ordering and selecting extreme populations by means of entropies and divergences this paper studies the simultaneous selection of extreme populations from a set of independent populations two types of subset selection rules for k populations are proposed and studied the first type selects one subset of populations that should contain the population with the smallest and another subset of populations that should contain the population with the largest f entropy the second type selects analogously but in terms of the extreme f divergences with respect a known control population properties of the proposed procedures are stated and studied examples are presented in order to illustrate the results

a simple solution of the bratu problem a brief survey of the properties and different treatments of the one dimensional 1d and 2d bratu problems is presented different iterative treatments of the resulting nonlinear system of equations are discussed the finite difference treatment of the problem is considered nonstandard finite difference methods with a simple sinusoidal starting function having an appropriate amplitude are recommended bounds on the amplitude for yielding both lower and upper solutions are given

a note on parameterization of the class of deadbeat controllers the problem of parameterizing the class of deadbeat controllers for a given discrete time system through the minimum number of parameters was solved by schlegel 1 this note shows how to utilize the above solution to study some problems in designing deadbeat controllers first an algorithm is developed to compute a controller which minimizes in an average sense a given objective function second a necessary and sufficient condition is given for the existence of an output deadbeat controller finally the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase variable block canonical form is reconsidered

an efficient iterative method for solving bratu type equations abstract in this paper an efficient analytical iterative method is introduced for solving the initial value and boundary value bratu problems a quasilinearization method with an optimal parameter is derived and utilized to reduce the highly nonlinear bratu equations to a sequence of linear problems an optimal picard iteration method is used to obtain approximate analytical solution of linearized versions of bratu s equations the numerical results presented the effectiveness and high performance of the proposed method and comparisons are made with many other existing numerical solution techniques the comparisons reveal the efficiency and applicability of the present work

goodness of fit tests based on rao s divergence under sparseness assumptions in many practical situations the classical fixed cells assumptions to test goodness of fit are inappropriate and we consider an alternative set of assumptions which we call sparseness assumptions it is proved that under general conditions the proposed family of statistics based on rao s divergence is asymptotically normal when the sample size n and the number of cells m n tend to infinity so that n m n n 0 this result is extended to contiguous alternatives and subsequently it is possible to find the asymptotically most efficient member of the family

divergence statistics for testing uniform association in cross classifications in this paper we consider the problem of testing uniform association in cross classifications having ordered categories taking as test statistic one in the family proposed by conde and salicru j conde m salicru uniform association in contingency tables associated to csiszar divergence statistics and probability letters 37 1998 149 154 we consider two approximations to the null distribution of the test statistics in this family an estimation of the asymptotic null distribution and a bootstrap estimator we prove that both approximations are asymptotically equivalent to study their finite sample performance we carried out two simulation experiments whose results are presented from the simulations it can be concluded that the bootstrap estimator behaves much better than the estimated asymptotic null distribution

robust fitting of the binomial model we consider the problem of robust inference for the binomial m pi model the discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results for example the maximum likelihood estimator mle is quite robust it cannot be improved on for m 1 but can be for m 1 we discuss four other classes of estimators m estimators minimum disparity estimators optimal mgp estimators and a new class of estimators which we call e estimators we show that e estimators have a non standard asymptotic theory which challenges the accepted relationship between robustness concepts and thereby provided new perspectives on these concepts

powerful goodness of fit tests based on the likelihood ratio summary a new approach of parameterization is proposed to construct a general goodnessof fit test it can not only generate traditional tests including the kolmogorov smirnov cramer von mises and anderson darling tests but also produce new types of omnibus tests which are generally much more powerful than the old ones

deadbeat algorithms for output controllers in discrete time multivariable systems abstract this paper studies the problem of designing output deadbeat controllers to force the state of discrete time multivariable systems to zero in a finite number of samples two algorithms are considered the first is based on the fact that the closed loop eigenstructure assignable by output feedback is constrained by the requirement that the left and right eigenvectors must be in certain subspaces in the second algorithm the output gain matrix is computed through the optimization of certain parameters of the controller while maintaining its structural constraints computer programs have been developed to realize the two algorithms and examples are given to illustrate the feasibility of the techniques

the design of deadbeat controllers by state transition graph two kinds of deadbeat control problems are considered one is the state deadbeat control problem and the other is the pointwise minimum time deadbeat control problem a simple graph called the state transition graph of a matrix is introduced and simple algorithms based on it giving deadbeat controllers are presented the set of pointwise minimum time deadbeat controllers is characterized the set of output feedback deadbeat controller is also considered

comments on design of optimal dead beat controllers it is shown that the system considered in the numerical example of the above paper belongs to a class of systems with n states and r inputs for which the set of all minimum time dead beat mtdb controllers is parameterized by an arbitrary matrix of order lambda 1 r n x n lambda r where is the greatest integer less than the ratio n r since the example treats the case of n 3 r 2 the mdtb controller is parameterized by a single scalar element

adomian decomposition method for a reliable treatment of the bratu type equations in this paper we present a framework to determine exact solutions of bratu type equations the algorithm rests mainly on the adomian decomposition method the proposed scheme is illustrated by studying two boundary value problems and an initial value problem of bratu type the first type gives a solution that blows up at the middle of the domain whereas the other equations give bounded solutions

the legendre wavelet method for solving initial value problems of bratu type the aim of this work is to study the legendre wavelets for the solution of initial value problems of bratu type which is widely applicable in fuel ignition of the combustion theory and heat transfer the properties of legendre wavelets together with the gaussian integration method are used to reduce the problem to the solution of nonlinear algebraic equations also a reliable approach for convergence of the legendre wavelet method when applied to a class of nonlinear volterra equations is discussed and an error estimation for the proposed method is also introduced illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results have been compared with the exact solution we finally show the high accuracy and efficiency of the proposed method

power and sample size for stratified prospective studies using the score method for testing relative risk we derive the asymptotic power function of the score test for detecting a common relative risk greater than unity from multiple 2 x 2 tables and formulate methods of sample size determination for use when designing stratified prospective studies the stratified score test is more efficient than the unstratified test when the latter is unbiased

confidence limits to the risk ratio for the problem of obtaining confidence limits to the risk ratio or the ratio of two binomial probabilities katz et al 1978 biometrics 34 469 474 proposed a method based on the logarithm of the observed ratio and using fieller s result we propose a method based on a power of the observed ratio the power being chosen to minimize the skewness of the pivotal random variable the method is simple to use and more stable than that of katz et al a continuity correction is suggested if a conservative interval is desired

high order analysis of the limit cycle of the van der pol oscillator we have applied the lindstedt poincare method to study the limit cycle of the van der pol oscillator obtaining the numerical coefficients of the series for the period and for the amplitude to order 859 hermite pade approximants have been used to extract the location of the branch cut of the series with unprecedented accuracy 100 digits both series have then been resummed using an approach based on pade approximants where the exact asymptotic behaviors of the period and the amplitude are taken into account our results improve drastically all previous results obtained on this subject

combining estimators to improve structural model estimation and inference under quadratic loss asymptotically semi parametric estimators of the parameters in linear structural models have the same sampling properties in finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice with a goal of improving asymptotic risk performance and finite sample efficiency properties we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics based on a quadratic loss measure we present evidence that the finite sample performance of the resulting combination estimator can be notably superior to that of a leading traditional moment based estimator

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

one point pseudospectral collocation for the one dimensional bratu equation abstract the one dimensional planar bratu problem is u xx exp u 0 subject to u 1 0 because there is an analytical solution this problem has been widely used to test numerical and perturbative schemes we show that over the entire lower branch and most of the upper branch the solution is well approximated by a parabola u x u 0 1 x 2 where u 0 is determined by collocation at a single point x the collocation equation can be solved explicitly in terms of the lambert w function as u 0 w 1 2 2 1 2 where both real valued branches of the w function yield good approximations to the two branches of the bratu function we carefully analyze the consequences of the choice of we also analyze the rate of convergence of a series of even chebyshev polynomials which extends the one point approximation to arbitrary accuracy the bratu function is so smooth that it is actually poor for comparing methods because even a bad inefficient algorithm is successful it is however a solution so smooth that a numerical scheme the collocation or pseudospectral method yields an explicit analytical approximation we also fill some gaps in theory of the bratu equation we prove that the general solution can be written in terms of a single parameter free x without knowledge of the explicit solution the analytical solution can only be evaluated by solving a transcendental eigenrelation whose solution is not known explicitly we give three overlapping perturbative approximations to the eigenrelation allowing the analytical solution to be easily evaluated throughout the entire parameter space

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

bootstrap confidence regions in multinomial sampling power divergences can be used to give a measure of distance between two probability vectors in multinomial sampling arguments can be substituted by empirical and theoretical proportions to obtain confidence regions of parameters in this paper the bootstrap versions of these confidence regions are constructed monte carlo simulation experiments are carried out to calculate average coverage probabilities and to compare the behavior of the introduced procedures

efficient derivative pricing by the extended method of moments in this paper we introduce the extended method of moments xmm estimator this estimator accommodates a more general set of moment restrictions than the standard generalized method of moments gmm estimator more specifically the xmm differs from the gmm in that it can handle not only uniform conditional moment restrictions i e valid for any value of the conditioning variable but also local conditional moment restrictions valid for a given fixed value of the conditioning variable the local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns the estimated derivative prices are consistent for a large time series dimension but a fixed number of cross sectionally observed derivative prices the asymptotic properties of the xmm estimator are nonstandard since the combination of uniform and local conditional moment restrictions induces different rates of convergence parametric and nonparametric for the parameters

power approximations to multinomial tests of fit abstract multinomial tests for the fit of iid observations x 1 xn to a specified distribution f are based on the counts ni of observations falling in k cells e 1 ek that partition the range of the x j the earliest such test is based on the pearson 1900 chi squared statistic x 2 k i 1 ni npi 2 npi where pi pf xj in ei are the cell probabilities under the null hypothesis a common competing test is the likelihood ratio test based on lr 2 k i 1 ni log ni npi cressie and read 1984 introduced a class of multinomial goodness of fit statistics r based on measures of the divergence between discrete distributions this class includes both x 2 when 1 and lr when 0 all of the r have the same chi squared limiting null distribution the power of the commonly used members of the class is usually approximated from a noncentral chi squared distribution that is also the same for all we propose new approximations to the power that vary with the statistic chosen bot

dynamics of the solution of bratu s equation abstract in the present report we examine the dynamics exhibited by the solution of bratu s equation it represents a one dimensional map with control parameter for certain values of the parameter it exhibits successive bifurcations and shows chaotic regimes this behaviour was confirmed by calculating the corresponding lyapunov exponent power spectra and cobweb diagrams indicating similarities with other well known one dimensional maps

chebyshev expansion on intervals with branch points with application to the root of kepler s equation a chebyshev hermite pade method when two or more branches of a function merge the chebyshev series of u l will converge very poorly with coefficients a n of t n l falling as o 1 n a for some small positive exponent a however as shown in j p boyd chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one dimensional bratu equation appl math comput 143 2002 189 200 it is possible to obtain approximations that converge exponentially fast in n if the roots that merge are denoted as u 1 l and u 2 l then both branches can be written without approximation as the roots of u u 1 l u u 2 l u email protected l email protected l by expanding the nonsingular coefficients of the quadratic b l and c l as chebyshev series and then applying the usual roots of a quadratic formula we can approximate both branches simultaneously with error that decreases proportional to exp email protected for some constant s 0 where n is the truncation of the chebyshev series this is dubbed the chebyshev shafer or chebyshev hermite pade method because it substitutes chebyshev series for power series in the generalized pade approximants known variously as shafer or hermite pade approximants here we extend these ideas first we explore square roots with branches that are both real valued and complex valued in the domain of interest illustrated by meteorological baroclinic instability second we illustrate triply branched functions via roots of the kepler equation f u l e email protected u email protected 0 only one of the merging roots is real valued and the root depends on two parameters l e rather than one nonetheless the chebyshev hermite pade scheme is successful over the whole two dimensional parameter plane we also discuss how to cope with poles and logarithmic singularities that arise in our examples at the extremes of the expansion domain

comparing diagnostic tests a simple graphic using likelihood ratios the diagnostic abilities of two or more diagnostic tests are traditionally compared by their respective sensitivities and specificities either separately or using a summary of them such as youden s index several authors have argued that the likelihood ratios provide a more appropriate if in practice a less intuitive comparison we present a simple graphic which incorporates all these measures and admits easily interpreted comparison of two or more diagnostic tests we show using likelihood ratios and this graphic that a test can be superior to a competitor in terms of predictive values while having either sensitivity or specificity smaller a decision theoretic basis for the interpretation of the graph is given by relating it to the tent graph of hilden and glasziou statistics in medicine 1996 finally a brief example comparing two serodiagnostic tests for lyme disease is presented published in 2000 by john wiley sons ltd

approximating the moments and distribution of the likelihood ratio statistic for multinomial goodness of fit abstract approximations were derived for the mean and variance of g 2 the likelihood ratio statistic for testing goodness of fit in a k cell multinomial distribution these approximate moments accurate to o n 3 may be used in fitting the distribution of g 2 extensive numerical studies of the exact and approximate distributions were performed in the special case of equiprobability the asymptotic chi squared distribution was found to fit poorly for k 4 satisfactory results were obtained using a multiplicative correction to the chi squared fit more sophisticated procedures using the beta distribution produced increased accuracy but at the cost of excessive computational labor

chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one dimensional bratu equation we introduce two methods for simultaneously approximating both branches of a two branched function using chebyshev polynomials both schemes remove the pernicious convergence wrecking effects of the square root singularity at the limit point where the two branches meet the chebyshev shafer method gives the approximants as the solution to a quadratic equation the mapping algorithm makes a quadratic change of variable for both the only input information is the set of values of f x at a set of discrete points there is little to choose between the two schemes in accuracy but the single expansion mapping method is more flexible in that it can accommodate different ranges on the two branches the eigenrelation for the one dimensional bratu equation is an interesting example because the upper branch is also singular at another point besides the limit point this too can be removed by subtracting the asymptotic solution which is the lambert w function from the upper branch only when the domain of the variable is infinite the quadratic change of variable can still be applied by substituting rational chebyshev functions which are basis functions for an unbounded interval for chebyshev polynomials we illustrate this by approximating the real valued root of the brill quintic u 5 u l l which was first solved by hermite using elliptic modular functions more than a century ago

information and entropy econometrics editor s view amos golan department of economics american university roper 200 4400 massachusetts ave nw washington dc 20016 usa

distributed estimation and detection for sensor networks using hidden markov random field models we develop a hidden markov random field hmrf framework for distributed signal processing in sensor network environments under this framework spatially distributed observations collected at the sensors form a noisy realization of an underlying random field that has a simple structure with markovian dependence we derive iterated conditional modes icm algorithms for distributed estimation of the hidden random field from the noisy measurements we consider both parametric and nonparametric measurement error models the proposed distributed estimators are computationally simple applicable to a wide range of sensing environments and localized implying that the nodes communicate only with their neighbors to obtain the desired results we also develop a calibration method for estimating markov random field model parameters from training data and discuss initialization of the icm algorithms the hmrf framework and icm algorithms are applied to event region detection numerical simulations demonstrate the performance of the proposed approach

maxallent maximizers of all entropies and uncertainty of uncertainty a b s t r a c t the entropy maximum approach maxent was developed as a minimization of the subjective uncertainty measured by the boltzmann gibbs shannon entropy many new entropies have been invented in the second half of the 20th century now there exists a rich choice of entropies for fitting needs this diversity of entropies gave rise to a maxent anarchism the maxent approach is now the conditional maximization of an appropriate entropy for the evaluation of the probability distribution when our information is partial and incomplete the rich choice of non classical entropies causes a new problem which entropy is better for a given class of applications we understand entropy as a measure of uncertainty which increases in markov processes in this work we describe the most general ordering of the distribution space with respect to which all continuous time markov processes are monotonic the markov order for inference this approach results in a set of conditionally most random distributions each distribution from this set is a maximizer of its own entropy this uncertainty of uncertainty is unavoidable in the analysis of nonequilibrium systems surprisingly the constructive description of this set of maximizers is possible two decomposition theorems for markov processes provide a tool for this description

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

using permutations to detect dependence between time series abstract in this paper we propose an independence test between two time series which is based on permutations the proposed test can be carried out by means of different common statistics such as pearson s chi square or the likelihood ratio we also point out why an exact test is necessary simulated and real data return exchange rates between several currencies reveal the capacity of this test to detect linear and nonlinear dependences

goodness of fit tests in models for life history data based on cumulative hazard rates to check the validity of an assumed parametric model for survival data one may compare t the nonparametric nelson aalen plot of the cumulative hazard rate with a t the estimated parametric cumulative hazard rate being for example the maximum likelihood estimator convergence in distribution of n t a t and more general processes is studied employing the general framework of counting processes which allows for quite general models for life history data and for quite general censoring schemes the results are applied to the construction of 2 type statistics for goodness of fit cramer von mises and kolmogorov smirnov type tests are presented in the case where the unknown parameter is one dimensional

efficient information theoretic inference for conditional moment restrictions abstract the generalised method of moments estimator may be substantially biased in finite samples especially so when there are large numbers of unconditional moment conditions this paper develops a class of first order equivalent semi parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel weighted version of the cressie read power divergence family of discrepancies this approach is similar in spirit to the empirical likelihood methods of kitamura et al 2004 empirical likelihood based inference in conditional moment restrictions models econometrica 72 1667 1714 and tripathi and kitamura 2003 testing conditional moment restrictions annals of statistics 31 2059 2095 these efficient local methods avoid the necessity of explicit estimation of the conditional jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations

a family of confidence intervals for the ratio of two binomial proportions the power divergence family of statistics introduced by cressie and read 1984 journal of the royal statistical society series b 46 440 464 is used to obtain approximate confidence intervals for the ratio of two proportions intervals based on inverting the pearson likelihood ratio and freeman tukey statistics are included in this family small sample comparisons of the intervals are presented

neglected heterogeneity in moment condition models abstract the central concern of this paper is parameter heterogeneity in models specified by a number of unconditional or conditional moment conditions and thereby the provision of a framework for the development of apposite optimal m tests against its potential presence we initially consider the unconditional moment restrictions framework optimal m tests against moment condition parameter heterogeneity are derived with the relevant jacobian matrix obtained in terms of the second order own derivatives of the moment indicator in a leading case gmm and gel tests of specification based on generalized information matrix equalities appropriate for moment based models are described and their relation to optimal m tests against moment condition parameter heterogeneity examined a fundamental and important difference is noted between gmm and gel constructions the paper is concluded by a generalization of these tests to the conditional moment context and the provision of a limited set of simulation experiments to illustrate the efficacy of the proposed tests

benford s law and the fsd distribution of economic behavioral micro data abstract in this paper we focus on the first significant digit fsd distribution of european micro income data and use information theoretic entropy based methods to investigate the degree to which benford s fsd law is consistent with the nature of these economic behavioral systems we demonstrate that benford s law is not an empirical phenomenon that occurs only in important distributions in physical statistics but that it also arises in self organizing dynamic economic behavioral systems the empirical likelihood member of the minimum divergence entropy family is used to recover country based income fsd probability density functions and to demonstrate the implications of using a benford prior reference distribution in economic behavioral system information recovery

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

robust and efficient estimation by minimising a density power divergence a minimum divergence estimation method is developed for robust parameter estimation the proposed approach uses new density based divergences which unlike existing methods of this type such as minimum hellinger distance estimation avoid the use of nonparametric density estimation and associated complications such as bandwidth selection the proposed class of density power divergences is indexed by a single parameter which controls the trade off between robustness and efficiency the methodology affords a robust extension of maximum likelihood estimation for which 0 choices of near zero afford considerable robustness while retaining efficiency close to that of maximum likelihood

robust estimation for grouped data here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data this class contains the classical maximum likelihood estimators for grouped data we find that the bias of these estimators due to deviations from the assumed underlying model can be large therefore we propose a more general class of estimators that allows us to construct robust procedures by analogy with hampel s theorem we define optimal bounded influence function estimators and by a simulation study we show that under small model contaminations these estimators are more stable than the classical estimators for grouped data finally we apply our results to a particular real example

letter to the editor on the integral solution of the one dimensional bratu problem a brief survey of the properties and different treatments of the one dimensional 1d planar bratu problem is presented the treatment using green s function is considered different iterative treatments of the resulting nonlinear system of equations are discussed starting the solution with simple sinusoidal function having appropriate amplitude is recommended then the resulting system is solved using a nonlinear conjugate gradient nl cg method the importance of the proper choice of the starting function as well as the stopping criterion of the iterative solution are stressed

the moment corrected phi divergence test statistics for symmetry in this paper we consider the family of f divergence test statistics t n f s for the problem of symmetry in ixi contingency tables whose asymptotic distribution is chi square with i i 1 2 degrees of freedom and we propose a moment corrected f divergence test statistic in order to improve the accuracy of the chi square approximation of the distribution of t n f s under the hypothesis of symmetry

data tilting for time series summary we develop a general methodology for tilting time series data attention is focused on a large class of regression problems where errors are expressed through autoregressive processes the class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression robust statistical inference and estimation subject to constraints the method can be viewed as empirical likelihood with nuisance parameters

tests of additional conditional moment restrictions abstract the primary focus of this article is the provision of tests for the validity of a set of conditional moment constraints additional to those defining the maintained hypothesis that are relevant for independent cross sectional data contexts the point of departure and principal contribution of the paper is the explicit and full incorporation of the conditional moment information defining the maintained hypothesis in the design of the test statistics thus the approach mirrors that of the classical parametric likelihood setting by defining restricted tests in contradistinction to unrestricted tests that partially or completely fail to incorporate the maintained information in their formulation the framework is quite general allowing the parameters defining the additional and maintained conditional moment restrictions to differ and permitting the conditioning variates to differ likewise gmm and generalised empirical likelihood test statistics are suggested the asymptotic properties of the statistics are described under both null hypothesis and a suitable sequence of local alternatives an extensive set of simulation experiments explores the practical efficacy of the various test statistics in terms of empirical size and size adjusted power confirming the superiority of restricted over unrestricted tests a number of restricted tests possess both sufficiently satisfactory empirical size and power characteristics to allow their recommendation for econometric practice

normal goodness of fit tests for multinomial models with large degrees of freedom abstract goodness of fit tests for independent multinomials with parameters to be estimated are usually based on pearson s x 2 or the likelihood ratio g 2 both are included in the family of power divergence statistics sd for increasing sample sizes each sd has an asymptotic x 2 distribution provided that the number of cells remains fixed we are dealing with an increasing cells approach where the number j of independent multinomials increases while the number of classes for each multinomial and the number of parameters remain fixed extending results on x 2 and g 2 the asymptotic normality of any sd is obtained for increasing cells the corresponding normal goodness of fit tests discussed here apply for models with large degrees of freedom with no restrictions imposed on the sizes n j of each multinomial allowing large as well as small expectations sparse data within each cell the asymptotic expectation and variance of sd are easy to compute for pearson s x 2 and simplify considerably for

new perturbation iteration solutions for bratu type equations perturbation iteration theory is systematically generated for both linear and nonlinear second order differential equations and applied to bratu type equations different perturbation iteration algorithms depending upon the number of taylor expansion terms are proposed using the iteration formulas derived using different perturbation iteration algorithms new solutions of bratu type equations are obtained solutions constructed using different perturbation iteration algorithms are contrasted with each other as well as with numerical solutions it is found that algorithms with more taylor series expansion terms yield more accurate results

five themes in chebyshev spectral methods applied to the regularized charney eigenproblem the charney problem a second order ordinary differential equation eigenproblem on z 0 with complex eigenvalues is of great historical importance in meteorology and oceanography here it is used as a testbed for several extensions of spectral methods the first is to parameterize a plane curve which is singular at an endpoint as very common in applications the second stretch is to extend the chebyshev tau method to compute eigenfunctions of the form m z log z v z where m z and v z are entire functions and where the approximation interval is a line segment in the complex plane third we offer a special procedure for finding the roots of a function which is not a polynomial but rather the combination of a polynomial plus a logarithm multiplied by a second polynomial lastly to resolve the very thin boundary layer of the regularized charney problem we combine a rational chebyshev t l n pseudospectral method with a change of coordinate which is quadratic at the ground remarkably best results are obtained by applying four boundary conditions even though the charney problem is a differential equation of only second order

score and profile likelihood confidence intervals for contingency table parameters a straightforward approach to computing score and profile likelihood confidence intervals for contingency table parameters is described the computational approach herein avoids two main limitations of existing methods 1 compared with existing methods this paper s approach is applicable to a much broader class of parameters 2 unlike existing methods this paper s approach is not case specific and hence lends itself to a general yet very simple computational algorithm this paper describes the sliding quadratic computational algorithm and illustrates its use on examples that have not been previously considered in the literature a small scale simulation study highlights the advantage of using score and profile likelihood intervals rather than wald intervals

block nystrom type integrator for bratu s equation abstract in this paper we use a block nystrom method bnm to obtain the numerical solution for one dimensional bratu s problem the convergence analysis of the method is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence the accuracy benefit of the bnm is demonstrated by comparing it to several other known methods given in the literature it is demonstrated that the bnm can also be used to solve bratu s problem associated with initial conditions by simply adjusting the boundary conditions in the algorithm

approximate confidence intervals for the parameters of a stationary binary markov chain the power divergence family of test statistics introduced by cressie and read 1984 is used to obtain approximate confidence intervals for the parameters of a stationary first order binary markov chain intervals based on inverting the likelihood ratio pearson and freeman tukey statistics are included in this family small sample comparisons are used to select the best intervals for the different parameters the results show that the best power divergence intervals for the probability of success and in particular the likelihood ratio interval have error rates closer to nominal levels than the sample proportion based intervals suggested by crow 1979 the properties of power divergence joint confidence regions for the transition probabilities are also explored

power divergence family of statistics for person parameters in irt models we generalize the power divergence pd family of statistics to the two parameter logistic irt model for the purpose of constructing hypothesis tests and confidence intervals of the person parameter the well known score test statistic is a special case of the proposed pd family we also prove the proposed pd statistics are asymptotically equivalent and converge in distribution to chi 1 2 in addition a moment matching method is introduced to compare statistics and choose the optimal one within the pd family simulation results suggest that the coverage rate of the associated confidence interval is well controlled even under small sample sizes for some pd statistics compared to some other approaches the associated confidence intervals exhibit smaller lengths while maintaining adequate coverage rates the utilities of the proposed method are demonstrated by analyzing a real data set

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

efficient robust regression via two stage generalized empirical likelihood large and finite sample efficiency and resistance to outliers are the key goals of robust statistics although often not simultaneously attainable we develop and study a linear regression estimator that comes close efficiency is obtained from the estimator s close connection to generalized empirical likelihood and its favorable robustness properties are obtained by constraining the associated sum of weighted squared residuals we prove maximum attainable finite sample replacement breakdown point and full asymptotic efficiency for normal errors simulation evidence shows that compared to existing robust regression estimators the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance the estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers

a tilting approach to ranking influence summary we suggest a new approach which is applicable for general statistics computed from random samples of univariate or vector valued or functional data to assessing the influence that individual data have on the value of a statistic and to ranking the data in terms of that influence our method is based on first perturbing the value of the statistic by tilting or reweighting each data value where the total amount of tilt is constrained to be the least possible subject to achieving a given small perturbation of the statistic and then taking the ranking of the influence of data values to be that which corresponds to ranking the changes in data weights it is shown both theoretically and numerically that this ranking does not depend on the size of the perturbation provided that the perturbation is sufficiently small that simple result leads directly to an elegant geometric interpretation of the ranks they are the ranks of the lengths of projections of the weights onto a line determined by the first empirical principal component function in a generalized measure of covariance to illustrate the generality of the method we introduce and explore it in the case of functional data where for example it leads to generalized boxplots the method has the advantage of providing an interpretable ranking that depends on the statistic under consideration for example the ranking of data in terms of their influence on the value of a statistic is different for a measure of location and for a measure of scale this is as it should be a ranking of data in terms of their influence should depend on the manner in which the data are used additionally the ranking recognizes rather than ignores sign and in particular can identify left and right hand tails of the distribution of a random function or vector

confidence intervals for the ratio of two binomial proportions sometimes the ratio of two binomial proportions is the parameter of major interest for instance as the risk ratio in a two group cohort study fleiss 1973 or as the likelihood ratio for a diagnostic test procedure mcneill keeler and adelstein 1975 let x and y be independent binomial variates based on sample sizes m and n and parameters p and p2 respectively let 0 pm p2 we consider the construction of confidence intervals for 0 santner and snell 1980 have proposed a nonanalytical procedure which guarantees a lower bound on the confidence coefficient of the 1 a interval for 0 their algorithm is usable for small m and n but may produce conservative intervals in 2 an analytical method for obtaining approximate confidence intervals for 0 is proposed and compared to the one recommended by katz et al 1978

a new class of asymptotically efficient estimators for moment condition models in this paper we propose a new class of asymptotically efficient estimators for moment condition models these estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators unlike the generalized empirical likelihood estimators our new estimators are much easier to compute a simulation study finds that our estimators have better finite sample performance than the two step gmm and compare well to several potential alternatives in terms of both computational stability and overall performance

estimating model discrepancy a quantity 2 is defined as the discrepancy between an actual and an assumed statistical model an estimator is developed for the case in which data are grouped the estimator is based on pearson

modelling trends in ordered correspondence analysis using orthogonal polynomials the core of the paper consists of the treatment of two special decompositions for correspondence analysis of two way ordered contingency tables the bivariate moment decomposition and the hybrid decomposition both using orthogonal polynomials rather than the commonly used singular vectors to this end we will detail and explain the basic characteristics of a particular set of orthogonal polynomials called emerson polynomials it is shown that such polynomials when used as bases for the row and or column spaces can enhance the interpretations via linear quadratic and higher order moments of the ordered categories to aid such interpretations we propose a new type of graphical display the polynomial biplot