adaptive estimation of regression models via moment restrictions abstract this paper considers adaptive estimation of regression models by means of generalized method of moments estimators two models are considered one with an i i d disturbance that is independent of the regressors and one with a conditionally symmetric but possibly heteroskedastic disturbance for both cases the paper develops linearized estimators that are asymptotically efficient if the number and variety of moment conditions are allowed to grow at an appropriate rate with the sample size in the general symmetric case no other adaptive estimator has yet been proposed also results of a small monte carlo study indicate that in the independence case the small sample performance of the generalized method of moments estimator can be quite good vis a vis other estimators previously proposed

an orlicz space approach to superlinear elliptic systems in this paper we study superlinear elliptic systems in hamiltonian form using an orlicz space setting we extend the notion of critical growth to superlinear nonlinearities which do not have a polynomial growth existence of nontrivial solutions is proved for superlinear nonlinearities which are subcritical in this generalized sense

highly flexible distributions to fit multiple frequency financial returns abstract financial data are usually studied via low flexible distributions independently of the frequency of the data due to their simplicity and analytical tractability in this paper we analyze two highly flexible five parameter distributions into fitting financial returns these are the skewed generalized t sgt and the generalized hyperbolic gh applications carried on two exchange rates euro dollar and dollar yen and two indexes s p 500 and nikkei 225 over four frequencies weekly daily 30 min and 5 min confirm the superiority of the sgt and gh in approximating the distribution of a given data at a remarkable precision moreover as we move from higher to lower frequency the distribution s overall shape does indeed change radically and the estimated parameters refute the tendency to normality which calls into question the aggregational gaussianity s stylized fact

adapting for heteroscedasticity in linear models in a heteroscedastic linear model it is known that if the variances are a parametric function of the design then one can construct an estimate of the regression parameter which is asymptotically equivalent to the weighted least squares estimate with known variances we show that the same is true when the only thing known about the variances is that they are determined by an unknown but smooth function of the design or the mean response

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

systems of frequency distributions for water and environmental engineering abstract a wide spectrum of frequency distributions are used in hydrologic hydraulic environmental and water resources engineering these distributions may have different origins are based on different hypotheses and belong to different generating systems review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include 1 differential equations 2 distribution elasticity 3 genetic theory 4 generating functions 5 transformations 6 bessel function 7 expansions and 8 entropy maximization this paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems it also proposes based on empirical evidence another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering

efficient semiparametric estimation via moment restrictions conditional moment restrictions can be combined through gmm estimation to construct more efficient semiparametric estimators this paper is about attainable efficiency for such estimators we define and use a moment tangent set the directions of departure from the truth allowed by the moments to characterize when the semiparametric efficiency bound can be attained the efficiency condition is that the moment tangent set equals the model tangent set we apply these results to transformed censored and truncated regression models e g finding that the conditional moment restrictions from powell s 1986 censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors

existence and multiplicity of solutions for asymptotically hamiltonian elliptic systems in rn abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h u x u v in r n v v x v h v x u v in r n u x 0 and v x 0 as x where the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain solutions for the above system

tails of lorenz curves the lorenz dominance criterion is the centre piece of inequality analysis yet the appeal of this criterion which requires considering lorenz curves in their entirety is undermined by the practical problem that many sample lorenz curves intersect in the tails the commonly used inferential methods based on central limit theorem arguments do not apply to the tails since these contain too few observations by contrast we propose a test procedure for distributions whose tails lie in the domain of attraction of the frechet distribution which fully takes into account the tail behaviour of lorenz curves our experiments and empirical examples demonstrate the good performance of the proposed test in many cases we are able to infer that despite sample tail crossings the population lorenz curves do in fact exhibit lorenz dominance

semiparametric and nonparametric estimation of sample selection models under symmetry this paper considers the semiparametric estimation of binary choice sample selection models under a joint symmetry assumption our approaches overcome various drawbacks associated with existing estimators in particular our method provides root n consistent estimators for both the intercept and slope parameters of the outcome equation in a heteroscedastic framework without the usual cross equation exclusion restriction or parametric specification for the error distribution and or the form of heteroscedasticity our two step estimators are shown to be consistent and asymptotically normal a monte carlo simulation study indicates the usefulness of our approaches

using parametric classification trees for model selection with applications to financial risk management abstract we describe two parametric classification tree methods which allow formal selection of a member of a class of generalised distributions in the paper we consider generalised beta distributions for non negative random variables and the generalised skew student distribution for random variables distributed on the real line we introduce a class of symmetric generalised multivariate student distributions members of which may also be selected using the classification trees we present two versions of the parametric classification tree specific to general and general to specific we apply the classification methods to daily returns on stocks from a selection of 15 major mid cap and emerging markets the results show that the majority of return distributions follow student s t but that a non negligible minority follow a symmetric generalised student distribution we confirm a well known stylised fact about skewness it tends not to be persistent by contrast kurtosis is persistent using the symmetric generalised multivariate student distribution we present a risk management study based on efficient portfolios constructed from ukftse250 stocks and specifically concerned with the computation of value at risk the case study demonstrates that the model selection procedures based on the classification trees lead to more accurate computation of var than those based on the normal distribution or on non parametric approaches the study also shows that the normal distribution may be used for var computations for larger portfolios when the holding period is longer

sparse certificates for 2 connectivity in directed graphs motivated by the emergence of large scale networks in today s applications we show how to compute efficiently smaller subgraphs that maintain some properties of an input graph in particular let g be a strongly connected directed graph we consider the problem of computing the smallest strongly connected spanning subgraph of g that maintains certain connectivity relations of g specifically for 2 edge connectivity we consider how to maintain the maximal 2 edge connected subgraphs 2ecs or the 2 edge connected components 2ecc of g or both the maximal 2 edge connected subgraphs and the 2 edge connected components 2ec similarly for 2 vertex connectivity we consider how to maintain the maximal 2 vertex connected subgraphs 2vcs or the 2 vertex connected components 2vcc of g or both the maximal 2 vertex connected subgraphs and the 2 vertex connected components 2vc all those problems are np hard and thus we are interested in approximation algorithms additionally we aim at designing algorithms with a good practical performance so that they are able to scale effectively to very large graphs while for 2ecs and 2vcs one can obtain an approximation ratio smaller than 2 by combining previously known results providing good approximations for the 2 edge and the 2 vertex components case seems more challenging here we present linear time approximation algorithms that achieve the following approximation guarantees 4 approximation for 2ecc and 2ec and 6 approximation for 2vcc and 2vc also augmented versions of our 2vcc algorithm computes a 6 approximation for maintaining both the 2 edge and the 2 vertex connected components 2cc and for maintaining all the 2 connectivity relations of g 2c i e both the 2 edge and the 2 vertex connected subgraphs and components moreover we provide heuristics that improve the size of the computed subgraphs in practice and conduct a thorough experimental study to assess their merits in practical scenarios

on hamiltonian elliptic systems with periodic or non periodic potentials abstract this paper is concerned with the following hamiltonian elliptic system u b x u v x u h v x u v v b x v v x v h u x u v for x r n existence and multiplicity of solutions are obtained for the systems with periodic or non periodic potentials v via variational methods

a note on superlinear hamiltonian elliptic systems this paper is concerned with the superlinear periodic elliptic systems of hamiltonian type in the whole space the existence of a ground state solution as well as an infinite number of geometrically distinct solutions is obtained

infinitely many solutions for diffusion equations without symmetry abstract we consider the following diffusion system t u x u b t x x u v x u h v t x u v t v x v b t x x v v x v h u t x u v t x r r n which is an unbounded hamiltonian system in l 2 r r n r 2 m z u v r r n r m r m b c r r n r n v c r n r and h c 1 r r n r 2 m r suppose that h b and v depend periodically on t and x and that h t x z is superquadratic in z as z without a symmetry assumption on h we establish the existence of infinitely many geometrically distinct solutions via a variational approach

comparisons of log normal mixture and pareto tails gb2 or log normal body of romania s all cities size distribution abstract modeling demographic data has been on the agenda of statisticians for many years some of the distributions used are pareto reverse pareto q exponential and log normal models an approach to this problem is to consider three statistical models one for the upper tail one for the middle range and another for the lower tail this paper deals with the size distribution of urban and rural agglomerations in romania for the 1992 2017 period by comparing the recently introduced three log normal mixture 3ln pareto tails log normal ptln and threshold double pareto generalized beta of second kind tdpgb2 models the tdpgb2 statistical model has the ptln distribution as a limiting case the maximum likelihood estimates of the distributions are computed and goodness of fit tests are performed using the kolmogorov smirnov ks cramer von mises cm and anderson darling ad statistics also we use the vuong and bayes factor log likelihood tests using both graphical and formal statistical tests our results rigorously confirm that the 3ln model is statistically equivalent to ptln and tdpgb2 distributions the preferred model being the ptln probability law both the ptln and tdpgb2 distributions have pareto tails but the 3ln model does not all the three models prove to be very well suited parameterizations of romania s city size data

rank estimation of a location parameter in the binary choice model abstract this paper proposes a rank based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition given an initial n consistent estimator for the slope parameter the estimator converges at the usual parametric rate compared with existing estimators no nonparametric smoothing is needed here a small monte carlo study illustrates the usefulness of the estimator we also point out that the location and slope parameters can be jointly estimated

existence of positive solutions for elliptic systems with nonstandard p x growth conditions via sub supersolution method abstract we mainly consider the system p x u f v in p x v g u in u v 0 on where p x c 1 r n is a radial symmetric function which satisfies sup p x and 1 inf p x sup p x where p x u div u p x 2 u is called p x laplacian b 0 r r n is a bounded radial symmetric domain where r is sufficiently large we prove the existence of a positive solution when lim u f m g u 1 p 1 u p 1 0 in particular we do not assume any sign condition on f 0 and g 0

a priori bounds and existence of positive solutions for semilinear elliptic systems abstract we provide a priori l bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v p and u q for any p q lying on the critical sobolev hyperbola our proof combines moving planes method and rellich pohozaev type identities for systems our analysis widens the known ranges of nonlinearities for which classical positive solutions of semilinear elliptic systems are a priori bounded using these a priori bounds and local and global bifurcation techniques we prove the existence of positive solutions for a corresponding parametrized semilinear elliptic system

on the upper tail of italian firms size distribution abstract in this paper we analyze the upper tail of the size distribution of italian companies with limited liability belonging to the cebi database size is defined in terms of net worth in particular we show that the largest firms follow a power law distribution according to the well known pareto law for which we give estimates of the shape parameter such a behavior seems to be quite persistent over time view that for almost 20 years of observations the shape parameter is always in the vicinity of 1 8 the power law hypothesis is also positively tested using graphical and analytical methods

existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight abstract we prove the existence of nonnegative solutions to the system u a x f v in v b x g u in u 0 v on where is a bounded domain in r n with a smooth boundary is a positive parameter by the method of monotone iteration and schauder fixed point theorem we prove the existence of a nonnegative solution to the above system for sufficiently small in this study we do not restrict the sign of a and b

asymptotically efficient estimation in the presence of heteroskedasticity of unknown form in a multiple regression model the residual variance is an unknown function of the explanatory variables and estimated by nearest neighbor nonparametric regression the resulting weighted least squares estimator of the regression coefficients is shown to be adaptive in the sense of having the same asymptotic distribution to first order as estimators based on knowledge of the actual variance function or a finite parameterization of it a similar result was established by carroll 1982 using kernel estimation and under substantially more restrictive conditions on the data generating process than ours extensions to various other models seem to be possible

a general functional form for approximating the lorenz curve abstract the purpose of this paper is to present several descriptive approximations of empirical lorenz curves each of these hypothetical forms is less restrictive than those considered before we compare these alternative forms by goodness of fit f tests of nested forms and measurement of the gini coefficient

elliptical lorenz curves abstract a family of elliptic lorenz curves is proposed for fitting grouped income data the associated distribution and density functions are displayed together with the gini indices estimation procedures are discussed comparisons are made with alternative models using australian 1967 68 income data

statistical inference for poverty measures with relative poverty lines relative poverty lines such as one half median income have been increasingly used in poverty studies this paper contributes to the literature by developing statistical inference for testing decomposable poverty measures with relative poverty lines the poverty lines we consider are percentages of mean income and percentages of quantiles we show that the estimates of poverty indices with relative poverty lines are asymptotically normally distributed and that the covariance structure can be consistently estimated as a consequence asymptotically distribution free statistical inference can be established in a straightforward manner

the exponentiated generalized birnbaum saunders distribution a new distribution called the exponentiated generalized birnbaum saunders distribution is proposed and studied the new distribution is quite flexible to model survival data reliability problems fatigue life studies and hydrological data it can have decreasing increasing upside down bathtub bathtub shaped increasing decreasing increasing and decreasing increasing decreasing hazard rate functions we provide a comprehensive account of the mathematical properties of the new distribution and various structural quantities are derived we discuss maximum likelihood estimation of the model parameters for uncensored and censored data two empirical applications of the new model to real data are presented for illustrative purposes

exponentiated beta distributions beta distributions are usually defined on the unit interval 0 1 for wider applicability we introduce six exponentiated beta distributions and derive several of their properties including the moment generating function expectation variance skewness kurtosis shannon entropy and the renyi entropy

heavy tailed distributions and the distribution of wealth evidence from rich lists in canada 1999 2017 abstract i examine whether a power law distribution fits the top wealth distribution i e the rich 100 from canada i use a maximum likelihood framework that considers the fit of the estimated distribution as well as allowing tests against alternative heavy tailed and skewed distributions i find that while a power law distribution does fit the data well it is not possible to distinguish it from a lognormal distribution truncated to the upper tail

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

more efficient estimation under non normality when higher moments do not depend on the regressors using residual augmented least squares under normality least squares is efficient however if the errors are not normal we can gain efficiency from the assertion that higher moments do not depend on the regressors in this paper we show how the assumption that higher moments do not depend on the regressors can be exploited in a gmm framework and we provide simple estimators that are asymptotically equivalent to the gmm estimators these estimators can be calculated by linear regressions which have been augmented with functions of the least squares residuals

the potential for efficiency gains in estimation from the use of additional moment restrictions it is frequently assumed that in generalised method of moments estimation the explicit utilization of valid additional moment restrictions will lead to asymptotic efficiency gains in this paper i develop a general framework for examining the possibility of such efficiency gains using this framework i then consider in more detail the potential for efficiency gains from utilizing a constant conditional disturbance variance restriction when estimating a single equation from a nonlinear simultaneous equations model sem by nonlinear two stage least squares 2sls in general such efficiency gains will arise however for a linear sem with constant disturbance covariances and zero third moments no efficiency gains arise for fairly general instrument sets this generalises in certain respects the usual result that 2sls is asymptotically efficient for estimating a single equation from a linear sem with independently identically distributed normal disturbances

general model of subtraction of stochastic variables attractor and stability analysis abstract we introduce a general process designed to model stochastic systems in which the dependence of random variables is not through addition only but combined addition and subtraction with bounded ranges and whose probabilistic factors have compact support we show that still retaining much of the general essence of the central limit theorem this process presents a functional attractor which is neither gaussian nor levy like and is precisely akin numerically to a probability density function shown in previous works to have ubiquitous character namely the two parameter beta distribution

geometrically concave univariate distributions in this paper our aim is to show that if a probability density function is geometrically concave convex then the corresponding cumulative distribution function and the survival function are geometrically concave convex too under some assumptions the proofs are based on the so called monotone form of l hospital s rule and permit us to extend our results to the case of the concavity convexity with respect to holder means to illustrate the applications of the main results we discuss in details the geometrical concavity of the probability density function cumulative distribution function and survival function of some common continuous univariate distributions moreover at the end of the paper we present a simple alternative proof to schweizer s problem related to the mulholland s generalization of minkowski s inequality

estimation of lorenz curves a bayesian nonparametric approach abstract in this article we estimate lorenz curves using the recent development of the bayesian nonparametric method with dirichlet process prior we also consider contaminated observations of income and propose a method for removing these contaminated observations further we present examples using both simulated data and real data to illustrate our approach

statistical inference for testing inequality indices with dependent samples this paper develops asymptotically distribution free inference for testing inequality indices with dependent samples it considers the interpolated gini coefficient and the generalized entropy class which includes several commonly used inequality indices we first establish inference tests for changes in inequality indices with completely dependent samples i e matched pairs and then generalize the inference procedures to cases with partially dependent samples the effects of sample dependency on standard errors of inequality changes are examined through simulation studies as well as through applications to the cps and psid data

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

universality in the tail of musical note rank distribution abstract although power laws have been used to fit rank distributions in many different contexts they usually fail at the tails languages as sequences of symbols have been a popular subject for ranking distributions and for this purpose music can be treated as such here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution which arises in the ranking of multiplicative stochastic processes the parameters a and b are obtained for classical jazz and rock music revealing interesting features specially we have obtained a clear trend in the values of the parameters for major and minor tonal modes finally we discuss the distribution of notes for each octave and its connection with the ranking of the notes

monte carlo evidence on adaptive maximum likelihood estimation of a regression on examine la performance des estimateurs du maximum de vraisemblance adaptatifs lorsque ces parametres sont preselectionnes ou alternativement determines par une methode du bootstrap basee sur les donnees

the design of simulation studies in medical statistics by andrea burton douglas g altman patrick royston and roger l holder statistics in medicine 2006 25 4279 4292

an ordered family of lorenz curves abstract a general method for building parametric functional families of lorenz curves generated from an initial lorenz curve which satisfies some regularity conditions is presented it is shown that these families can be ordered in a manner which leads to a hierarchy of lorenz curves the method starts from a generating lorenz curve l 0 p and builds the family by increasing the number of parameters which can be easily interpreted in terms of the elasticities of l 0 p the method is applied to a family we term the pareto family since they use the pareto lorenz curves as their generating curves the family is shown to contain an important number of classical lorenz curves used in the existing literature several properties of this family are analyzed these include the population function inequality measures and lorenz orderings a general method for the estimation of these family is given and applied to the pareto family finally an application is presented for data from various countries the results are very robust across data sources the pareto models fit very well in a number of applications

using incomplete moments to measure inequality abstract incomplete moments of the income distribution form natural building blocks for measuring inequality for example income quintiles the lorenz curve pietra and gini measures of inequality all depend upon the incomplete moments of the income distribution this paper discusses these relationships and shows that they are easily calculated for a very broad family of distributions because they possess a closure property empirical illustrations are given for the white family income distribution for the 1948 to 1980 period

edgeworth expansions and normalizing transforms for inequality measures abstract finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness we study these aspects formally by deriving the second order expansion of the first and third cumulant of the studentized inequality measure we state distribution free expressions for the bias and skewness coefficients in the second part we improve over first order theory by deriving edgeworth expansions and normalizing transforms these normalizing transforms are designed to eliminate the second order term in the distributional expansion of the studentized transform and converge to the gaussian limit at rate o n 1 this leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order o n 3 2 we illustrate our procedure with an application to regional inequality measurement in cote d ivoire

a generalization of the beta distribution with applications abstract this paper introduces a five parameter beta distribution gb which nests the generalized beta and gamma distributions and includes more than thirty distributions as limiting or special cases the generalized beta leads to an exponential generalized beta egb distribution which includes generalized forms of the logistics exponential gompertz and gumbell distributions and the normal as special cases the egb family of distributiosn provides the basis for partially adaptive estimation of econometric models with possibly skewed and leptokurtic error distributions applications of the models to investigating the distribution of income stock returns and in regression analysis are considered

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

2 vertex connectivity in directed graphs given a directed graph two vertices v and w are 2 vertex connected if there are two internally vertex disjoint paths from v to w and two internally vertex disjoint paths from w to v in this paper we show how to compute this relation in o m n time where n is the number of vertices and m is the number of edges of the graph as a side result we show how to build in linear time an o n space data structure which can answer in constant time queries on whether any two vertices are 2 vertex connected additionally when two query vertices v and w are not 2 vertex connected our data structure can produce in constant time a witness of this property by exhibiting a vertex or an edge that is contained in all paths from v to w or in all paths from w to v we are also able to compute in linear time a sparse certificate for 2 vertex connectivity i e a subgraph of the input graph that has o n edges and maintains the same 2 vertex connectivity properties as the input graph

lorentz sobolev spaces and systems of schrodinger equations in rn abstract we study the connection between the improvement of limiting sobolev s embeddings within the context of lorentz spaces and the variational approach to systems of nonlinear schrodinger equations we show that lorentz sobolev spaces appear as a natural function space domain for the related energy functional moreover in this framework the nonlinearity may exhibit a supercritical growth with respect to the maximal growth prescribed by the poho aev trudinger moser inequality and still preserving a variational structure

exploring positive noise in estimation theory estimation of the mean of a stochastic variable observed in noise with positive support is considered it is well known from the literature that order statistics gives one order of magnitude lower estimation variance compared to the best linear unbiased estimator blue we provide a systematic survey of some common distributions with positive support and provide derivations of minimum variance unbiased estimators mvue based on order statistics including blue for comparison the estimators are derived with or without knowledge of the hyperparameters of the underlying noise distribution though the uniform exponential and rayleigh distributions respectively we consider are standard in literature the problem of estimating the location parameter with additive noise from these distribution seems less studied and we have not found any explicit expressions for blue and mvue for these cases in addition to additive noise with positive support we also consider the mixture of uniform and normal noise distribution for which an order statistics based unbiased estimator is derived finally an iterative global navigation satellite system gnss localization algorithm with uncertain pseudorange measurements is proposed which relies on the derived estimators for receiver clock bias estimation simulation data for gnss time estimation and experimental gnss data for joint clock bias and position estimation are used to evaluate the performance of the proposed methods

existence and multiplicity of solutions for asymptotically linear nonperiodic hamiltonian elliptic system abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v v v x v h u x u v x r n u x v x 0 as x where z u v r n r r n 3 assuming the potential v is nonperiodic and sign changing h x z is nonperiodic in x and asymptotically quadratic in z u v existence and multiplicity of solutions are obtained via a variational approach

financial data and the skewed generalized t distribution this paper develops a skewed extension of the generalized t gt distribution introducedby mcdonald and newey 1988 in particular the paper derives the mathematical moments and other properties of the distribution and assesses its ability to fit the empirical distribution of several financial series characterized by skewness and excess kurtosis in all cases the skewed gt provides an excellent fit to the empirical distribution of data

efficiency improvements in inference on stationary and nonstationary fractional time series we consider a time series model involving a fractional stochastic component whose integration order can lie in the stationary invertible or nonstationary regions and be unknown and an additive deterministic component consisting of a generalized polynomial the model can thus incorporate competing descriptions of trending behavior the stationary input to the stochastic component has parametric autocorrelation but innovation with distribution of unknown form the model is thus semiparametric and we develop estimates of the parametric component which are asymptotically normal and achieve an m estimation efficiency bound equal to that found in work using an adaptive lam lan approach a major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies this is relevant also when the innovation density is parameterized and we provide a result for that case also our semiparametric estimates employ nonparametric series estimation which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models our work thus also contributes to methods and theory for nonfractional time series models such as autoregressive moving averages a monte carlo study of finite sample performance of the semiparametric estimates is included

the existence of solutions for superquadratic hamiltonian elliptic systems on rn abstract this paper is concerned with the following hamiltonian elliptic system u v x u h u x u v in r n v v x v h v x u v in r n u x 0 and v x 0 as x where v x c r n r and h x z is superquadratic in z as z with z u v by applying a critical point theorem for strongly indefinite functionals we obtain infinitely many solutions for the above system

existence and multiplicity of semiclassical solutions for asymptotically hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system e 2 u v x u h u x u v in r n e 2 v v x v h v x u v in r n u x 0 and v x 0 as x where e 0 is a small parameter and the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain the existence of multiple semiclassical solutions for the above system

ground state solutions of hamiltonian elliptic systems in dimension two the aim of this paper is to study hamiltonian elliptic system of the form 0 1 where 2 is a bounded domain in the second place we present existence results for the following stationary schrodinger systems defined in the whole plane 0 2 we assume that the nonlinearities f g have critical growth in the sense of trudinger moser by using a suitable variational framework based on the generalized nehari manifold method we obtain the existence of ground state solutions of both systems 0 1 and 0 2

partially adaptive robust estimation of regression models and applications abstract this paper provides an accessible exposition of recently developed partially adaptive estimation methods and their application these methods are robust to thick tailed or asymmetric error distributions and should be of interest to researchers and practitioners in data mining agent learning and mathematical modeling in a wide range of disciplines in particular partially adaptive estimation methods can serve as robust alternatives to ordinary regression analysis as well as machine learning methods developed by the artificial intelligence and computing communities results from analysis of three problem domains demonstrate application of the theory

multiple solutions for asymptotically quadratic and superquadratic elliptic system of hamiltonian type this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v x r n v v x v h u x u v x r n u x 0 v x 0 as x where z u v r n r i r n 3 and the potential v x is nonperiodic and sign changing by applying a generalized linking theorem for strongly indefinite functionals we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity

explicit expressions of the pietra index for the generalized function for the size distribution of income abstract the importance of the pietra index in socioeconomic systems and econophysics has been highlighted by eliazar and sokolov 2010 in this paper we obtain closed expressions for the pietra index for the generalized function for the size of income proposed by mcdonald 1984 this family is composed of three classes of distributions the generalized gamma distribution gg the generalized beta of the first kind gb1 and the generalized beta of the second kind gb2 for the different distributions we obtain closed and simple expressions of the pietra index which can be easily computed we also obtain the pietra index for other relevant income models including finite mixtures of distributions and the generalized distribution clementi et al 2008 finally two empirical applications with real income data are given

entropy maximization under the constraints on the generalized gini index and its application in modeling income distributions abstract in economics and social sciences the inequality measures such as gini index pietra index etc are commonly used to measure the statistical dispersion there is a generalization of gini index which includes it as special case in this paper we use principle of maximum entropy to approximate the model of income distribution with a given mean and generalized gini index many distributions have been used as descriptive models for the distribution of income the most widely known of these models are the generalized beta of second kind and its subclass distributions the obtained maximum entropy distributions are fitted to the us family total money income in 2009 2011 and 2013 and their relative performances with respect to generalized beta of second kind family are compared

linear time algorithms for two disjoint paths problems on directed acyclic graphs we present an algorithm that given two vertices s 1 and s 2 of a directed acyclic graph constructs in linear time a data structure using linear space that for each pair u v of two vertices u and v in constant time can output a tuple s 1 t 1 s 2 t 2 with t 1 t 2 u v such that there are two disjoint paths p 1 from s 1 to t 1 and p 2 from s 2 to t 2 if such a tuple exists the data structure is simpler than such a data structure for general directed graphs that can be obtained from results of georgiadis and tarjan disjoint can mean vertex as well as edge disjoint as an application and main result we show that the data structure can be used to solve the 2 disjoint paths problem on directed acyclic graphs optimally i e in linear time

estimating parameters in continuous univariate distributions with a shifted origin summary a general method of estimating parameters in continuous univariate distributions is proposed it is especially suited to cases where one of the parameters is an unknown shifted origin this occurs for example in the three parameter lognormal gamma and weibull models for such distributions it is known that maximum likelihood ml estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators properties of the proposed method are described in particular it is shown to give consistent estimators with asymptotic efficiency equal to ml estimators when these exist moreover it gives consistent asymptotically efficient estimators in situations where ml fails examples are given including numerical ones showing the advantages of the method

existence of solutions for nonperiodic superquadratic hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u r v x u v in r n v v x v r u x u v in r n u x 0 and v x 0 as x where r x z is superquadratic in z as z with z u v by applying a critical point theorem for strongly indefinite functionals we prove the existence of solution for the above system

income distribution and inequality measurement the problem of extreme values we examine the statistical performance of inequality indices in the presence of extreme values in the data and show that these indices are very sensitive to the properties of the income distribution estimation and inference can be dramatically affected especially when the tail of the income distribution is heavy even when standard bootstrap methods are employed however use of appropriate semiparametric methods for modelling the upper tail can greatly improve the performance of even those inequality indices that are normally considered particularly sensitive to extreme values

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

two flexible functional form approaches for approximating the lorenz curve abstract this paper introduces two flexible form approaches to approximate lorenz curves the first approach expands the inverse function of an income distribution in an exponential polynomial series and derives the lorenz curve from it the required convexity condition can be imposed using a bayesian method the second approach approximates the lorenz curve with a sequence of berstein polynomial functions the required convexity condition is automatically established in this approach we compare these approaches with other well known fixed functional form approaches we evaluate the performance of these functional forms by comparing approximation errors maximum error and the estimates of the gini coefficient produced by various approaches

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates