partial derivatives and making use of the estimators of nuisance parameters μ and σ2, we construct the empirical Bayes (EB) estimators of parameter vector α = (α1,…，αa)T Under the existence condition of the second order moment on prior distribution, we obtain their asymptotic optimality

Abstract: It is proved that the method of minimal element almost always constructs an asymptotically optimal plan for multi-index planar decision problem under some additional conditions for the coefficients of the objective function.