inference for multiple change points in time series via likelihood ratio scan statistics summary we propose a likelihood ratio scan method for estimating multiple change points in piecewise stationary processes using scan statistics reduces the computationally infeasible global multiple change point estimation problem to a number of single change point detection problems in various local windows the computation can be efficiently performed with order o npt log n consistency for the estimated numbers and locations of the change points are established moreover a procedure is developed for constructing confidence intervals for each of the change points simulation experiments and real data analysis are conducted to illustrate the efficiency of the likelihood ratio scan method

a hybrid lower bound for parameter estimation of signals with multiple change points change point estimation has received much attention in the literature as it plays a significant role in several signal processing applications however the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters namely the parameters associated with the noise distribution and the change point locations in this paper we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters specifically we propose a hybrid cramer rao weiss weinstein bound and derive its associated closed form expressions numerical simulations assess the tightness of the proposed bound in the case of gaussian and poisson observations

most recent changepoint detection in panel data detecting recent changepoints in time series can be important for short term prediction as we can then base predictions just on the data since the changepoint in many applications we have panel

bayesian single and double variable sampling plans for the weibull distribution with censoring the sampling inspection problem is one of the main research topics in quality control in this paper we employ bayesian decision theory to study single and double variable sampling plans for the weibull distribution with type ii censoring a general loss function which includes the sampling cost the time consuming cost the salvage value and the after sales cost is proposed to determine the bayes risk and the corresponding optimal sampling plan explicit expressions for the bayes risks for both single and double sampling plans are derived respectively numerical examples are given to illustrate the effectiveness of the proposed method comparisons between single and double sampling plans are made and sensitivity analysis is performed

a new class of bayesian cyclic bounds for periodic parameter estimation many practical signal processing applications involve estimation of parameters with periodic nature such as phase frequency and direction of arrival estimation the commonly used mean squared error mse risk does not take periodicity into account and thus is inappropriate for periodic parameter estimation in which one is interested in the modulo t error rather than the plain error value as a result mse lower bounds are not valid for periodic estimation in addition conventional bayesian mse lower bounds such as the bayesian cramer rao bound bcrb and the bobrovsky zakai bound bzb require restrictive regularity conditions and usually do not exist in periodic settings an alternative risk which is commonly used in periodic parameter estimation problems is the mean cyclic error mce in this paper we establish a new class of bayesian lower bounds on the mce of any estimator the new class includes cyclic versions of the bcrb and the bzb that have less restrictive regularity conditions than those of the conventional bcrb and bzb respectively the tightest bound in the proposed class is derived and its tightness is discussed in addition the proposed class is extended to mixed vector parameter estimation with both periodic and nonperiodic parameters the new cyclic lower bounds are compared with the mce performance of the minimum mce and maximum a posteriori probability estimators for von mises parameter estimation and for frequency estimation

a general class of lower bounds in parameter estimation a general class of bayesian lower bounds on moments of the error in parameter estimation is formulated and it is shown that the cramer rao the bhattacharyya the bobrovsky zakai and the weiss weinstein lower bounds are special cases in the class the bounds can be applied to the estimation of vector parameters and any given function of the parameters the extension of these bounds to multiple parameter is discussed

capturing the distributional behaviour of the maximum likelihood estimator of a changepoint we consider the problem of estimating the unknown changepoint in a sequence of time ordered observations upper and lower bounds are derived for the asymptotic distribution of the maximum likelihood estimator and methods of approximation are suggested a computationally efficient algorithm is presented for deriving the bounds and approximations for the asymptotic probabilities of the maximum likelihood estimator when the parameters before and after the changepoint are unknown we also show an essentially exponential rate of convergence of the probability distribution of the maximum likelihood estimator from finite samples to the case of infinite samples we apply the algorithm to the cases of normal and exponential distributions for the exponential distribution the lower and upper bounds for the right tail probabilities of the maximum likelihood estimator and the two approximations are identical this is not the case for the normal distribution finally we apply our changepoint analysis for the case of the exponential distribution to data on explosions in british coal mines keywords maximum likelihood estimator maximum of a random walk negative drift parameter change

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

on lower bounds for nonstandard deterministic estimation we consider deterministic parameter estimation and the situation where the probability density function p d f parameterized by unknown deterministic parameters results from the marginalization of a joint p d f depending on random variables as well unfortunately in the general case this marginalization is mathematically intractable which prevents from using the known standard deterministic lower bounds lbs on the mean squared error mse actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard lb can be transformed into a modified one fitted to nonstandard deterministic estimation at the expense of tightness however furthermore these modified lbs mlbs appears to include the submatrix of hybrid lbs which is an lb for the deterministic parameters moreover since in the nonstandard estimation maximum likelihood estimators mles can be no longer derived suboptimal nonstandard mles nsmles are proposed as being a substitute we show that any standard lb on the mse of mles has a nonstandard version lower bounding the mse of nsmles we provide an analysis of the relative performance of the nsmles as well as a comparison with the mlbs for a large class of estimation problems last the general approach introduced is exemplified among other things with a new look at the well known gaussian complex observation models

weiss weinstein bound on multiple change points estimation in the context of multiple change points estimation performance analysis of estimators such as the maximum likelihood is often difficult to assess since the regularity assumptions are not met focusing on the estimators variance one can however use lower bounds on the mean square error in this paper we derive the so called weiss weinstein bound wwb that is known to be an efficient tool in signal processing to obtain a fair overview of the estimation behavior contrary to several works about performance analysis in the change point literature our study is adapted to multiple changes first useful formulas are given for a general estimation problem whatever the considered distribution of the data second closed form expressions are given in the cases of gaussian observations with changes in the mean and or the variance and changes in the mean rate of a poisson distribution furthermore a semidefinite programming formulation of the minimization procedure is given in order to compute the tightest wwb specifically it consists of finding the unique minimum volume covering the set constituted by hyperellipsoid elements that are generated using the derived candidate wwb matrices w r t the so called loewner partial ordering finally simulation results are provided to show the good behavior of the proposed bound

a fresh look at the bayesian bounds of the weiss weinstein family minimal bounds on the mean square error mse are generally used in order to predict the best achievable performance of an estimator for a given observation model in this paper we are interested in the bayesian bound of the weiss weinstein family among this family we have bayesian cramer rao bound the bobrovsky mayerwolf zakai bound the bayesian bhattacharyya bound the bobrovsky zakai bound the reuven messer bound and the weiss weinstein bound we present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator mmsee and on a constrained optimization problem with this approach we obtain a useful theoretical framework to derive new bayesian bounds for that purpose we propose two bounds first we propose a generalization of the bayesian bhattacharyya bound extending the works of bobrovsky mayer wolf and zakai second we propose a bound based on the bayesian bhattacharyya bound and on the reuven messer bound representing a generalization of these bounds the proposed bound is the bayesian extension of the deterministic abel bound and is found to be tighter than the bayesian bhattacharyya bound the reuven messer bound the bobrovsky zakai bound and the bayesian cramer rao bound we propose some closed form expressions of these bounds for a general gaussian observation model with parameterized mean in order to illustrate our results we present simulation results in the context of a spectral analysis problem

asymptotic design of quantizers for decentralized mmse estimation conceptual and practical encoding decoding aimed at accurately reproducing remotely collected observations has been heavily investigated since the pioneering works by shannon about source coding however when the goal is not to reproduce the observables but making inference about an embedded parameter and the scenario consists of many unconnected remote nodes the landscape is less certain we consider a multiterminal system designed for efficiently estimating a random parameter according to the minimum mean square error mmse criterion the analysis is limited to scalar quantizers followed by a joint entropy encoder and it is performed in the high resolution regime where the problem can be more easily mathematically tackled focus is made on the peculiarities deriving from the estimation task as opposed to that of reconstruction as well as on the multiterminal as opposite to centralized character of the inference the general form of the optimal nonuniform quantizer is derived and examples are given

confidence regions and tests for a change point in a sequence of exponential family random variables summary maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables with particular emphasis on the exponential distribution the exact null and alternative distributions of the test statistics are found and the power is compared with a test based on a linear trend statistic exact and approximate confidence regions for the change point are based on the values accepted by a level x likelihood ratio test and a modification of the method proposed by cox spj0tvoll 1982 the methods are applied to a classical data set on the time intervals between coal mine explosions and the change in variation of stock market returns in both cases the confidence regions for the change point cover historical events that may have caused the changes

on the high snr conditional maximum likelihood estimator full statistical characterization in the field of asymptotic performance characterization of the conditional maximum likelihood cml estimator asymptotic generally refers to either the number of samples or the signal to noise ratio snr value the first case has been already fully characterized although the second case has been only partially investigated therefore this correspondence aims to provide a sound proof of a result i e asymptotic in snr gaussianity and efficiency of the cml estimator in the multiple parameters case generally regarded as trivial but not so far demonstrated

random effects weibull regression model for occupational lifetime abstract with great interest we read the recent publication of sohn et al sohn s y chang i s moon t h 2007 random effects weibull regression model for occupational lifetime european journal of operational research 179 124 131 on a weibull regression model with random effects for modelling occupational lifetime we congratulate sohn and colleagues on their comprehensive and clearly written paper nevertheless we would like to comment on two points the first regarding the moments of the underlying weibull distribution the second regarding the relations of sohn s model to the class of frailty models

barankin type lower bound on multiple change point estimation we compute lower bounds on the mean square error of multiple change point estimation in this context the parameters are discrete and the cramer rao bound is not applicable consequently we focus on computing the barankin bound bb the greatest lower bound on the covariance of any unbiased estimator which is still valid for discrete parameters in particular we compute the multi parameter version of the hammersley chapman robbins which is a barankin type lower bound we first give the structure of the so called barankin information matrix bim and derive a simplified form of the bb we show that the particular case of two change points is fundamental to finding the inverse of this matrix several closed form expressions of the elements of bim are given for changes in the parameters of gaussian and poisson distributions the computation of the bb requires finding the supremum of a finite set of positive definite matrices with respect to the loewner partial ordering although each matrix in this set of candidates is a lower bound on the covariance matrix of the estimator the existence of a unique supremum w r t to this set i e the tightest bound might not be guaranteed to overcome this problem we compute a suitable minimal upper bound to this set given by the matrix associated with the loewner john ellipsoid of the set of hyper ellipsoids associated to the set of candidate lower bound matrices finally we present some numerical examples to compare the proposed approximated bb with the performance achieved by the maximum likelihood estimator

inferences for the linear errors in variables with changepoint models abstract a new linear structural errors in variables regression with changepoint model is considered in this model we consider the likelihood ratio test based on the maximum hotelling t 2 for the test of no change against the alternative of exactly one change if there is a change either known a priori or by testing then we estimate the unknown changepoint parameter and some other related parameters by maximum likelihood the limiting distribution of the changepoint estimator is investigated and it is shown that the asymptotic efficiency increases as the absolute regression slope coefficient increases a monte carlo study shows that the proposed estimator performs satisfactorily

bayesian bounds for matched field parameter estimation matched field methods concern estimation of source locations and or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation because of the nonlinear parameter dependence of the signal field the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal to noise ratio snr to study the matched field performance three bayesian lower bounds on mean square error are developed the bayesian crame spl acute r rao bound bcrb the weiss weinstein bound wwb and the ziv zakai bound zzb particularly for a multiple frequency multiple snapshot random signal model a closed form minimum probability of error associated with the likelihood ratio test is derived which facilitates error analysis in a wide scope of applications analysis and example simulations demonstrate that 1 unlike the local crb the bcrb is not achieved by the maximum likelihood estimate mle even at high snr if the local performance is not uniform across the prior parameter space 2 the zzb gives the closest mle performance prediction at most snr levels of practical interest 3 the zzb can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the mle at a given snr 4 incoherent frequency averaging which is a popular multitone processing approach reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline and finally 5 effects of adding additional parameters e g environmental uncertainty can be well predicted from the parameter coupling

estimation and inference in unstable nonlinear least squares models there is compelling evidence that many macroeconomic and financial variables are not generated by linear models this evidence is based on testing linearity against either smooth nonlinearity or piece wise linearity but there is no framework that encompasses both this paper provides an econometric framework that allows for both breaks and smooth nonlinearity in between breaks we estimate the unknown break dates simultaneously with other parameters via nonlinear least squares using new central limit results for nonlinear processes we provide inference methods on break dates and parameter estimates and several instability tests we illustrate our methods via simulated and empirical smooth transition models with breaks

extended ziv zakai lower bound for vector parameter estimation the bayesian ziv zakai bound on the mean square error mse in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than mse the extended bound is evaluated for some representative problems in time delay and bearing estimation the resulting bounds have simple closed form expressions and closely predict the simulated performance of the maximum likelihood estimator in all regions of operation

a class of weiss weinstein bounds and its relationship with the bobrovsky mayer wolf zakai bounds a fairly general class of bayesian large error lower bounds of the weiss weinstein family essentially free from regularity conditions on the probability density functions support and for which a limiting form yields a generalized bayesian cramer rao bound bcrb is introduced in a large number of cases the generalized bcrb appears to be the bobrovsky mayer wolf zakai bound bmzb interestingly enough a regularized form of the bobrovsky zakai bound bzb applicable when the support of the prior is a constrained parameter set is obtained modified weiss weinstein bound and bzb which limiting form is the bmzb are proposed in expectation of an increased tightness in the threshold region some of the proposed results are exemplified with a reference problem in signal processing the gaussian observation model with parameterized mean and uniform prior

analytic sequential weiss weinstein bounds in this paper we explore a sequential bayesian bound for state space models focusing on hybrid continuous and discrete random states we provide an analytic recursion for the sequential weiss weinstein sww bound for linear state space models with solutions for gaussian uniform and exponential distributions as derived as well as for a combination of these we compare the sww bound for discretized states with the corresponding bound for the continuous states the sww bound is contrasted with the sequential cramer rao bound for gaussian distributions practical issues of sww bounds are discussed and numerical simulation results provide insights into their behavior

logistic regression with brownian like predictors this article introduces a new type of logistic regression model involving functional predictors of binary responses and provides an extension of this approach to generalized linear models the predictors are trajectories that have certain sample path properties in common with brownian motion time points are treated as parameters of interest and confidence intervals are developed under prospective and retrospective case control sampling designs in an application to functional magnetic resonance imaging data signals from individual subjects are used to find the portion of the time course that is most predictive of the response this allows the identification of sensitive time points specific to a brain region and associated with a certain task which can be used to distinguish between responses a second application concerns gene expression data in a case control study involving breast cancer where the aim is to identify genetic loci along a chromosome that best discriminate between cases and controls

a lower bound on the mean square error in random parameter estimation corresp a new lower bound on mean square error in parameter estimation is presented the bound is tighter than the cramer rao and bobrovsky zakai lower bounds it requires no bias or regularity assumptions it is computationally simple and it can be applied to estimates of vector parameters or functions of the parameters

a comment on the weiss weinstein bound for constrained parameter sets the weiss weinstein bound wwb provides a lower limit on the mean squared error mse achievable by an estimator of an unknown random parameter in this correspondence it is shown that some previously proposed simplified versions of the bound do not always hold for constrained parameters i e parameters whose distribution has finite support these simplifications can produce results which are no longer lower bounds on the mse sufficient conditions are provided for the reductions to be valid

an economic production lot size model with deteriorating items stock dependent demand inflation and partial backlogging in this paper we present an optimization framework to derive optimal production over a fixed planning horizon for items with a stock dependent demand rate and under inflationary conditions we consider a perishable item that follows a two parameter weibull distribution shortage is allowed and partially backlogged at a fixed rate a numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

a scaling method and its applications to problems in fractional dimensional space a scaling method is proposed to find 1 the volume and the surface area of a generalized hypersphere in a fractional dimensional space and 2 the solid angle at a point for the same space it is demonstrated that the total dimension of the fractional space can be obtained by summing the dimension of the fractional line element along each axis the regularization condition is defined for functions depending on more than one variable this condition is applied 1 to find a closed form expression for the fractional gaussian integral 2 to establish a relationship between a fractional dimensional space and a fractional integral 3 to develop the bochner theorem and 4 to obtain an expression for the fractional integral of the mittag leffler function some possible extensions of this work are also discussed

a comprehensive extension of the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity recently kreng and tan expert systems with applications 37 2010 5514 5522 developed an economic order quantity eoq model under two levels of trade credit policy in which the supplier offers to the wholesaler a permissible delay period m and the wholesaler also provides its retailers a permissible delay period n with m n in this paper we point out some inappropriate mathematical expressions in both interest charged and interest earned in kreng and tan for generality we then extend their model to allow the following facts 1 the interest rate i c charged by the supplier is not necessarily higher than the interest rate i e earned by the wholesaler and 2 the permissible delay period m offered by the supplier is independent of the permissible delay period n offered by the wholesaler furthermore we study the necessary and sufficient conditions for finding the optimal solution and thus establish several theoretical results to characterize the solution that provides the minimum annual total relevant cost finally numerical examples are given to illustrate the theoretical results and obtain some managerial insights

finding optimal s s policies is about as simple as evaluating a single policy in this paper a new algorithm for computing optimal s s policies is derived based upon a number of new properties of the infinite horizon cost function c s s as well as a new upper bound for optimal order up to levels s and a new lower bound for optimal reorder levels s the algorithm is simple and easy to understand its computational complexity is only 2 4 times that required to evaluate a specific single s s policy the algorithm applies to both periodic review and continuous review inventory systems

fractional market dynamics a new extension of a fractality concept in nancial mathematics has been developed we have introduced a new fractional langevin type stochastic dierential equation that diers from the standard langevin equation i by replacing the rst order derivative with respect to time by the fractional derivative of order and ii by replacing white noise gaussian stochastic force by the generalized shot noise each pulse of which has a random amplitude with the stable levy distribution as an application of the developed fractional non gaussian dynamical approach the expression for the probability distribution function pdf of the returns has been established it is shown that the obtained fractional pdf ts well the central part and the tails of the empirical distribution of s p 500 returns c 2000 elsevier science b v all rights reserved

application of the collocation method for solving nonlinear fractional integro differential equations in this paper using the collocation method we solve the nonlinear fractional integro differential equations nfide of the form f t y t a cd t a 0y t a cd t a ry t email protected t y t a tk t s f s y s ds y k a d k k 0 1 m 0 1 we study the convergence and the stability analysis of this method for f t y t a cd t a 0y t a cd t a ry t y t email protected j 0 rb j a cd t a jy t g t some numerical examples are given to show the efficiency of the presented method

an efficient algorithm for computing optimal s s policies this paper presents an algorithm to compute an optimal s s policy under standard assumptions stationary data well behaved one period costs discrete demand full backlogging and the average cost criterion the method is iterative starting with an arbitrary given s s policy and converging to an optimal policy in a finite number of iterations any of the available approximations can thus be used as an initial solution each iteration requires only modest computations also a lower bound on the true optimal cost can be computed and used in a termination test empirical testing suggests very fast convergence

nonparametric inference on structural breaks this paper proposes estimators of location and size of structural breaks in a possibly dynamic nonparametric regression model the structural breaks can be located at given periods of time and or they can be explained by the values taken by some regressor as in threshold models no previous knowledge of the underlying regression function is required the paper also studies the case in which several regressors explain the breaks we derive the rate of convergence and provide central limit theorems for the estimators of the location s and size s a monte carlo experiment illustrates the performance of our estimators in small samples

lattice fractional calculus integration and differentiation of non integer orders for n dimensional physical lattices with long range particle interactions are suggested the proposed lattice fractional derivatives and integrals are represented by kernels of lattice long range interactions such that their fourier series transformations have a power law form with respect to components of wave vector continuous limits for these lattice fractional derivatives and integrals give the continuum derivatives and integrals of non integer orders with respect to coordinates lattice analogs of fractional differential equations that include suggested lattice differential and integral operators can serve as an important element of microscopic approach to nonlocal continuum models in mechanics and physics

fuzzy inventory model for deteriorating items with permissible delay in payment in this paper we extend jamal et al a m m jamal b r sarker s wang an ordering policy for deteriorating items with allowable shortage and permissible delay in payment journal of operations research society 48 1997 826 833 model by fuzzifying the carrying cost rate interest paid rate and interest earned rate simultaneously based on the interval valued fuzzy numbers and triangular fuzzy number to fit the real world we then prove that the estimate of total variable cost per unit time in the fuzzy sense is a strictly pseudo convex function as a result there exists a unique optimal solution to our proposed model moreover we apply the jamal et al example to show the results and to compare with the jamal et al model

estimating structural changes in regression quantiles this paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions the analysis covers time series models as well as models with repeated cross sections we estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates the limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations a procedure to determine the number of breaks is also discussed empirical applications to the quarterly us real gdp growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone

mean squared error and threshold snr prediction of maximum likelihood signal parameter estimation with estimated colored noise covariances an interval error based method mie of predicting mean squared error mse performance of maximum likelihood estimators mles is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix an intermediate step central to adaptive array detection and parameter estimation the successful application of mie requires good approximations of two quantities 1 interval error probabilities and 2 asymptotic snrrarrinfin local mse performance of the mle exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein that in conjunction with the union bound provide accurate prediction of the required interval error probabilities the crameacuter rao bound crb often provides adequate prediction of the asymptotic local mse performance of mle the signal parameters however are decoupled from the colored noise parameters in the fisher information matrix for the deterministic signal model rendering the crb incapable of reflecting loss due to colored noise covariance estimation a new modification of the crb involving a complex central beta random variable different from but analogous to the reed mallett and brennan beta loss factor provides a working solution to this problem facilitating mse prediction well into the threshold region with remarkable accuracy

weiss weinstein lower bounds for markovian systems part 1 theory being essentially free from regularity conditions the weiss weinstein estimation error lower bound can be applied to a larger class of systems than the well known crameacuter rao lower bound thus this bound is of special interest in applications involving hybrid systems i e systems with both continuously and discretely distributed parameters which can represent in practice fault prone systems however the requirement to know explicitly the joint distribution of the estimated parameters with all the measurements makes the application of the weiss weinstein lower bound to markovian dynamic systems cumbersome a sequential algorithm for the computation of the crameacuter rao lower bound for such systems has been recently reported in the literature along with the marginal state distribution the algorithm makes use of the transitional distribution of the markovian state process and the distribution of the measurements at each time step conditioned on the appropriate states both easily obtainable from the system equations a similar technique is employed herein to develop sequential weiss weinstein lower bounds for a class of markovian dynamic systems in particular it is shown that in systems satisfying the crameacuter rao lower bound regularity conditions the sequential weiss weinstein lower bound derived herein reduces for a judicious choice of its parameters to the sequential crameacuter rao lower bound

a bound on mean square estimation error with background parameter mismatch in typical parameter estimation problems the signal observation is a function of the parameter set to be estimated as well as some background environmental system parameters assumed known the assumed background could differ from the true one leading to biased estimates even at high signal to noise ratio snr to analyze this background mismatch problem a ziv zakai type lower bound on the mean square error mse is developed based on the mismatched likelihood ratio test mlrt at high snr the bound incorporates the increase in mse due to estimation bias at low snr it includes the threshold effect due to estimation ambiguity the kernel of the bound s evaluation is the error probability associated with the mlrt a closed form expression for this error probability is derived under a random signal model typical of the bearing estimation passive source localization problem the mismatch is then analyzed in terms of the related ambiguity functions examples of bearing estimation with system array shape mismatch demonstrate that the developed bound describes the simulations of the maximum likelihood estimate well including the sidelobe introduced threshold behavior and the bias at high snr

an epq model with partial backorders considering two backordering costs abstract we propose an epq model with partial backorders considering linear and fixed backordering costs time intervals rather than ordering size and backordering level are used as decision variables to derive the closed form optimal solution our approach analyzes different optimal inventory policies and decides whether shortage period should be scheduled in addition a critical backordering rate is derived to determine the feasible optimal solution the numerical example is provided to illustrate the solution procedure

nonparametric estimation of structural change points in volatility models for time series we propose a hybrid estimation procedure that combines the least squares and nonparametric methods to estimate change points of volatility in time series models its main advantage is that it does not require any specific form of marginal or transitional densities of the process we also establish the asymptotic properties of the estimators when the regression and conditional volatility functions are not known the proposed tests for change points of volatility are shown to be consistent and more powerful than the nonparametric ones in the literature finally we provide simulations and empirical results using the hong kong stock market index hsi series

an epq model with inflation in an imperfect production system in this paper a production inventory model is considered for stochastic demand with the effect of inflation generally every manufacturing system wants to produce perfect quality items however due to real life problems labor problems machine breakdown etc a certain percentage of products are of imperfect quality the imperfect items are reworked at a cost the lifetime of a defective item follows a weibull distribution due to the production of imperfect quality items a product shortage occurs the profit function is derived by using both a general distribution of demand and the uniform rectangular distribution of demand computational experiments along with graphical illustrations are presented to discuss the optimality of the probability functions

exact discretization of fractional laplacian abstract an exact discretization of fractional order laplacian for n dimensional space is suggested particular solutions of fractional order partial difference equations with the proposed discrete laplace operators are suggested

optimization models and a ga based algorithm for stochastic time cost trade off problem in real life projects both the trade off between the project cost and the project completion time and the uncertainty of the environment are considerable aspects for decision makers however the research on the time cost trade off problem seldom concerns stochastic environments besides optimizing the expected value of the objective is the exclusive decision making criterion in the existing models for the stochastic time cost trade off problem in this paper two newly developed alternative stochastic time cost trade off models are proposed in which the philosophies of chance constrained programming and dependent chance programming are adopted for decision making in addition a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi optimal schedules under different decision making criteria the goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments

continuous review inventory model in mixed fuzzy and stochastic environment in this paper we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting since demand plays an important role in such type of inventory systems we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand after fuzzifying the random lead time demand we consider the annual average demand as a fuzzy random variable we provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value since the expected value of a fuzzy random variable is a fuzzy quantity a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution a numerical example is presented to illustrate the proposed model

two storage inventory problem with dynamic demand and interval valued lead time over finite time horizon under inflation and time value of money a finite time horizon inventory problem for a deteriorating item having two separate warehouses one is a own warehouse ow of finite dimension and other a rented warehouse rw is developed with interval valued lead time under inflation and time value of money due to different preserving facilities and storage environment inventory holding cost is considered to be different in different warehouses the demand rate of item is increasing with time at a decreasing rate shortages are allowed in each cycle and backlogged them partially shortages may or may not be allowed in the last cycle and under this circumstance there may be three different types of model here it is assumed that the replenishment cycle lengths are of equal length and the stocks of rw are transported to ow in continuous release pattern for each model different scenarios are depicted depending upon the re order point for the next lot representing the lead time by an interval number and using the interval arithmetic the single objective function for profit is changed to corresponding multi objective functions these functions are maximized and solved by fast and elitist multi objective genetic algorithm femga the models are illustrated numerically and the results are presented in tabular form

new distribution theory for the estimation of structural break point in mean abstract based on the girsanov theorem this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model the exact distribution is asymmetric and tri modal indicating that the estimator is biased these two properties are also found in the finite sample distribution of the least squares ls estimator of structural break point in the discrete time model suggesting the classical long span asymptotic theory is inadequate the paper then builds a continuous time approximation to the discrete time model and develops an in fill asymptotic theory for the ls estimator the in fill asymptotic distribution is asymmetric and tri modal and delivers good approximations to the finite sample distribution to reduce the bias in the estimation of both the continuous time and the discrete time models a simulation based method based on the indirect estimation ie approach is proposed monte carlo studies show that ie achieves substantial bias reductions

stability and non standard finite difference method of the generalized chua s circuit in this paper we develop a framework to obtain approximate numerical solutions of the fractional order chua s circuit with memristor using a non standard finite difference method chaotic response is obtained with fractional order elements as well as integer order elements stability analysis and the condition of oscillation for the integer order system are discussed in addition the stability analyses for different fractional order cases are investigated showing a great sensitivity to small order changes indicating the poles locations inside the physical s plane the grunwald letnikov method is used to approximate the fractional derivatives numerical results are presented graphically and reveal that the non standard finite difference scheme is an effective and convenient method to solve fractional order chaotic systems and to validate their stability

multi item imperfect production lot size model with hybrid number cost parameters in this study we have developed a multi item finite production lot size model with reworking of imperfect quality items when production stops defected items are assumed to rework at a constant rate the cost parameters in this model are taken here as hybrid numbers i e some of the costs are fuzzy numbers as well as random variables then the model is converted into a multi objective geometric programming gp problem a numerical example is given to support the problem a sensitivity analysis has given to study the nature of the objective functions

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

common breaks in means and variances for panel data this paper establishes the consistency of the estimated common break point in panel data consistency is obtainable even when a regime contains a single observation making it possible to quickly identify the onset of a new regime we also propose a new framework for developing the limiting distribution for the estimated break point and show how to construct confidence intervals the least squares method is used for estimating breaks in means and the quasi maximum likelihood qml method is used to estimate breaks in means and in variances qml is shown to be more efficient than the least squares even if there is no change in the variances

an eoq model with delay in payments and stock dependent demand in the presence of imperfect production abstract in real life situation supplier generally offers a delay period to the retailer to buy more in this connection a mathematical model is considered to investigate the retailer s optimal replenishment policy under permissible delay in payment with stock dependent demand within the eoq economic order quantity framework most of the eoq models are considered with infinite replenishment rate in this article the model is considered with finite replenishment rate under progressive payment scheme with the production of defective items within the cycle time the mathematical models have been derived for obtaining the optimal cycle time so that the annual total relevant cost is minimized numerical examples along with graphical representation and sensitivity analysis are provided to illustrate the model

toward lattice fractional vector calculus an analog of fractional vector calculus for physical lattice models is suggested we use an approach based on the models of three dimensional lattices with long range inter particle interactions the lattice analogs of fractional partial derivatives are represented by kernels of lattice long range interactions where the fourier series transformations of these kernels have a power law form with respect to wave vector components in the continuum limit these lattice partial derivatives give derivatives of non integer order with respect to coordinates in the three dimensional description of the non local continuum the fractional differential operators have the form of fractional partial derivatives of the riesz type as examples of the applications of the suggested lattice fractional vector calculus we give lattice models with long range interactions for the fractional maxwell equations of non local continuous media and for the fractional generalization of the mindlin and aifantis continuum models of gradient elasticity

inference regarding multiple structural changes in linear models with endogenous regressors this paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times it is shown that minimization of a generalized method of moments criterion yields inconsistent estimators of the break fractions but minimization of the two stage least squares 2sls criterion yields consistent estimators of these parameters we develop a methodology for estimation and inference of the parameters of the model based on 2sls the analysis covers the cases where the reduced form is either stable or unstable the methodology is illustrated via an application to the new keynesian phillips curve for the us

joint segmentation of multivariate astronomical time series bayesian sampling with a hierarchical model astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series this paper approaches such problems using bayesian priors to represent relationships between signals with various degrees of certainty and not just rigid constraints the segmentation is conducted by using a hierarchical bayesian approach to a piecewise constant poisson rate model a gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

discretizations of nonlinear differential equations using explicit nonstandard methods abstract in a recent paper chen and solis investigated the appearance of spurious solutions when first order odes are discretized using runge kutta schemes they concluded that the reliability of the numerical solutions to a particular ode could be verified only by constructing several discrete models and comparing their numerical results with the known properties of the exact solutions we demonstrate that by using nonstandard schemes all the difficulties found by chen and solis can be eliminated and that qualitatively correct numerical solutions are obtained for all values of the step size we illustrate these issues by applying nonstandard finite difference techniques to the logistic sine cubic and monod equations

fractals with point impact in functional linear regression this paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process when evaluated at a sensitive time point is associated with a scalar response the proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years the trajectories are assumed to have fractal self similar properties in common with a fractional brownian motion with an unknown hurst exponent bootstrap confidence intervals based on the least squares estimator of the sensitive time point are developed misspecification of the point impact model by a functional linear model is also investigated non gaussian limit distributions and rates of convergence determined by the hurst exponent play an important role

τ estimators of regression models with structural change of unknown location abstract this paper concerns with robust estimation of linear regression models with structural change of unknown location under possibly contaminated distributions both for the regressors and for the perturbance term existing estimators will be inefficient in this context furthermore they may protect against outlying yt but cannot cope with leverage points namely outliers in the factor space which could have large influence on the fit as a result these estimators could not discriminate between outlier observations and structural break points misplacing the shift location this fact can be of special importance in practice therefore it may be advisable to consider robust estimators under possible leverage points in a structural change context thus we propose the estimator introduced by yohai and zamar j am stat assoc 83 1988 406 in the standard context of no change this type of estimator is qualitatively robust with the best possible breakdown point and highly efficient under normal errors the asymptotic distribution of the break location estimator is obtained both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases the analysis is carried out in the framework of general ned dependence conditions for the data monte carlo experiments illustrates the performance of our estimators in finite samples

an eoq model for a deteriorating item with time dependent quadratic demand under permissible delay in payment abstract in this paper an eoq economic order quantity model is developed for a deteriorating item having time dependent demand when delay in payment is permissible the deterioration rate is assumed to be constant and the time varying demand rate is taken to be a quadratic function of time mathematical models are also derived under two different circumstances i e case i the credit period is less than or equal to the cycle time for settling the account and case ii the credit period is greater than the cycle time for settling the account the results are illustrated with numerical examples justification for considering a time quadratic demand and permissible delay in payment are discussed

fractional liouville equation on lattice phase space abstract in this paper we propose a lattice analog of phase space fractional liouville equation the liouville equation for phase space lattice with long range jumps of power law types is suggested we prove that the continuum limit transforms this lattice equation into liouville equation with conjugate riesz fractional derivatives of non integer orders with respect to coordinates of continuum phase space an application of the fractional liouville equation with these riesz fractional derivatives to describe properties of plasma like nonlocal media is considered

optimal selling price and lotsize with time varying deterioration and partial backlogging the article deals with an eoq economic order quantity model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted the rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle based on the partial backlogging and lost sale cases the author develops the criterion for the optimal solution for the replenishment schedule and proves the optimal ordering policy is unique moreover the article suggests to new functions regarding price dependent demand and time varying deterioration rate finally numerical examples are illustrated to test the model in various issues

outlier probability of generalized chirpogram based estimators for multicomponent polynomial phase signals outliers are often encountered by estimators that have a nonlinear nature in this paper the probability of outliers is derived concerning the generalized chirpogram gc based estimators for polynomial phase signals pps to derive the approximate theoretical expressions we develop an approach that is based on the extrema theory of complex gaussian envelope and the asymptotic poisson model the semi aliasing effect of pps is also considered in order to predict the outliers more accurately then expressions of the probability of outliers are presented for several typical cases of pps including single tone and chirp signals and their two component versions the gc with the hamming windowing is also incorporated numerical examples of computer simulations are also provided to show the accuracy of the theoretical expressions