statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

nonlinear growth in weighted networks with neighborhood preferential attachment abstract we propose a nonlinear growing model for weighted networks with two significant characteristics i the new weights triggered by new edges at each time step grow nonlinearly with time and ii a neighborhood local world exists for local preferential attachment which is defined as one selected node and its neighbors global strength driven and local weight driven preferential attachment mechanisms are involved in our model we study the evolution process through both mathematical analysis and numerical simulation and find that the model exhibits a wide range power law distribution for node degree strength and weight in particular a nonlinear degree strength relationship is obtained this nonlinearity implies that accelerating growth of new weights plays a nontrivial role compared with accelerating growth of edges because of the specific local world model a small world property emerges and a significant hierarchical organization independent of the parameters is observed

hac estimation in a spatial framework abstract we suggest a non parametric heteroscedasticity and autocorrelation consistent hac estimator of the variance covariance vc matrix for a vector of sample moments within a spatial context we demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models we allow for more than one measure of distance each of which may be measured with error monte carlo results suggest that our estimator is reasonable in finite samples we then consider a spatial model containing various complexities and demonstrate that our hac estimator can be applied in the context of that model

representations of the space of distributions useful in robust estimation of location summary in many situations it is useful to have a low dimensional representation of the space of distributions this paper gives one two and three dimensional representations which are particularly relevant to the study of robust estimation of location based on rank estimators the distances are defined as functions of the asymptotic relative efficiency of the most efficient rank estimator for one distribution when used on data from another distribution values of these distance functions are computed for a large number of pairs

local preferential attachment model for hierarchical networks abstract in real life networks incomers may only connect to a few others in a local area for their limited information and individuals in a local area are likely to have close relations accordingly we propose a local preferential attachment model here a local area network stands for a node and all its neighbors and the new nodes perform nonlinear preferential attachment k i k i in local areas the stable degree distribution and clustering degree correlations are analytically obtained with the increasing of the clustering coefficient increases while assortativity decreases from positive to negative in addition by adjusting the parameter the model can generate different kinds of degree distribution from exponential to power law the hierarchical organization independent of is the most significant character of this model

a constrained maximum likelihood approach to estimating switching regressions abstract it is widely known that the likelihood function for the switching regression model is unbounded if the error variances are unconstrained this paper shows that a constrained maximum likelihood formulation makes the likelihood function bounded relatively mild constraints are imposed on the parameters and if the true parameters satisfy the constraints there is a global maximizer of the likelihood function on the constrained parameter space which is consistent asymptotically normal and efficient a well known em algorithm is modified in order to compute constrained maximizers of the likelihood function

a laplace approximation to the moments of a ratio of quadratic forms summary the laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables the technique utilises the existence of a dominating peak at the boundary point on the range of integration as closed form and tractable formulae do not exist in general this simple approximation which only entails basic algebraic operations has evident practical appeal we exploit the approximation to provide an approximate mean bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation

instrumental variable estimation based on conditional median restriction abstract we develop a method named the l 1 iv estimator to estimate structural equations based on the conditional median restriction imposed on the error terms we study its asymptotic behavior and show how to estimate its asymptotic covariance matrix we also discuss the point identification in the l 1 iv estimation and propose an over identifying restriction test we further demonstrate the performance of the l 1 iv estimator in comparison with the familiar two stage least squares estimator the proposed method is applied to estimate the labor supply and wage offer functions for working married women

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

linearity testing for fuzzy rule based models in this paper we introduce a linearity test for fuzzy rule based models in the framework of time series modeling to do so we explore a family of statistical models the regime switching autoregressive models and the relations that link them to the fuzzy rule based models from these relations we derive a lagrange multiplier linearity test and some properties of the maximum likelihood estimator needed for it finally an empirical study of the goodness of the test is presented

generic uniform convergence and equicontinuity concepts for random functions abstract equicontinuity type concepts for random functions which are important for establishing convergence results for such functions have increasingly been used in the econometrics literature in this paper we define and discuss various equicontinuity type concepts for random functions and employ those concepts to provide sufficient conditions for uniform convergence and in particular for uniform laws of large numbers furthermore we clarify the differences and similarities between uniform laws of large numbers based on pointwise and local laws of large numbers given in the recent literature as they relate to differences in the employed equicontinuity type concepts

the randomly organized structure of urban ground bus transport networks in china in this paper the evolution dynamical properties of four topological urban ground bus transport networks btns in china are empirically researched as the statistical results of some common used measurements show that there are large fluctuations because of small sample sizes to induce some indistinct conclusions and there are even incorrect btn structure pictures as positive degree relation of the adjacent vertices in those btns though they are actually uncorrelated at all i e exhibiting pseudo positive connectivity correction thus in order to uncover the randomly organized architecture of btns new measurements of the average sum of the nearest neighbors degree degree correlation dnn k and the degree average edges among the nearest neighbors l k are proposed the obtained results of two new measurements do reflect that the considered btns are organized randomly in this point those empirical results provide one new framework for a more realistic btn model which will capture the underlying evolution principles of a btn in the geographical topology r 2007 elsevier b v all rights reserved

a comprehensive weighted evolving network model abstract many social technological biological and economical systems are best described by weighted networks whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes however most existing research work on complex network models are concentrated on network structures with connection weights among their nodes being either 1 or 0 in this paper we propose a new weighted evolving network model numerical simulations indicate that this network model yields three power law distributions for the node degrees connection weights and node strengths respectively particularly some other properties of the distributions such as the droop head and heavy tail effects can also be reflected by this model

local global neural networks a new approach for nonlinear time series modeling we propose the local global neural networks model within the context of time series models this formulation encompasses some already existing nonlinear models and also admits the mixture of experts approach we emphasize the linear expert case and extensively discuss the theoretical aspects of the model stationarity conditions existence consistency and asymptotic normality of the parameter estimates and model identifiability the proposed model consists of a mixture of stationary and nonstationary linear models and is able to describe intermittent dynamics the system spends a large fraction of time in a bounded region but sporadically develops an instability that grows exponentially for some time and then suddenly collapses intermittency is a commonly observed behavior in ecology and epidemiology fluid dynamics and other natural systems a model building strategy is also considered and the parameters are estimated by concentrated maximum likelihood the procedure is illustrated with two real

assortativity and act degree distribution of some collaboration networks empirical investigation results on weighted and un weighted assortativity act degree distribution degree distribution and node strength distribution of nine real world collaboration networks have been presented the investigations propose that act degree distribution degree distribution and node strength distribution usually show so called shifted power law spl function forms which can continuously vary from an ideal power law to an ideal exponential decay two parameters a and z can be used for description of the distribution functions another conclusion is that assortativity coefficient and the parameter a or z is monotonously dependent on each other by the collaboration network evolution model introduced in a reference p zhang et al physica a 360 2006 599 we analytically derived the spl distributions which typically appeared in general situations where nodes are selected partially randomly with a probability p and partially by linear preferential principle with the probability 1 p the analytic discussion gives an explicit expression on the relationship between the random selection proportion p and the parameters a and z the numerical simulation results by the model show a monotonic dependence of assortativity on the random selection proportion p the empirically obtained assortativity versus a or z curve for the four collaboration networks with small maximal act size t max shows a good agreement with the model prediction according to the curves one can qualitatively judge the random selection proportion of the real world network in its evolution process r 2007 elsevier b v all rights reserved

a note on sargan densities abstract this note reconsiders the general class of sargan densities studied by goldfeld and quandt 1981 and missiakoulis 1983 in the context of approximating normal densities in regression models some errors in these papers are pointed out and the sargan densities are re computed to the contrary of missiakoulis conclusion the first two order densities are not the best choice higher order densities are better approximations though the best choice appears to be the second order density based on the goldfeld quandt criteria

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

an algorithmic proof theory for hypergeometric ordinary and q multisum integral identities it is shown that every proper hypergeometric multisum integral identity orq identity with a fixed number of summations and or integration signs possesses a short computer constructible proof we give a fast algorithm for finding such proofs most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here we give many examples of the method including computer generated proofs of identities of mehta dyson selberg hille hardy q saalschutz and others the prospect of using the method for proving multivariate identities that involve an arbitrary number of summations integrations is discussed

exactly distribution free inference in instrumental variables regression with possibly weak instruments abstract this paper introduces a rank based test for the instrumental variables regression model that dominates the anderson rubin test in terms of finite sample size and asymptotic power in certain circumstances the test has correct size for any distribution of the errors with weak or strong instruments the test has noticeably higher power than the anderson rubin test when the error distribution has thick tails and comparable power otherwise like the anderson rubin test the rank tests considered here perform best relative to other available tests in exactly identified models

bayes prediction in regressions with elliptical errors abstract in this paper the prediction problem is considered for linear regression models with elliptical errors when the bayes prior is non informative we show that the bayes prediction density under the elliptical errors assumption is exactly the same as that obtained with normally distributed errors thus assuming that the errors have a normal distribution when the true distribution is elliptical will not lead to incorrect predictive inferences if the error variance structure is correctly specified this extends the results of zellner 1976 finally based on monte carlo numerical integration procedures computations are provided in a model with multiplicative heteroscedasticity

resistant estimation for simultaneous equations models using weighted instrumental variables in this paper we present a weighted instrumental variables estimator that is resistant2 to heavy tailed errors aberrant data in either the endogenous or exogenous variables and certain other model failures the estimator is analogous to the weighted least squares approach to robustness proposed by krasker and welsch 21 for ordinary regression we will discuss the theory that motivated this estimator derive some of its properties describe our computational algorithm and using an empirical example illustrate the estimator s utility as a tool for data analysis in structural models the evolution of robust estimators for simultaneous equations models has closely resembled the development of robust methods for ordinary regression in both cases research focused at first on the well documented effects of long tailed error distributions on the classical procedures for ordinary regression models statisticians have studied the properties of least absolute deviations lad estimators see bassett and koenker 2 and amemiya 1 and maximum likelihood type estimators called m estimators see huber 14 for simultaneous equations models lad can be generalized in several different ways to modify two stage least squares or instrumental variables amemiya 1 has presented these estimators in a unified framework and powell 31 has proven their asymptotic normality under weak assumptions fair 8 has compared two stage lad estimates of a u s macroeconomic model with two stage least squares and full information maximum likelihood estimates the m estimator concept can also be generalized to simultaneous equations for example prucha and kelejian 32 have considered maximum likelihood estimation under the assumption that the disturbance vector is multivariate student t although lad and m estimators maintain a high efficiency when the error distribution is heavy tailed they are not robust in the stronger sense of hampel 10 which roughly speaking requires an estimator to have a limited sensitivity to any small fraction of the data 3 lad and m estimators fail under this criterion because a single observation whose values for the right side variables are highly anomalous can have an arbitrarily large effect on lad estimates or m estimates just as on the classical procedures consequently these estimators do not provide insurance against the sort of gross errors that occur in some data sets nor do they serve as reliable diagnostics for departures from linearity occurring in extreme regions of the space of right side variables for linear models the estimators that satisfy the strong hampel robustness criterion have become known as bounded influence estimators several such estimators have been

effect of node deleting on network structure abstract the ever increasing knowledge of the structure of various real world networks has uncovered their complex multi mechanism governed evolution processes therefore a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner in this paper we introduce a new type of network growth rule which comprises addition and deletion of nodes and propose an evolving network model to investigate the effect of node deleting on network structure it is found that with the introduction of node deleting network structure is significantly transformed in particular degree distribution of the network undergoes a transition from scale free to exponential forms as the intensity of node deleting increases at the same time nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model we also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small in addition it is found that node deleting will weaken but not eliminate the small world effect of a growing network and generally it will decrease the clustering coefficient in a network

the rank version of von neumann s ratio test for randomness abstract although rank tests for randomness were proposed in the literature as early as 1943 no such test has gained wide acceptance comparable to say spearman s rho test this may be due to the lack of small sample theory and of tables of critical values to enable such a test to be carried out on small samples in this article we consider the rank version of the von neumann ratio statistic and we obtain the critical values of this statistic under the randomization hypothesis in a monte carlo experiment we then show that the resulting nonparametric test for randomness has far greater power than the test based on the number of runs up and down moreover under normality its power vis a vis the normal theory von neumann ratio test is also very good it is therefore suggested that with the tables presented in this article the rank von neumann ratio test for randomness provides an easy and powerful alternative to nonparametric tests now in common use

predictive inference on equicorrelated linear regression models beyond the customary analysis through the estimation and hypothesis testing about the parameters of the multiple regression models often a natural interest is to predict the responses for a given set of values of the predictors the main objective of this article is to obtain the prediction distribution for a set of future responses from a multiple linear regression model which follow equicorrelation structure it derives the marginal likelihood estimate for the equicorrelation parameter r and then uses the invariant differentials to compute the joint distribution of the unobserved but realized future errors the prediction distribution is derived by using the structural relation of the model the main finding of this paper is that the prediction distribution turned out to be a student t which depends only on the estimated r and is invariant to the degrees of freedom of the original student t distribution

age based model for weighted network with general assortative mixing abstract in this paper we propose an evolutionary model for weighted networks by introducing an age based mutual selection mechanism our model generates power law distributions of degree weight and strength which are confirmed by analytical predictions and are consistent with real observations the investigation of the relationship between clustering and the connectivity of nodes suggests hierarchical organization in the weighted networks furthermore both assortative and disassortative properties can be naturally obtained by tuning a parameter which controls the strength of age based preferential attachments since the age information of nodes is easier to acquire than the degree and strength of nodes and almost all empirically observed structural and weighted properties can be reproduced by the simple evolutionary regulation our model may reveal some underlying mechanisms that are key for the evolution of weighted complex networks

complex network properties of chinese natural science basic research in this paper we studied the research areas of chinese natural science basic research from a point view of complex network two research areas are considered to be connected if they appear in one fund proposal the explicit network of such connections using data from 1999 to 2004 is constructed the analysis of the real data shows that the degree distribution of the bf research areas network ran may be better fitted by the exponential distribution it displays small world effect in which randomly chosen pairs of research areas are typically separated by only a short path of intermediate research areas the average distance of ran decreases with time while the average clustering coefficient increases with time which indicates that the scientific study would like to be integrated together in terms of the studied areas the relationship between the clustering coefficient c k and the degree k indicates that there is no hierarchical organization in ran

strength distribution of novel local world networks abstract it is discovered that there are two important characters local world character and weight driven character in many real life complex networks motivated by this fact a weight driven local world network model is proposed which incorporates the weight dynamics and the fixed local world property by means of mathematical analysis and numerical simulation the strength distribution of the network model has been obtained the results are applied to epidemic spreading theory

a note on sargan densities abstract this note reexamines the general class of sargan densities analyzed by goldfeld and quandt 1981 kafei and schmidt 1985 and others in the context of approximating normal densities in certain econometric models it suggests a third order sargan density which complies with the goldfeld and quandt criteria is unimodal and is the best approximation to the normal for orders less than or equal to 3 some errors in goldfeld and quandt paper are corrected

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

efficient estimation of the semiparametric spatial autoregressive model efficient semiparametric and parametric estimates are developed for a spatial autoregressive model containing non stochastic explanatory variables and innovations suspected to be non normal the main stress is on the case of distribution of unknown nonparametric form where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest these estimates are as efficient as the ones based on a correct form in particular they are more efficient than pseudo gaussian maximum likelihood estimates at non gaussian distributions two different adaptive estimates are considered relying on somewhat different regularity conditions a monte carlo study of finite sample performance is included

on tests applied to residuals abstract the null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals it might be expected however that the dependence decreases as the sample size increases so that the limiting null distribution is the same as if the test were based on independent observations the author investigates whether this large sample equivalence holds for tests of correlation scale difference regression and location difference particular emphasis is placed on showing when rank tests based on residuals have a strongly asymptotically distribution free property u statistic theorems are used to investigate these issues

exact permutation tests for non nested non linear regression models abstract this paper proposes exact distribution free permutation tests for the specification of a non linear regression model against one or more possibly non nested alternatives the new tests may be validly applied to a wide class of models including models with endogenous regressors and lag structures these tests build on the well known j test developed by davidson and mackinnon 1981 several tests for model specification in the presence of alternative hypotheses econometrica 49 781 793 and their exactness holds under broader assumptions than those underlying the conventional j test the j type test statistics are used with a randomization or monte carlo resampling technique which yields an exact and computationally inexpensive inference procedure a simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions the test procedure developed is illustrated by an application to inflation dynamics

econometric modelling with non normal disturbances abstract this paper analyzes a general class of non normal density functions dubbed sargan densities in the context of the ordinary regression model and the simple one market disequilibrium model use of the normal density in disequilibrium models is unwieldy especially for multimarket models since the application of maximum likelihood methods requires numerical evaluation of multiple integrals these difficulties are avoided with the sargan densities and based on both asymptotic results and limited sampling experiments these densities appear to offer a promising alternative to the normal in disequilibrium models

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

sargan densities which one abstract goldfeld and quandt 1981 suggest the use of sargan distribution as a viable alternative to normal distribution in econometric models this paper examines the resemblance of a sargan type family of densities to the normal density and concludes that the first two order cases are the best choice

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

robustness of size of tests of autocorrelation and heteroscedasticity to nonnormality abstract a comprehensive empirical examination is made of the sensitivity of tests of disturbance covariance in the linear regression model to nonnormal disturbance behaviour tests of autocorrelation appear to be quite robust except for extreme nonnormality but tests for heteroscedasticity are highly susceptible to kurtosis

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

a flexible coefficient smooth transition time series model we consider a flexible smooth transition autoregressive star model with multiple regimes and multiple transition variables this formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network this proposal has the major advantage of nesting several nonlinear models such as the self exciting threshold autoregressive setar the autoregressive neural network ar nn and the logistic star models furthermore if the neural network is interpreted as a nonparametric universal approximation to any borel measurable function our formulation is directly comparable to the functional coefficient autoregressive far and the single index coefficient regression models a model building procedure is developed based on statistical inference arguments a monte carlo experiment showed that the procedure works in small samples and its performance improves as it should in medium size samples several real examples are also addressed

large sample properties of method of moment estimators under different data generating processes abstract in this paper we study the large sample properties of method of moment estimators mme of population parameters that result as explicit or implicit solitions of equations 0 where is a vector of moments the distribution of the corresponding large sample estimator b resulting from solving m b 0 where m is a sample moment estimator of is shown to vary with the sample design we study the case of a random sample of a pooled sample a sample from a known population distribution and a so called repeated sample also we provide a numerical example our main conclusion is that any seemingly harmless assumption on the sample design may have severe repercussions on the estimation of confidence bounds therefore we advocate to take a kind of minimal set of assumptions unless we have hard a priori knowledge

chi square diagnostic tests for econometric models introduction and applications abstract this paper extends the pearson chi square testing method to non dynamic parametric econometric models in particular models with covariates the paper introduces the test and discusses a variety of applications these applications include testing for goodness of fit of a parametric model as well as testing particular aspects of a parametric model the cells used to construct the test statistic may be random and can be specified in a general form

approximations to di and tri logarithms we propose hypergeometric constructions of simultaneous approximations to polylogarithms these approximations suit for computing the values of polylogarithms and satisfy 4 term apery like polynomial recursions

the structure of simultaneous equation estimators a generalization towards nonnormal disturbances a general linear simultaneous equation system with a multivariate student t disturbance vector is considered the normal equations of the corresponding maximum likelihood estimator are used as estimator generating equations to introduce a new class of estimators properties of large subclasses of these estimators are determined for disturbance vectors other than the multivariate student t

power law strength degree correlation from resource allocation dynamics on weighted networks many weighted scale free networks are known to have a power law correlation between strength and degree of nodes which however has not been well explained we investigate the dynamic behavior of resource traffic flow on scale free networks the dynamical system will evolve into a kinetic equilibrium state where the strength defined by the amount of resource or traffic load is correlated with the degree in a power law form with tunable exponent the analytical results agree well with simulations

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

rational approximations to the dilogarithm the irrationality proof of the values of the dilogarithmic function l 2 z at rational points z 1 k for every integer k 5 7 is given to show this we develop the method of pade type approximations using legendre type polynomials which also derives good irrationality measures of l 2 1 k moreover the linear independence over q of the numbers 1 log 1 1 k and l 2 1 k is also obtained for each integer k 5 7

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

diophantine properties of numbers related to catalan s constant 1 as a linear form in 1 and even beta valuesonly the following lemma 2 is almost the same as the correspondingone in br and we only include a sketch of the proof we would like toemphasise the fact that it is essentially the well poisedness of the series thatenables us to produce this parity dependant behaviour when

weighted scale free networks with stochastic weight assignments we propose a model of weighted scale free networks incorporating a stochastic scheme for weight assignments to the links taking into account both the popularity and fitness of a node as the network grows the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1 ensuremath p numerical results show that the total weight exhibits a power law distribution with an exponent ensuremath sigma that depends on the probability p the exponent ensuremath sigma decreases continuously as p increases for p 0 the scaling behavior is the same as that of the connectivity distribution an analytical expression for the total weight is derived so as to explain the features observed in the numerical results numerical results are also presented for a generalized model with a fitness dependent link formation mechanism

a new range reduction algorithm range reduction is a key point for getting accurate elementary function routines we introduce a new algorithm that is fast for input arguments belonging to the most common domains yet accurate over the full double precision range

mutual selection model for weighted networks for most networks the connection between two nodes is the result of their mutual affinity and attachment in this paper we propose a mutual selection model to characterize the weighted networks by introducing a general mechanism of mutual selection the model can produce power law distributions of degree weight and strength as confirmed in many real networks moreover we also obtained the nontrivial clustering coefficient c degree assortativity coefficient r and degree strength correlation depending on a single parameter m these results are supported by present empirical evidence studying the degree dependent average clustering coefficient c k and the degree dependent average nearest neighbors degree k nn k also provide us with a better description of the hierarchies and organizational architecture of weighted networks

new irrationality measures for q logarithms the three main methods used in diophantine analysis of q series are combined to obtain new upper bounds for irrationality measures of the values of the q logarithm function when p 1 q z 0 1 and z q

a class of partially adaptive one step m estimators for the non linear regression model with dependent observations in this paper we consider a class of partially adaptive one step m estimators for the non linear regression model with dependent observations those estimators adapt themselves with respect to a measure of the tailthickness of the disturbance distribution as well as to a measure of the scale the large sample behavior of those estimators is examined theoretically for general disturbance distributions and numerically for various specific ones the estimators considered are motivated by the student r maximum likelihood estimator given appropriate specifications of the adaptation parameter the estimators are asymptotically efficient on the family of student t distributions including the normal distribution

robustness to nonnormality of the durbin watson test for autocorrelation abstract this study investigates the robustness to nonnormality of the null distribution of the durbin watson test for autocorrelation in regression errors the first four moments of the null distribution are derived to the order o 1 n 3 when the regression errors are nonnormal with n the sample size it is found that nonnormality has an insignificant effect on the mean and the fourth central moment of the distribution the variance tends to be deflated inflated if the error distribution is long tailed short tailed the third central moment is reduced if the error distribution is skewed left or right both skewness and kurtosis of the distribution are affected by nonnormality but these effects are negligible in large samples it seems the test is relatively robust for moderate nonnormality and moderately large sample size these effects are also found to have insignificant influence from the regressors

partially adaptive estimation via a normal mixture abstract this paper proposes a new partially adaptive regression estimator the estimator is derived by modeling the disturbance distribution as a variance mixture of normal distributions yet the true disturbance distribution need not be a variance mixture in order for the proposed estimator to be consistent and asymptotically normal moreover the partially adaptive estimator is shown to be less sensitive to extreme values than the ordinary least squares estimator a point that is illustrated with some monte carlo experiments the paper also provides some easily programmed em algorithms for computing estimates

asymptotic behavior of general m estimates for regression and scale with random carriers let xini y i be a sequence of independent identically distributed random variables where x i r p and y i r and let r p be an unknown vector such that y i x i u i where u i is independent of x i and has distribution function f u where 0 is an unknown parameter this paper deals with a general class of m estimates of regression and scale defined as solutions of the system sum limits i phi text x i r i x i 0 sum limits i chi r i 0 where r y i xi1 with r p r r and r r this class contains estimators of proposed by huber mallows and krasker and welsch the consistency and asymptotic normality of the general m estimators are proved assuming general regularity conditions on and and assuming the joint distribution of x i y i to fulfill the model only approximately

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved