Abstract: Using a dynamic linear equation that has a conditionally homoscedastic moving average disturbance, we compare two parameterizations of a commonly used instrumental variables estimator to one that is asymptotically optimal in a class of estimators that includes the conventional one. We find that, for some plausible data-generating processes, the optimal one is distinctly more efficient asymptotically. Simulations indicate that in samples of size typically available, asymptotic theory describes the distribution of the parameter estimates reasonably well but that test statistics sometimes are poorly sized.

Abstract: A concept of asymptotically efficient estimation is presented when a misspecified parametric time series model is fitted to a stationary process. Efficiency of several minimum distance estimates is proved and the behavior of the Gaussian maximum likelihood estimate is studied. Furthermore, the behavior of estimates that minimize the h-step prediction error is discussed briefly. The paper answers to some extent the question what happens when a misspecified model is fitted to time series data and one acts as if the model were true.

Abstract: Two applications of sparsification to parametric computing are given. The first is a fast algorithm for enumerating all distinct minimum spanning trees in a graph whose edge weights vary linearly with a parameter. The second is an asymptotically optimal algorithm for the minimum ratio spanning tree problem, as well as other search problems, on dense graphs.

Abstract: Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.

Abstract: The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful. Asymptotic minimax-type lower bounds are obtained for the unconditional regret, and empirical Bayes rules based on kernel density estimates are shown to possess a certain optimal asymptotic minimax property.

Abstract: Concatenated encoders are found in many digital communication systems. A concatenated receiver for such a system consists of a chain of independently working estimators ended with an outer detector. Each stage of the receiver chain corresponds to a certain code in the system. Maximum likelihood sequence detection with a concatenated receiver requires soft information consisting of symbol aposteriori probabilities to be transferred between the receiver stages. In this paper the optimal inner estimator is derived and further simplified into a new asymptotically optimal one by imposing a tree structure on the inner code. By mapping several suboptimal inner estimators onto the tree structure and noting which approximations they make, a theoretical performance ranking is obtained. The asymptotical performance of the optimal concatenated detector at high signal-to-noise ratios (SNRs) is investigated. The decision variables underlying the pairwise error event probability are shown to be asymptotically Gaussian and consequently a free Euclidean distance can be found for the optimal concatenated detector.

Abstract: In this paper, we treat an optimal control problem of a stochastic two-machine flowshop with machines subject to random breakdown and repair. While the problem is difficult to solve, it can be approximated by a deterministic problem when the rates of machine failure and repair become large. Furthermore, beginning with the solution of the deterministic problem, we can construct a feedback control for the stochastic flowshop that is asymptotically optimal with respect to the rates of changes in machine states. We also show that a threshold type control known also as Kanban control is asymptotically optimal in some cases and not in others.

Abstract: Page's test for the quick detection of a change in distribution is optimized by utilizing the log-likelihood ratio (LLR) as a detector nonlinearity. For signal detection applications, locally optimal nonlinearities are optimal as the signal strength /spl gamma/ goes to zero, however, for non-zero values of /spl gamma/, the performance of Page's test may be improved by applying a subtractive bias. The bias that maximizes an asymptotic (i.e. as the average time between false alarms goes to infinity) performance measure for Page's test for a fixed signal strength is derived for a general detector nonlinearity. Additionally, the bias is derived to minimize the signal strength required to achieve a desired asymptotic performance. These two methods for choosing the bias are shown to be equivalent The asymptotically optimal bias for the LLR nonlinearity is shown to be zero, which is consistent with the optimality of the LLR. Subject to a first order approximation, it is shown that the proposed asymptotically optimal bias is equivalent to an extension of the bias derived by Dyson (1986) which approximately maximizes the relative efficiency between Page's test with the biased locally optimal nonlinearity and Page's test with the LLR nonlinearity. The use of the asymptotically optimal bias is illustrated through an example.

Abstract: We propose a new class of interconnection networks called macro-star networks, which belong to the class of Cayley graphs and use the star graph as a basic building module. A macro-star network can have a node degree that is considerably smaller than that of a star graph of the same size, and diameter that is asymptotically within a factor of 1.25 from a universal lower bound (given its node degree). We show that algorithms developed for star graphs can be emulated on suitably constructed macro-stars with asymptotically optimal slowdown. In particular we obtain asymptotically optimal algorithms to execute the multinode broadcast and total exchange communication tasks in a macro-star network, under both the single-port and the all-port communication models.

Abstract: We consider the empirical Bayes decision problem where the component problem is the sequential estimation of the mean θ of one-parameter exponential family of distributions with squared error loss for the estimation error and a cost c>0 for each observation. The present paper studies the untruncated sequential component case. In particular, an untruncated asymptotically pointwise optimal sequential procedure is employed as the component. With sequential components, an empirical Bayes decision procedure selects both a stopping time and a terminal decision rule for use in the component with parameter θ. The goodness of the empirical Bayes sequential procedure is measured by comparing the asymptotic behavior of its Bayes risk with that of the component procedure as the number of past data increases to infinity. Asymptotic risk equivalence of the proposed empirical Bayes sequential procedure to the component procedure is demonstrated.

Abstract: We study the problem of decentralization of flow control in packet-switching networks under the isarithmic scheme. An incoming packet enters the network only if there are permits available at the entry port when it arrives. The actions of the controllers refer to the routing of permits in the network and the control variables are the corresponding probabilities. We study the behavior of adaptive algorithms implemented at the controllers to update these probabilities and seek optimal performance. This problem can be stated as a routing problem in a closed queueing network. The centralized version of a learning automation is a general framework presented along with the proof of asymptotic optimality. Decentralization of the controller gives rise to non-uniqueness of the optimal control parameters. Non-uniqueness can be exploited to construct asymptotically optimal learning algorithms that exhibit different behavior. We implement two different algorithms for the parallel operation and discuss their differences. Convergence is established using the weak convergence methodology. In addition to our theoretical results, we illustrate the main results using the flow control problem as a model example and verify the predicted behavior of the two proposed algorithms through computer simulations, including an example of tracking.

Abstract: In many areas of application, one searches within finite populations for items of interest, where the probability of sampling an item is proportional to a random size attribute from an i.i.d. superpopulation of attributes which may or may not be observable upon discovery. Here we treat the problem of asymptotically optimal stopping rules for size-dependent searches of this type, as the size of the underlying population grows, where the loss function includes an asymptotically smooth time-dependent cost, a constant cost per item sampled and a cost per undiscovered item which may depend on the size attribute of the undiscovered item. Under some regularity and convexity conditions related to the asymptotic expected loss, we characterize asymptotically optimal rules even when the initial population size and the distribution of size attributes are unknown. We direct especial attention to applications in software reliability, where the items of interest are software faults ("bugs"). In this setting, the size attributes will not be observable when faults are found, and, in addition, our search model allows new bugs to be introduced into the software when faults are detected "imperfect debugging"). Our results extend those of Dalal and Mallows and Kramer and Starr, and are illustrated in the perfect-debugging case on a previously analyzed dataset of Musa.

Abstract: We present an efficient method for assigning any number of processors to tasks associated with the cells of a rectangular uniform grid. Load balancing equi-partition constraints are observed while approximately minimizing the total perimeter of the partition, which corresponds to the amount of interprocessor communication. This method is based upon decomposition of the grid into stripes of “optimal” height. We prove that under some mild assumptions, as the problem size grows large in all parameters, the error bound associated with this feasible solution approaches zero. We also present computational results from a high level parallel Genetic Algorithm that utilizes this method, and make comparisons with other methods. On a network of workstations, our algorithm solves within minutes instances of the problem that would require one billion binary variables in a Quadratic Assignment formulation.

Abstract: We study the problem of approximating a stochastic process Y = {Y(t: t ∈ T} with known and continuous covariance function R on the basis of finitely many observations Y(t 1,), …, Y(t n ). Dependent on the knowledge about the mean function, we use different approximations Ŷ and measure their performance by the corresponding maximum mean squared error sub t∈T E(Y(t) − Ŷ(t))2. For a compact T ⊂ ℝ p we prove sufficient conditions for the existence of optimal designs. For the class of covariance functions on T 2 = [0, 1]2 which satisfy generalized Sacks/Ylvisaker regularity conditions of order zero or are of product type, we construct sequences of designs for which the proposed approximations perform asymptotically optimal.

Abstract: censored observation, and if 6, = 1, X, denotes a survival time, which is the variable of interest In this paper, we apply the martingale method for counting processes to study asymptotic properties for the kernel estimator of the density function of the survival times We also derive an asymptotic expression for the mean integrated square error of the kernel density estimator, which can be used to obtain an asymptotically optimal bandwidth

Abstract: This paper deals with an optimal control problem of stochastic two-machine flowshops with machines subject to random breakdowns and repairs. Since the sizes of both internal and external buffers are practically finite, the problem is one with state constraints. As the problem is extremely difficult to solve, it can be approximated by a deterministic problem in which the stochastic machines' capacities are replaced by their average capacities when the rates of machine failures and repairs become large. An explicit optimal feedback control for the deterministic problem is obtained based on a "constraint domain approximation" approach. Furthermore, beginning with the solution of the deterministic problem, a feedback control for the stochastic flowshops is constructed, which is proved to be asymptotically optimal with respect to the rate of change in machine states.

Abstract: The large deviations of recursive minimum contrast estimators are studied and the asymptotic optimality of these procedures is investigated. A two-stage decision rule which attains the asymptotically optimal rate is suggested

Abstract: Asymptotically optimal and admissible compound decision rules are obtained in a Hilbert-parameterized Gaussian shift experiment. The component parameter set is restricted to compact. For the squared error loss, every compound Bayes estimator is admissible and every compound estimator Bayes versus full support hyperprior mixture of iid priors on the compound parameter is asymptotically optimal. For the latter class of rules induced by full support hyperpriors, asymptotic optimality and admissibility extend to equi- (in decisions) uniformly continuous and bounded risk functions. Normality of certain mixtures of the standard Gaussian process and qualitative robustness of the component Bayes estimator (results of independent interest used in the paper) are derived.

Abstract: In the module allocation problem we are given n tasks to be executed by m processors, subject to both execution and communication costs. The problem is to find an assignment of the tasks to the processors which minimizes the overall cost. We consider various random versions of this problem In particular: When the communication graph GC has an edge probability independent of n we obtain asymptotically optimal (as n→∞) allocation algorithms. When GC is regular with a fixed degree r, we give a simple algorithm with an uniformly bounded approximation ratio.