Narrow Results

Effective call admission control (CAC) is one of the most important techniques to provide the desired quality of service (QoS) in wireless networks. This paper investigates the call admission control problem for the power-controlled CDMA systems. With a macroscopic description for the power control problem, the call admission control for the power-constrained system is analyzed and an admissibility condition is derived. Based on the derived condition, we propose two CAC algorithms. One is an interactive method that provides the optimum performance, but requires some information exchange between base stations. The other can be implemented in a distributed manner and provide a reasonable performance. Through simulations, we show that the proposed algorithms provide an improved performance.

The estimation of the reliability of a series system of k(≥ 2) independent components, where the life time of each component is exponentially distributed, has been considered. First, sufficient conditions for obtaining improvements over scale equivariant estimators for the one-parametric model are derived. As a consequence, we derive estimators that improve upon the maximum likelihood estimator (MLE), an analog of the uniformly minimum variance unbiased estimator (UMVUE) and the best-scale equivariant estimator (BSEE). Bayes and generalized Bayes estimators are also obtained and are shown to be admissible. We consider also the case where the lifetimes follow two-parametric exponential distributions and derive the UMVUE of the system reliability. Further, the MLE and the modified MLE (MMLE) are discussed for this case. Finally, the risks of these estimators are compared numerically for the case k = 2.

We propose a solution to the closed-end fund puzzle in financial markets without a free lunch with vanishing risk. Our results are consistent with both the time-series and the cross-sectional aspect of the closed-end fund puzzle. It turns out that a closed-end fund cannot exist if the fund manager is supposed to receive a fee although he is not able to find mispriced assets in the market. By contrast, a premium can typically be observed at the initial public offering because the fund manager has access to information that enables him to create a dominant strategy. As soon as this weak arbitrage opportunity evaporates, a premium can no longer occur. The reason why a premium quickly turns into a discount might be that the fund manager stops applying a superior trading strategy at some point in time. Another possibility is that abnormal profits are transient in a competitive financial market. In any case, when the fund manager is no longer willing or able to maintain a superior strategy, the fund must trade at a discount in order to compensate for his management fee.

We characterize completely the notion of an exponential dichotomy in average in terms of an admissibility property. The notion corresponds to a generalization of that of an exponential dichotomy to measurable cocycles acting on L¹ functions with respect to a given probability measure. The admissibility property is described in terms of the injectivity and surjectivity of a certain linear operator in the space of bounded sequences of L¹ functions. The characterization is then used to establish in a simple manner the robustness of the notion, in the sense that it persists under sufficiently small linear perturbations. We note that we consider both ℤ-cocycles and ℕ-cocycles.

It is known that a tempered exponential dichotomy (which is the version of nonuniform exponential dichotomy for random dynamical systems) can be described by admissibility of a pair of function classes defined in terms of Lyapunov norms. Moreover, for MET-systems (i.e. random dynamical systems which satisfy the assumptions of the Multiplicative Ergodic Theorem) over an ergodic base system, tempered exponential dichotomy can be described by admissibility of a pair of function spaces which are defined in terms of the original norm. In present paper, we find an admissibility description of tempered exponential dichotomies for MET-systems in terms of new output and input classes. These classes can be regarded as a critical case of admissibility classes in the known result. Finally, we use our new pair of admissible spaces to prove the roughness of tempered exponential dichotomies for parametric MET-systems and give a Hölder continuous dependence of the associated projections on the parameter.

Using established techniques from operations research (linear programming) and well-known measures of probability and value, we present a computational representation and evaluation of imperfect, imprecise user statements in decision analysis. The presentation starts with the structure of a decision problem and a model of the situation is discussed. The courses of action are represented by consequence sets in the decision structure. Statements could have an interval form to reflect the translation of the imperfect input data.

Statistical decision theory is utilized to discriminate between alternatives. Dealing with imprecise statements means encountering decision situations where different alternatives are to prefer in different parts of the consistent solution space to the constraints. Consequently, selection rules based on traditional admissibility are not enough to indicate preferred choices. New admissibility concepts and a procedure for analyzing such situations are discussed. An algorithm for optimizing bilinear functions that does not even require LP is presented.

In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.

We establish regularity properties of weak solutions to linear partial differential equations in terms of the continuous wavelet transform of the data. Our arguments rely on the existence of radial functions that remain radial under the operator defined by the highest order terms of the linear equation and a variant of the inversion formula introduced by Grossmann, Morlet and Paul.

We examine the vanishing adsorption limit of solutions of Riemann problems for the Glimm–Isaacson model of chemical flooding of a petroleum reservoir. A contact discontinuity is deemed admissible if it is the limit of traveling waves or rarefaction waves for an augmented system that accounts for weak chemical adsorption onto the rock. We prove that this criterion justifies the admissibility criteria adopted previously by Keyfitz–Kranzer, Isaacson–Temple and de Souza–Marchesin, provided that the fractional flow function depends monotonically on chemical concentration. We also demonstrate that the adsorption criterion selects the undercompressive contact discontinuities required to solve the general Riemann problem in an example model with non-monotone dependence.

Simultaneous estimation of the vector of variance components under general variance components models with respect to the scale quadratic loss function is considered. A new method of constructing a better estimator and how to deal with the admissibility of quadratic estimators of variance components when the covariance matrix may be singular is presented. Using this method, a necessary condition for admissibility of nonnegative quadratic estimators is given.

Two properties of preferences and representations for choice under uncertainty which play an important role in decision theory are: (i) admissibility, the requirement that weakly dominated actions should not be chosen; and (ii) the existence of well defined conditional probabilities, that is, given any event a conditional probability which is concentrated on that event and which corresponds to the individual's preferences. The conventional Bayesian theory of choice under uncertainty, subjective expected utility (SEU) theory, fails to satisfy these properties — weakly dominated acts may be chosen, and the usual definition of conditional probabilities applies only to nonnull events. This chapter develops a non-Archimedean variant of SEU where decision makers have lexicographic beliefs; that is, there are (first-order) likely events as well as (higher-order) events which are infinitely less likely but not necessarily impossible. This generalization of preferences, from those having an SEU representation to those having a representation with lexicographic beliefs, can be made to satisfy admissibility and yield well defined conditional probabilities and at the same time to allow for “null” events. The need for a synthesis of expected utility with admissibility, and to provide a ranking of null events, has often been stressed in the decision theory literature. Furthermore, lexicographic beliefs are appropriate for characterizing refinements of Nash equilibrium. In this chapter we discuss: axioms on, and behavioral properties of, individual preferences which characterize lexicographic beliefs; probability-theoretic properties of the representations; and the relationships with other recent extensions of Bayesian SEU theory.

Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement — that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide an epistemic framework in which to address this question. Specifically, we formulate conditions of rationality and mth-order assumption of rationality (RmAR) and rationality and common assumption of rationality (RCAR). We show that (i) RCAR is characterized by a solution concept we call a “self-admissible set”; (ii) in a “complete” type structure, RmAR is characterized by the set of strategies that survive m + 1 rounds of elimination of inadmissible strategies; (iii) under certain conditions, RCAR is impossible in a complete structure.

Best-response sets (Pearce [1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger, Friedenberg, and Keisler [2008]) characterizes “rationality and common assumption of rationality.” We analyze the behavior of SAS's in some games of interest — Centipede, the Finitely Repeated Prisoner's Dilemma, and Chain Store. We then establish some general properties of SAS's, including a characterization in perfect-information games.