on the shannon measure of entropy abstract this paper deals with the axiomatic characterization of shannon s entropy for generalized probability distributions a renyi 1961 also the author has extended shannon s entropy to subsets of n dimensional euclidean space n 1 2 3 finally he has introduced a functional equation which is a generalization of the one due to t w chaundy and j b mcleod 1963

change point estimation using nonparametric regression we consider a regression model in which the mean function may have a discontinuity at an unknown point we propose an estimate of the location of the discontinuity based on one side nonparametric regression estimates of the mean function the change point estimate is shown to converge in probability at rate 0 n 1 and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models confidence regions for the location and size of the change are also discussed

a co evolutionary multi objective optimization algorithm based on direction vectors most real world multi objective problems mops have a complicated solution space facing such problems a direction vectors based co evolutionary multi objective optimization algorithm dvcmoa that introduces the decomposition idea from moea d to co evolutionary algorithms is proposed in this paper it is novel in the sense that dvcmoa applies the concept of direction vectors to co evolutionary algorithms dvcmoa first divides the entire population into several subpopulations on the basis of the initial direction vectors in the objective space then it solves mops through the co evolutionary interaction among the subpopulations in which individuals are classified according to their direction vectors finally it explores the less developed regions to maintain the relatively uniform distribution of the solution space in this way dvcmoa has advantages in convergence diversity and uniform distribution of the non dominated solution set which are explained through comparison with other state of the art multi objective optimization evolutionary algorithms moeas in this paper dvcmoa is shown to be effective on 6 multi objective 0 1 knapsack problems

efficient estimation of conditional variance functions in stochastic regression author s fan jianqing yao qiwei abstract conditional heteroscedasticity has been often used in modelling and understanding the variability of statistical data under a general setup which includes the nonlinear time series model as a special case we propose an e cient and adaptive method for estimating the conditional variance the basic idea is to apply a local linear regression to the squared residuals we demonstrate that without knowing the regression function we can estimate the conditional variance asymptotically as well as if the regression were given this asymptotic result established under the assumption that the observations are made from a strictly stationary and absolutely regular process is also veri ed via simulation further the asymptotic result paves the way for adapting an automatic bandwidth selection scheme an application with nancial data illustrates the usefulness of the proposed techniques

classification of crossed product algebras associated with characters on free groups we study the classification problem of crossed product c algebras of the form cr g x z where g is a discrete group x is a one dimensional character of g and a x is the unique automorphism of cr g such that if u is the left regular representation of g then ax ug x g ug g e g when g fn the free group on n generators we have a complete classification of these crossed products up to isomorphism which generalizes the classification of irrational and rational rotation c algebras we show that these crossed products are determined by two k theoretic invariants that these two invariants correspond to two orbit invariants of the characters under the natural aut fn action and that these two orbit invariants completely classify the characters up to automorphisms of fn the classification of crossed products follows from these results we also consider the same problem for g some other groups

pragmatical adaptive synchronization new fuzzy model of two different and complex chaotic systems by new adaptive control abstract in this paper 1 a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and 2 a new adaptive approach and a new control lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors by using this new model the numbers of fuzzy rules of chaotic systems can be reduced from 2 n to 2 n and only 2 subsystems are needed where n is the number of nonlinear terms the fuzzy systems become much simpler in addition through the new fuzzy model the new fuzzy systems are much simpler than t s fuzzy systems when nonlinear systems are complicated and can be used to any other kind of application in fuzzy logic control or fuzzy modeling mathieu van der pol system which is called m v system in this paper and quantum cellular neural networks nanosystem which is called q cnn system in this paper are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control lyapunov function the t s fuzzy modeling and traditional adaptive control are also given in appendix b t s fuzzy model of chaotic systems appendix c traditional adaptive method for comparison

a cooperative swarm intelligence algorithm for multi objective discrete optimization with application to the knapsack problem abstract we propose a novel cooperative swarm intelligence algorithm to solve multi objective discrete optimization problems modp our algorithm combines a firefly algorithm fa and a particle swarm optimization pso basically we address three main points the effect of fa and pso cooperation on the exploration of the search space the discretization of the two algorithms using a transfer function and finally the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of pareto optimal solutions we compared the results of our algorithm with the results of five well known meta heuristics on nine multi objective knapsack problem benchmarks the experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior

fusing ant colony optimization with lagrangian relaxation for the multiple choice multidimensional knapsack problem the multiple choice multidimensional knapsack problem mmkp concerns a wide variety of practical problems it is strongly constrained and np hard thus searching for an efficient heuristic approach for mmkp is of great significance in this study we attempt to solve mmkp by fusing ant colony optimization aco with lagrangian relaxation lr the algorithm used here follows the algorithmic scheme of max min ant system for its outstanding performance in solving many other combinatorial optimization problems the lagrangian value of the item in mmkp obtained from lr is used as the heuristic factor in aco since it performs best among the six domain based heuristic factors we define furthermore a novel infeasibility index is proposed for the development of a new repair operator which converts possibly infeasible solutions into feasible ones the proposed algorithm was compared with four existing algorithms by applying them to three groups of instances computational results demonstrate that the proposed algorithm is capable of producing competitive solutions

the functional law of the iterated logarithm for stationary strongly mixing sequences let x i i z be a strictly stationary and strongly mixing sequence of real valued mean zero random variables let a n n 0 be the sequence of strong mixing coefficients we define the strong mixing function by t t and we denote by q the quantile function of x 0 assume that 0 1 1 t q 2 t dt where f 1 denotes the inverse of the monotonic function f the main result of this paper is that the functional law of the iterated logarithm lil holds whenever x i i z satisfies moreover it follows from doukhan massart and rio that for any positive there exists a stationary sequence x i i z with strong mixing coefficients n of the order of n such that the bounded lil does not hold if condition is violated the proof of the functional lil is mainly based on new maximal exponential inequalities for strongly mixing processes which are of independent interest

convergence of multi objective evolutionary algorithms to a uniformly distributed representation of the pareto front in evolutionary multi objective optimization emo the convergence to the pareto set of a multi objective optimization problem mop and the diversity of the final approximation of the pareto front are two important issues in the existing definitions and analyses of convergence in multi objective evolutionary algorithms moeas convergence with probability is easily obtained because diversity is not considered however diversity cannot be guaranteed by combining the convergence with diversity this paper presents a new definition for the finite representation of a pareto set the b pareto set and a convergence metric for moeas based on a new archive updating strategy the convergence of one such moea to the b pareto sets of mops is proved numerical results show that the obtained b pareto front is uniformly distributed along the pareto front when according to the new definition of convergence the algorithm is convergent

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

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

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

use of cumulative sums of squares for retrospective detection of changes of variance abstract this article studies the problem of multiple change points in the variance of a sequence of independent observations we propose a procedure to detect variance changes based on an iterated cumulative sums of squares icss algorithm we study the properties of the centered cumulative sum of squares function and give an intuitive basis for the icss algorithm for series of moderate size i e 200 observations and beyond the icss algorithm offers results comparable to those obtained by a bayesian approach or by likelihood ratio tests without the heavy computational burden required by these approaches simulation results comparing the icss algorithm to other approaches are presented

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

an adaptive population multi objective quantum inspired evolutionary algorithm for multi objective 0 1 knapsack problems abstract the multi objective quantum inspired evolutionary algorithm mqea is a relatively recent technique for solving multi objective optimization problems mops in the mqea quantum bit q bit individuals are classified into several groups with each group assigned one objective solution one of the non dominated solutions found so far as the reference sign string for a fixed population size the number of q bit individuals assigned to each objective solution decreases with increasing number of found non dominated solutions as a result more or fewer q bit individuals assigned to each objective solution may lead a confused order of local and global search to mitigate this issue an adaptive population mqea apmqea is proposed in this work in the apmqea the number of q bit individuals assigned to each objective solution is fixed and the population size is adaptively changed according to the number of found non dominated solutions experimental results for the multi objective 0 1 knapsack problem show that the apmqea finds solutions close to the pareto optimal front and maintains a good spread of the non dominated set

local polynomial estimators of the volatility function in nonparametric autoregression abstract in this paper we consider a class of dynamic models in which both the conditional mean and the conditional variance volatility are unknown functions of the past we first derive probabilistic conditions under which nonparametric estimation of these functions is possible we then construct an estimator based on local polynomial fitting we examine the rates of convergence of these estimators and give a result on their asymptotic normality the local polynomial fitting of the volatility function is applied to different foreign exchange rate series we find an asymmetric u shaped smiling face form of the volatility function

nonparametric quasi likelihood the quasi likelihood function proposed by wedderburn broadened the scope of generalized linear models by specifying the variance function instead of the entire distribution however complete specification of variance functions in the quasi likelihood approach may not be realistic we define a nonparametric quasi likelihood by replacing the specified variance function in the conventional quasi likelihood with a nonparametric variance function estimate this nonparametric variance function estimate is based on squared residuals from an initial model fit the rate of convergence of the nonparametric variance function estimator is derived it is shown that the asymptotic limiting distribution of the vector of regression parameter estimates is the same as for the quasi likelihood estimates obtained under correct specification of the variance function thus establishing the asymptotic efficiency of the nonparametric quasi likelihood estimates we propose bandwidth selection strategies based on deviance and pearson s chi square statistic it is demonstrated in simulations that for finite samples the proposed nonparametric quasi likelihood method can improve upon extended quasi likelihood or pseudo likelihood methods where the variance function is assumed to fall into a parametric class with unknown parameters we illustrate the proposed methods with applications to dental data and cherry tree data

change points in nonparametric regression analysis an otherwise smooth regression model are proposed the assumptions needed are much weaker than those made in parametric models the proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change points of slope and of higher order curvature the proposed estimators are based on a comparison of left and right one sided kernel smoothers weak convergence of a stochastic process in local differences to a gaussian process is established for properly scaled versions of estimators of the location of a change point the continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change point estimators these rates are typically faster than n 1 2 rates of global lp convergence of curve estimates with appropriate kernel modifications adapting to estimated change points are derived as a consequence it is shown that these rates of convergence are the same as if the location of the change point was known the methods are illustrated by means of the well known data on the annual flow volume of the nile river between 1871 and 1970 1 introduction nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions sometimes a generally smooth curve might contain an isolated discontinuity or change point in the curve or in a possibly higher order derivative and in many cases interest focuses on the occurrence of such change points in parametric approaches to the regression change point problem simple linear regressions before and after a possible change point are assumed and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative or equivalently a slope change is incorporated into the model see for instance hinkley 1969 and brown durbin and evans 1975 the analysis of change points which describe sudden localized changes typically occurring in economics medicine and the physical sciences has recently found increasing interest general smoothness assumptions allowing for a large class of regression functions to be considered seem to be more appropriate in a variety of applied problems than parametric modelling an