stability of a general mixed additive cubic functional equation in non archimedean fuzzy normed spaces we establish some stability results concerning the general mixed additive cubic functional equation in non archimedean fuzzy normed spaces in addition we establish some results of approximately general mixed additive cubic mappings in non archimedean fuzzy normed spaces the results improve and extend some recent results

two stage least squares estimation of average causal effects in models with variable treatment intensity abstract two stage least squares tsls is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted variables bias in single equation estimation we show here that tsls can also be used to estimate the average causal effect of variable treatments such as drug dosage hours of exam preparation cigarette smoking and years of schooling the average causal effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment given mild regularity assumptions the probability limit of tsls is a weighted average of per unit average causal effects along the length of an appropriately defined causal response function the weighting function is illustrated in an empirical example based on the relationship between schooling and earnings

efficient estimation and inference in linear pseudo panel data models we consider pseudo panel data models constructed from repeated cross sections in which the number of individuals per group is large relative to the number of groups and time periods first we show that when time invariant group fixed effects are neglected the ols estimator does not converge in probability to a constant but rather to a random variable second we show that while the fixed effects fe estimator is consistent the usual t statistic is not asymptotically normally distributed and we propose a new robust t statistic whose asymptotic distribution is standard normal third we propose efficient gmm estimators using the orthogonality conditions implied by grouping and we provide t tests that are valid even in the presence of time invariant group effects our monte carlo results show that the proposed gmm estimator is more precise than the fe estimator and that our new t test has good size and is powerful

approximate homomorphisms and derivations between c ternary algebras in 1940 ulam proposed the famous ulam stability problem in this paper we introduce a general cauchy jensen functional equation and prove the generalized ulam stability of c ternary homomorphisms and c ternary derivations in c ternary algebras for the general cauchy jensen equation

minimum mse estimation of a regression model with fixed effects from a series of cross sections if panel data are not available but repeated cross sections are the parameters in a regression model with fixed individual effects can be estimated consistently using the cohort approach proposed by deaton 1985 in this paper we show that deaton s estimator is inconsistent if the number of time periods is small even if the number of cohorts tends to infinity moreover we propose an alternative estimator which does not suffer from a bias due to a small number of sampling periods and we introduce a new class of estimators containing both estimators mentioned above we discuss minimum mean squared error estimation within this class our results show that it may be optimal to eliminate only part of the measurement error in the cohort averages since the implied bias is offset by a smaller variance

grouped data estimation and testing in simple labor supply models abstract inappropriate identifying assumptions and measurement error in hourly wage data may account for the poor performance of some empirical labor supply models this paper discusses an efficient generalization of wald s method of fitting straigth lines that is robust to measurement error imposes mild identifying assumptions and is useful for the estimation of labor supply models with panel data a two stage least squares tsls equivalent of the efficient wald estimator is presented and a tsls overidentification test statistic is shown to be a test statistic for the equality of alternative wald estimates of the same parameter in an emperical example estimated labor supply elasticities range from 0 6 to 0 8 a test for measurement error based on the difference between efficient wald and analysis of covariance estimators is also proposed application of the test indicates that measurement error may be responsible for low or negative estimates of labor supply elasticities

identification of miso nonlinear regressions in the presence of a wide class of disturbances a nonparametric algorithm based on multiple fourier series for identification of miso multidimensional input single output systems is investigated it is shown that the algorithm converges for a wide class of noise

hypersymmetry a z3 graded generalization of supersymmetry we propose a generalization of non commutative geometry and gauge theories based on ternary z3 graded structures in the new algebraic structures we define all products of two entities are left free the only constraining relations being imposed on ternary products these relations reflect the action of the z3 group which may be either trivial i e abc bca cab generalizing the usual commutativity or non trivial i e abc jbca with j e 2 i 3 the usual z2 graded structures such as grassmann lie and clifford algebras are generalized to the z3 graded case certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed

estimating a distribution function with truncated and censored data a minor modification of the product limit estimator is proposed for estimating a distribution function not necessarily continuous when the data are subject to either truncation or censoring or to both by independent but not necessarily identically distributed truncation censoring variables making use of martingale integral representations and empirical process theory uniform strong consistency of the estimator is established and weak convergence results are proved for the entire observable range of the function numerical results are also given to illustrate the usefulness of the modification particularly in the context of truncated data

almost certain convergence in double arrays for double arrays of constants ani 1 i k n n 1 and i i d random variables x x i i 1 conditions are given under which the row sums sum limits i 1 k n a ni x i xrightarrow text a text c text 0 both cases k n and k n are treated in general the hypotheses involve a trade off between moment requirements on x and the magnitude of the itani a marcinkiewicz zygmund type strong law is obtained for the special case a ni a i mathord left vphantom a i left sum limits j 1 n a j p right 1 p right kern nulldelimiterspace left sum limits j 1 n a j p right 1 p a i 0 text sum limits text 1 n a j p to infty text 0 p 2

a law of the iterated logarithm for kernel estimators of regression functions for fixed design regression data kernel estimation is widely used to estimate v t thev th derivative of t denoting such an estimator by hat mu nv t this paper is concerned with the almost sure convergence of hat mu nv t e hat mu nv t it is shown that under several inserting procedures a law of iterated logarithm holds

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

on foundation of the generalized nambu mechanics we outline basic principles of a canonical formalism for the nambu mechanics a generalization of hamiltonian mechanics proposed by yoichiro nambu in 1973 it is based on the notion of a nambu bracket which generalizes the poisson bracket a binary operation on classical observables on the phase space to the multiple operation of higher ordern 3 nambu dynamics is described by the phase flow given by nambu hamilton equations of motion a system of ode s which involvesn 1 hamiltonians we introduce the fundamental identity for the nambu bracket a generalization of the jacobi identity as a consistency condition for the dynamics we show that nambu bracket structure defines a hierarchy of infinite families of subordinated structures of lower order including poisson bracket structure which satisfy certain matching conditions the notion of nambu bracket enables us to define nambu poisson manifolds phase spaces for the nambu mechanics which turn out to be more rigid than poisson manifolds phase spaces for the hamiltonian mechanics we introduce the analog of the action form and the action principle for the nambu mechanics in its formulation dynamics of loops n 2 dimensional chains for the generaln ary case naturally appears we discuss several approaches to the quantization of nambu mechanics based on the deformation theory path integral formulation and on nambu heisenberg commutation relations in the latter formalism we present an explicit representation of the nambu heisenberg relation in then 3 case we emphasize the role ternary and higher order algebraic operations and mathematical structures related to them play in passing from hamilton s to nambu s dynamical picture

performance analysis of averaging based distributed estimation algorithm with additive quantization model abstract in this paper we consider the distributed sensor fusion problem over sensor networks under directed communication links and bandwidth constraint we investigate the impact of the additive quantization model on the proposed two stage averaging based algorithm existing works on the effect of the additive model show that convergence can be guaranteed only if the quantization error variances form a convergent series we show that the proposed algorithm achieves the performance of the optimal centralized estimate even if the quantization error variances are not vanishing this is guaranteed by establishing a law of the iterated logarithm for weighted sums of independent random vectors moreover an explicit bound of the convergence rate of the proposed algorithm is given to quantify its almost sure performance

estimation of models with grouped and ungrouped data by means of 2sls abstract this paper deals with a special case of estimation with grouped data where the dependent variable is only available for groups whereas the endogenous regressor s is available at the individual level by estimating the first stage using the available individual data and then estimating the second stage at the aggregate level it might be possible to gain efficiency relative to the ols and 2sls estimators that use only grouped data we term this the mixed 2sls estimator m2sls the m2sls estimator is consistent and asymptotically normal we also provide a test of efficiency of m2sls relative to ols and 2sls estimators

numerical measure of a complex matrix we introduce a natural probability measure over the numerical range of a complex matrix a mn input amssym bbb c this numerical measure a can be defined as the law of the random variable ax x input amssym bbb c when the vector x input amssym bbb c n is uniformly distributed on the unit sphere if the matrix a is normal we show that a has a piecewise polynomial density fa which can be identified with a multivariate b spline in the general nonnormal case we relate the radon transform of a to the spectrum of a family of hermitian matrices and we deduce an explicit representation formula for the numerical density that is appropriate for theoretical and computational purposes as an application we show that the density fa is polynomial in some regions of the complex plane that can be characterized geometrically and we recover some known results about lacunae of symmetric hyperbolic systems in 2 1 dimensions finally we prove under general assumptions that the numerical measure of a matrix a mn input amssym bbb c concentrates to a dirac mass as the size n goes to infinity 2011 wiley periodicals inc

on system identification by nonparametric function fitting a new nonparametric algorithm for function fitting is proposed and its application to a broad class of system identification problems is discussed

comment on approximate ternary jordan derivations on banach ternary algebras bavand savadkouhi et al j math phys 50 042303 2009 let a be a banach ternary algebra over c and x a ternary banach a module a c linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a bavand savadkouhi et al j math phys 50 042303 2009 investigated ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x and proved the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras the mapping f in lemma 2 2 of bavand savadkouhi et al is identically zero and all of the results are trivial in this note we correct the statements of the results and the proofs

generalized method of moments specification testing abstract this paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions it shows that any such test may fail against general misspecification that causes estimator inconsistency the mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived applications to testing for exogeneity of a set of instrumental variables are presented

on optimal global rate of convergence of some nonparametric identification procedures a study of orthogonal series procedures for function fitting motivated by an interest in nonparametric identification of linear dynamic systems is reported it is shown that the procedures attain the optimal rate of convergence for the fourier and the walsh orthonormal systems these rates cannot be exceeded by any method of estimation this is the first analytical result giving a clear answer to the question of which orthonormal system is the best one for the purpose of system identification

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

on special classes of n algebras we define n algebras as linear spaces on which the internal composition law involves n elements m v n v it is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics using the notion of a commutant of two subalgebras of an n algebra we distinguish certain classes of n algebras with reasonable properties semisimple abelian nilpotent solvable we also consider a few examples of n algebras of different types and show their properties

approximate ternary jordan derivations on banach ternary algebras let a be a banach ternary algebra over a scalar field r or c and x be a ternary banach a module a linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a in this paper we investigate ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x moreover we prove the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras