on fuzzy subgroups abstract in this communication we prove that n g where n g is the set of all fuzzy normal subgroups of g is a commutative idempotent semisimple semigroup also we give a fuzzy analog of the following well known result if g is a group h l and k are subgroups of g such that h l g and k g then l hk h l k

decentralized data reduction with quantization constraints a guiding principle for data reduction in statistical inference is the sufficiency principle this paper extends the classical sufficiency principle to decentralized inference i e data reduction needs to be achieved in a decentralized manner we examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models we then consider the impact of quantization on decentralized data reduction which is often needed when communications among sensors are subject to finite capacity constraints the central question we intend to ask is if each node in a decentralized inference system has to summarize its data using a finite number of bits is it still optimal to implement data reduction using global sufficient statistics prior to quantization we show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal they include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable

asymptotically optimal quantizers for detection of i i d the asymptotic probability of error for quantization in maximum likelihood tests is analyzed the authors assume quantizers with large numbers of levels generated from a companding function a theorem that relates the companding function to the asymptotic probability of error is proved the companding function is then optimized

design of binary quantizers for distributed detection under secrecy constraints in this paper we investigate the design of distributed detection networks in the presence of an eavesdropper eve we consider the problem of designing binary sensor quantizers that maximize the kullback leibler kl divergence at the fusion center fc when subject to a tolerable constraint on the kl divergence at eve we assume that the channels between the sensors and the fc likewise the channels between the sensors and the eve are modeled as binary symmetric channels bscs in the case of i i d received symbols at both the fc and eve we prove that the structure of the optimal binary quantizers is a likelihood ratio test lrt we also present an algorithm to find the threshold of the optimal lrt and illustrate it for the case of additive white gaussian noise awgn observation models at the sensors in the case of non i i d received symbols at both fc and eve we propose a dynamic programming based algorithm to find efficient quantizers at the sensors numerical results are presented to illustrate the performance of the proposed network

group ordered sprt for decentralized detection the problem of decentralized detection in a large wireless sensor network is considered an adaptive decentralized detection scheme group ordered sequential probability ratio test go sprt is proposed this scheme groups sensors according to the informativeness of their data fusion center collects sensor data sequentially starting from the most informative data and terminates the process when the target performance is reached wald s approximations are shown to be applicable even though the problem setting deviates from that of the traditional sequential probability ratio test sprt to analyze the efficiency of go sprt the asymptotic equivalence between the average sample number of go sprt which is a function of a multinomial random variable and a function of a normal random variable is established closed form approximations for the average sample number are then obtained compared with fixed sample size test and traditional sprt the proposed scheme achieves significant savings in the cost of data fusion

identifiability and estimation of structural vector autoregressive models for subsampled and mixed frequency time series causal inference in multivariate time series is challenging because the sampling rate may not be as fast as the time scale of the causal interactions so the observed series is a subsampled version of the desired series furthermore series may be observed at different sampling rates yielding mixed frequency series to determine instantaneous and lagged effects between series at the causal scale we take a model based approach that relies on structural vector autoregressive models we present a unifying framework for parameter identifiability and estimation under subsampling and mixed frequencies when the noise or shocks is non gaussian by studying the structural case we develop identifiability and estimation methods for the causal structure of lagged and instantaneous effects at the desired time scale we further derive an exact expectation maximization algorithm for inference in both subsampled and mixed frequency settings we validate our approach in simulated scenarios and on a climate and an econometric dataset

high rate vector quantization for detection we investigate high rate quantization for various detection and reconstruction loss criteria a new distortion measure is introduced which accounts for global loss in best attainable binary hypothesis testing performance the distortion criterion is related to the area under the receiver operating characteristic roc curve specifically motivated by sanov s theorem we define a performance curve as the trajectory of the pair of optimal asymptotic type i and type ii error rates of the most powerful neyman pearson test of the hypotheses the distortion measure is then defined as the difference between the area under the curve auc of the optimal pre encoded hypothesis test and the auc of the optimal post encoded hypothesis test as compared to many previously introduced distortion measures for decision making this distortion measure has the advantage of being independent of any detection thresholds or priors on the hypotheses which are generally difficult to specify in the code design process a high resolution zador gersho type of analysis is applied to characterize the point density and the inertial profile associated with the optimal high rate vector quantizer the analysis applies to a restricted class of high rate quantizers that have bounded cells with vanishing volumes the optimal point density is used to specify a lloyd type algorithm which allocates its finest resolution to regions where the gradient of the pre encoded likelihood ratio has greatest magnitude

classification error analysis in stereo vision abstract depth perception in humans is obtained by comparing images generated by the two eyes to each other given the highly stochastic nature of neurons in the brain this comparison requires maximizing the mutual information mi between the neuronal responses in the two eyes by distributing the coding information across a large number of neurons unfortunately mi is not an extensive quantity making it very difficult to predict how the accuracy of depth perception will vary with the number of neurons n in each eye to address this question we present a two arm distributed decentralized sensors detection model we demonstrate how the system can extract depth information from a pair of discrete valued stimuli represented here by a pair of random dot matrix stereograms using the theory of large deviations we calculated the rate at which the global average error probability of our detector and the mi between the two arms output vary with n we found that mi saturates exponentially with n at a rate which decays as 1 n the rate function approached the chernoff distance between the two probability distributions asymptotically our results may have implications in computer stereo vision that uses hebbian based algorithms for terrestrial navigation

quantization via empirical divergence maximization empirical divergence maximization edm refers to a recently proposed strategy for estimating f divergences and likelihood ratio functions this paper extends the idea to empirical vector quantization where one seeks to empirically derive quantization rules that maximize the kullback leibler divergence between two statistical hypotheses we analyze the estimator s error convergence rate leveraging tsybakov s margin condition and show that rates as fast as n 1 are possible where n equals the number of training samples we also show that the flynn and gray algorithm can be used to efficiently compute edm estimates and show that they can be efficiently and accurately represented by recursive dyadic partitions the edm formulation have several advantages first the formulation gives access to the tools and results of empirical process theory that quantify the estimator s error convergence rate second the formulation provides a previously unknown derivation for the flynn and gray algorithm third the flexibility it affords allows one to avoid a small cell assumption common in other approaches finally we illustrate the potential use of the method through an example

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

fuzzy sets and sheaves part ii this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete w valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

on the subexponential decay of detection error probabilities in long tandems we consider the problem of bayesian decentralized binary hypothesis testing in a network of sensors arranged in a tandem we show that the rate of error probability decay is always subexponential establishing the validity of a long standing conjecture under the additional assumption of bounded kullback leibler kl divergences we show that for all d 1 2 the error probability is omega e c nd where c is a positive constant furthermore the bound omega e c logn d for all d 1 holds under an additional mild condition on the distributions this latter bound is shown to be tight

asymptotic optimality theory for decentralized sequential hypothesis testing in sensor networks the decentralized sequential hypothesis testing problem is studied in sensor networks where a set of sensors receive independent observations and send summary messages to the fusion center which makes a final decision in the scenario where the sensors have full access to their past observations the first asymptotically bayes sequential test is developed having the same asymptotic performance as the optimal centralized test that has access to all sensor observations next in the scenario where the sensors do not have full access to their past observations a simple but asymptotically bayes sequential tests is developed in which sensor message functions are what we call tandem quantizer where each sensor only uses two different sensor quantizers with at most one switch between these two possibilities moreover a new minimax formulation of optimal stationary sensor quantizers is proposed and is studied in detail in the case of additive gaussian sensor noise finally our results show that in the simplest models feedback from the fusion center does not improve asymptotic performance in the scenario with full local memory however even a one shot one bit feedback can significantly improve performance in the case of limited local memory

high rate vector quantization for the neyman pearson detection of correlated processes this paper investigates the effect of quantization on the performance of the neyman pearson test it is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process each sample is passed through an n point quantizer and transmitted to a decision device which performs a binary hypothesis test for any false alarm level it is shown that the miss probability of the neyman pearson test converges to zero exponentially as the number of samples tends to infinity assuming that the observed process satisfies certain mixing conditions the main contribution of this paper is to provide a compact closed form expression of the error exponent in the high rate regime i e when the number n of quantization levels tends to infinity generalizing previous results of gupta and hero to the case of nonindependent observations if d represents the dimension of one sample it is proved that the error exponent converges at rate n2 d to the one obtained in the absence of quantization as an application relevant high rate quantization strategies which lead to a large error exponent are determined numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error

the ϑ lower and t upper fuzzy rough approximation operators on a semigroup in this paper we consider a semigroup as a universal set and investigate the properties of q lower and t upper fuzzy rough approximation operators a new fuzzy algebraic structure called a tl fuzzy rough semigroup is introduced and some related properties are studied finally the homomorphism properties of q lower and t upper fuzzy rough approximation operators are investigated

representation of lattices by fuzzy weak congruence relations fuzzy lattice valued weak congruences of abstract algebras are investigated for an algebra the family of all such fuzzy relations is a complete lattice its structure and cut properties are investigated and fully described these fuzzy weak congruences are applied in representation of complete and algebraic lattices a wider class of lattices can be represented in such a fuzzy framework than in classical algebra we prove that there is a straightforward representation of any complete lattice using it as a co domain in a more general case it is proved that several subdirect powers of lattices are also representable by fuzzy weak congruences

quantization effect on the log likelihood ratio and its application to decentralized sequential detection it is well known that quantization cannot increase the kullback leibler divergence which can be thought of as the expected value or first moment of the log likelihood ratio in this paper we investigate the quantization effects on the second moment of the log likelihood ratio it is shown via the convex domination technique that quantization may result in an increase in the case of the second moment but the increase is bounded above by 2 e the result is then applied to decentralized sequential detection problems not only to provide simpler sufficient conditions for asymptotic optimality theories in the simplest models but also to shed new light on more complicated models in addition some brief remarks on other higher order moments of the log likelihood ratio are also provided

on the optimality of the likelihood ratio test for local sensor decision rules in the presence of nonideal channels distributed detection has been intensively studied in the past in this correspondence we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center under the conditional independence assumption among multiple sensor observations we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood ratio test lrt given a particular constraint on the fusion rule this constraint turns out to be quite general and is easily satisfied for most sensible fusion rules a design example using a parallel sensor fusion structure with binary symmetric channels bscs between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations the study that incorporates the transmission channel in the sensor system design may have potential applications in the emerging field of wireless sensor networks

distributivity in lattices of fuzzy subgroups the main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive we obtain a characterization of these groups which is similar to a well known result of group theory

information bounds and quickest change detection in decentralized decision systems the quickest change detection problem is studied in decentralized decision systems where a set of sensors receive independent observations and send summary messages to the fusion center which makes a final decision in the system where the sensors do not have access to their past observations the previously conjectured asymptotic optimality of a procedure with a monotone likelihood ratio quantizer mlrq is proved in the case of additive gaussian sensor noise if the signal to noise ratios snr at some sensors are sufficiently high this procedure can perform as well as the optimal centralized procedure that has access to all the sensor observations even if all snrs are low its detection delay will be at most pi 2 1ap 57 larger than that of the optimal centralized procedure next in the system where the sensors have full access to their past observations the first asymptotically optimal procedure in the literature is developed surprisingly the procedure has the same asymptotic performance as the optimal centralized procedure although it may perform poorly in some practical situations because of slow asymptotic convergence finally it is shown that neither past message information nor the feedback from the fusion center improves the asymptotic performance in the simplest model

fuzzy congruences in groups the purpose of this paper is to introduce some basic concepts of fuzzy congruence and to prove some fundamental properties we obtain several results which are analogs of some basic theorems of group theory in particular we prove that in a group g the lattice of some fuzzy normal subgroups is modular

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

quantization for maximin are in distributed estimation we consider the design of optimal quantizers for the distributed estimation of a deterministic parameter in particular we design deterministic scalar quantizers to maximize the minimum asymptotic relative efficiency are between quantized and unquantized ml estimators we first design identical quantizers using the class of score function quantizers sfq we show that the structure of sfqs generally depend on the parameter value but can be expressed as thresholds on the sufficient statistic for a large class of distributions we provide a convergent iterative algorithm to obtain the best sfq that maximizes the minimum are for distributions of that class we compare the performance of the optimal sfq with a general quantizer designed without making any restrictions on the structure this general quantizer is hard to implement due to lack of structure but is optimal if the iterative design algorithm does not encounter local minima through numerical simulations we illustrate that the two quantizers designed are identical in other words the optimal quantizer structure is that of an sfq for a distributed estimation setup designing identical quantizers is shown to be suboptimal we therefore propose a joint multiple quantizer design algorithm based on a person by person optimization technique employing the sfq structure using numerical examples we illustrate the gain in performance due to designing nonidentical quantizers

detection in sensor networks the saddlepoint approximation this paper presents a computationally simple and accurate method to compute the error probabilities in decentralized detection in sensor networks the cost of the direct computation of these probabilities e g the probability of false alarm the probability of a miss or the average error probability is combinatorial in the number of sensors and becomes infeasible even with small size networks the method is based on the theory of large deviations in particular the saddlepoint approximation and applies to generic parallel fusion sensor networks including networks with nonidentical sensors nonidentical observations and unreliable communication links the paper demonstrates with parallel fusion sensor network problems the accuracy of the saddlepoint methodology 1 computing the detection performance for a variety of small and large sensor network scenarios and 2 designing the local detection thresholds elsewhere we have used the saddlepoint approximation to study tradeoffs among parameters for networks of arbitrary size

asymptotic optimality theory for decentralized sequential multihypothesis testing problems the bayesian formulation of sequentially testing m 3 hypotheses is studied in the context of a decentralized sensor network system in such a system local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations asymptotically optimal decentralized sequential tests are developed from a class of two stage tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage it is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most m 1 unambiguous likelihood quantizers ulq we first present in detail our results for the system with a single sensor and binary sensor messages and then extend to more general cases involving any finite alphabet sensor messages multiple sensors or composite hypotheses

groups operating on fuzzy sets in crisp environment the notions of normal subgroup and group operating on a set are well known due to many applications in this paper we study extensions of these classical notions to the larger universe of fuzzy sets we obtain a characterization of operations of a fuzzy group on a fuzzy set in terms of homomorphisms of crisp groups

fuzzy sets and sheaves part ii sheaf theoretic foundations of fuzzy set theory with applications to algebra and topology this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

the dimensionality of the aliasing problem in models with rational spectral densities this paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data it analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models it focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of the time series data this abstract was borrowed from another version of this item

on optimal quantization rules for some problems in sequential decentralized detection we consider the design of systems for sequential decentralized detection a problem that entails several interdependent choices the choice of a stopping rule specifying the sample size a global decision function a choice between two competing hypotheses and a set of quantization rules the local decisions on the basis of which the global decision is made this correspondence addresses an open problem of whether in the bayesian formulation of sequential decentralized detection optimal local decision functions can be found within the class of stationary rules we develop an asymptotic approximation to the optimal cost of stationary quantization rules and exploit this approximation to show that stationary quantizers are not optimal in a broad class of settings we also consider the class of blockwise stationary quantizers and show that asymptotically optimal quantizers are likelihood based threshold rules

embedding lattices of fuzzy subalgebras into lattices of crisp subalgebras abstract given a universal algebra a we define an algebra a where a and a are of the same type and generate the same variety of algebra next we define a map e lf a lc a where lf a is the lattice of fuzzy subalgebras of a and lc a is the lattice of crisp subalgebras of a for many algebras a the map e is shown to be a lattice embedding as a corollary of this fact we derive the results that the lattice of fuzzy normal subgroups of a group and the lattice of fuzzy ideals of a ring are both modular lattices

fine quantization in signal detection and estimation the performance lost to data quantization in signal detection and estimation procedures is considered the performance is measured by f divergences which are useful indices of discrimination information between statistical hypotheses some properties of the f divergences are briefly discussed and a general result for the loss in divergence due to uniform data quantization is obtained several applications of this result in specific problems of signal detection and estimation being developed and some numerical results that illustrate the asymptotic behavior of the divergence in these applications are given the divergence lost to finite nonuniform quantization through the use of a companding model is considered and the asymptotically optimum nonuniform quantizer within this class is derived some interesting problems that remain open are discussed

distributed structures sequential optimization and quantization for detection in the design of distributed quantization systems one inevitably confronts two types of constraints those imposed by a distributed system s structure and those imposed by how the distributed system is optimized structural constraints are inherent properties of any distributed quantization system and are normally summarized by functional relationships defining the inputs and outputs of their component quantizers the use of suboptimal optimization methods are often necessitated by the computational complexity encountered in distributed problems this correspondence briefly explores the impact and interplay of these two types of constraints in the context of distributed quantization for detection we introduce two structures that exploit interquantizer communications and that represent extremes in terms of their structural constraints we then develop a sequential optimization scheme that maximizes the kullback leibler divergence takes advantage of statistical dependencies in the distributed system s output variables and leads to simple parameterizations of the component quantization rules we present an illustrative example from which we draw insights into how these constraints influence the quantization boundaries and affect performance relative to lower and upper bounds

bayesian detection in bounded height tree networks we study the detection performance of large scale sensor networks configured as trees with bounded height in which information is progressively compressed as it moves towards the root of the tree we show that under a bayesian formulation the error probability decays exponentially fast and we provide bounds for the error exponent we then focus on the case where the tree has certain symmetry properties we derive the form of the optimal exponent within a restricted class of easily implementable strategies as well as optimal strategies within that class we also find conditions under which suitably defined majority rules are optimal finally we provide evidence that in designing a network it is preferable to keep the branching factor small for nodes other than the neighbors of the leaves

optimum quantization for detection vector quantization is a procedure widely used in communications the problem has been solved for the basic detection situation using the locally optimal procedure and with some constraints on the quantization scheme it is stated in its widest sense which consists of finding the partition of the observation space and the values associated with it in such a way that the detection performance is optimal it is solved completely with the deflection criterion and the solution introduces the concept of quantization by a likelihood ratio procedure

linear precoders for the detection of a gaussian process in wireless sensors networks we investigate the performance of neyman pearson detection of a stationary gaussian process in noise using a large wireless sensor network wsn in our model each sensor compresses its observation sequence using a linear precoder and a final decision is taken by a fusion center fc based on the compressed information two families of precoders are studied random i i d precoders and orthogonal precoders we analyse their performance under a regime where both the number of sensors k and the number of samples n per sensor tend to infinity at the same rate that is k n c 0 1 contributions are as follows 1 using results from random matrix theory and large toeplitz matrices we prove that when the above families of precoders are used the miss probability of the neyman pearson detector converges exponentially to zero closed form expressions of the corresponding error exponents are derived 2 in particular we propose a practical orthogonal precoding strategy the principal frequencies strategy pfs which achieves the best error exponent among all orthogonal strategies and which requires very little signaling overhead between the central processor and the nodes of the network 3 when the pfs is used a simplified low complexity testing procedure can be implemented at the fc we show that the proposed suboptimal test enjoys the same error exponent as the neyman pearson test which indicates a similar asymptotic behavior of the performance we illustrate our findings by numerical experiments on several examples

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

quantization in multisensor random signal detection optimum detection schemes based on quantized data are of great interest in radar and sonar applications the design and properties of multisensor schemes are considered here for detection of weak random signals in additive possibly non gaussian noise signal to noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided the best schemes for originally quantizing the observations are also studied for the case of asymptotically large observation sample sizes these schemes are shown to minimize the mean squared error between the best weak signal test statistic based on unquantized observations and the best weak signal test statistic based on quantized observations under signal absent numerical results indicate it is sometimes best for each quantizer to use different size alphabets when a quantizer is located at each sensor

on optimum and nearly optimum data quantization for signal detection the application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered this application is twofold allowing for greater simplicity in both analysis and design of quantizers for detection systems most computational methods for designing optimum most efficient quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions companding approximation theory is used here to obtain suitable initial conditions for this problem furthermore the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large in this design iteration is not needed to derive the parameters of the quantizer and the design procedure is very simple in this paper we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems

adaptive learning vector quantization for online parametric estimation this paper addresses the problem of parameter estimation in a quantized and online setting a sensing unit collects random vector valued samples from the environment these samples are quantized and transmitted to a central processor which generates an online estimate of the unknown parameter this paper provides a closed form expression of the excess mean square error mse caused by quantization in the high rate regime i e when the number of quantization levels is supposed to be large next we determine the quantizers which mitigate the excess mse the optimal quantization rule unfortunately depends on the unknown parameter to circumvent this issue we introduce a novel adaptive learning vector quantization scheme which allows to simultaneously estimate the parameter of interest and select an efficient quantizer

cooperative sequential spectrum sensing based on level triggered sampling we propose a new framework for cooperative spectrum sensing in cognitive radio networks that is based on a novel class of nonuniform samplers called the event triggered samplers and sequential detection in the proposed scheme each secondary user su computes its local sensing decision statistic based on its own channel output and whenever such decision statistic crosses certain predefined threshold values the secondary user will send one or several bit of information to the fusion center fc the fc asynchronously receives the bits from different sus and updates the global sensing decision statistic to perform a sequential probability ratio test sprt to reach a sensing decision we provide an asymptotic analysis for the above scheme and under different conditions we compare it against the cooperative sensing scheme that is based on traditional uniform sampling and sequential detection simulation results show that the proposed scheme using even 1 bit can outperform its uniform sampling counterpart that uses infinite number of bits under changing target error probabilities snr values and number of sus

extended yule walker identification of varma models with single or mixed frequency data chen and zadrozny 1998 developed the linear extended yule walker xyw method for determining the parameters of a vector autoregressive var model with available covariances of mixed frequency observations on the variables of the model if the parameters are determined uniquely for available population covariances then the var model is identified the present paper extends the original xyw method to an extended xyw method for determining all arma parameters of a vector autoregressive moving average varma model with available covariances of single or mixed frequency observations on the variables of the model the paper proves that under conditions of stationarity regularity miniphaseness controllability observability and diagonalizability on the parameters of the model the parameters are determined uniquely with available population covariances of single or mixed frequency observations on the variables of the model so that the varma model is identified with the single or mixed frequency covariances

extremal properties of likelihood ratio quantizers m hypotheses and a random variable y with a different probability distribution under each hypothesis are considered a quantizer is applied to form a quantized random variable gamma y the extreme points of the set of possible probability distributions of gamma y as gamma ranges over all quantizers is characterized optimality properties of likelihood ratio quantizers are established for a very broad class of quantization problems including problems involving the maximization of an ali silvey 1966 distance measure and the neyman pearson variant of the decentralized detection problem

dynamic identification of dynamic stochastic general equilibrium models this paper studies dynamic identification of parameters of a dynamic stochastic general equilibrium model from the first and second moments of the data classical results for dynamic simultaneous equations do not apply because the state space solution of the model does not constitute a standard reduced form full rank of the jacobian matrix of derivatives of the solution parameters with respect to the parameters of interest is necessary but not sufficient for identification we use restrictions implied by observational equivalence to obtain two sets of rank and order conditions one for stochastically singular models and another for nonsingular models measurement errors mean long run and a priori restrictions can be accommodated an example is considered to illustrate the results

data fusion trees for detection does architecture matter we consider the problem of decentralized detection in a network consisting of a large number of nodes arranged as a tree of bounded height under the assumption of conditionally independent and identically distributed i i d observations we characterize the optimal error exponent under a neyman pearson formulation we show that the type ii error probability decays exponentially fast with the number of nodes and the optimal error exponent is often the same as that corresponding to a parallel configuration we provide sufficient as well as necessary conditions for this to happen for those networks satisfying the sufficient conditions we propose a simple strategy that nearly achieves the optimal error exponent and in which all non leaf nodes need only send 1 bit messages