finite size scaling in the driven lattice gas we present a monte carlo study of the high temperature phase of the two dimensional driven lattice gas at infinite driving field we define a finite volume correlation length verify that this definition has a good infinite volume limit independent of the lattice geometry and study its finite size scaling behavior the results for the correlation length are in good agreement with the predictions based on the field theory proposed by janssen schmittmann leung and cardy the theoretical predictions for the susceptibility and the magnetization are also well verified we show that the transverse binder parameter vanishes at the critical point in all dimensions d geqslant 2 and discuss how such result should be expected in the theory of janssen et al in spite of the existence of a dangerously irrelevant operator our results confirm the gaussian nature of the transverse excitations

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

analytic smoothing for equipercentile equating under the common item nonequivalent populations design a cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described statistical techniques based on bootstrap estimation are presented that are designed to aid in choosing an equating method degree of smoothing these include a asymptotic significance tests that compare no equating and linear equating to equipercentile equating b a scheme for estimating total equating error and for dividing total estimated error into systematic and random components the smoothing technique and statistical procedures are explored and illustrated using data from forms of a professional certification test

reliability inference for a multicomponent stress strength model based on kumaraswamy distribution abstract in this paper inference for a multicomponent stress strength mss model is studied under censored data when both latent strength and stress random variables follow kumaraswamy distributions with common shape parameters the maximum likelihood estimate of mss reliability is established and associated approximate confidence interval is constructed using the asymptotic distribution theory and delta method moreover pivotal quantities based generalized point and confidence interval estimates are presented for the mss reliability furthermore likelihood and generalized pivotal based estimates are also presented when the strength and stress variables have unequal shape parameters for complementary and comparison bootstrap confidence intervals are provided as well under common and unequal parameter cases in addition to compare the equivalence between strength and stress shape parameters the likelihood ratio test for hypothesis of interest is also discussed finally simulation study and a real data example are provided to investigate the performance of proposed procedures

assessing the performance of an allocation rule the problem of estimating the error rates of a sample based rule on the basis of the same sample used in its construction is considered the apparent error rate is an obvious nonparametric estimate of the conditional error rate of a sample rule but unfortunately it provides too optimistic an assessment attention is focussed on the formation of improved estimates mainly through appropriate bias correction of the apparent error rate in this respect the role of the bootstrap a computer based methodology is highlighted

bidirectional solitons on water a theory of bidirectional solitons on water is developed by using an integrable boussinesq surface variable equation we present an explicit transformation between the system and a member of the ablowitz kaup newell segur system and derive an exact multisoliton solution by using a darboux transformation the phase shifts and the maximum wave heights during the interaction are studied for two soliton overtaking and head on collisions they agree with the korteweg de vries solution for overtaking collision and the perturbation solution for head on collision

occupational segregation in the multidimensional case decomposition and tests of significance a new multidimensional version of the g segregation index is developed and applied to the study of occupational segregation u s current population survey data are used to measure the difference in occupational segregation between races as well as the change between time periods decomposition of the difference change into occupation mix and gender composition components indicates the contribution of each factor because these inequality measures are computed from sample data distributional information required to test hypotheses is lacking two computer intensive methods for estimating the distributional properties are demonstrated the approximate randomization and bootstrap methodologies are used to test for statistically significant differences in segregation between races and for changes over time in addition the components of the decomposition are examined for statistical significance

darboux transformation for the modified veselov novikov equation a darboux transformation is constructed for the modified veselov novikov equation by means of the darboux transformation two families of explicit solutions of this equation are given

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

holder regularity of horocycle foliations let m be a c nonpositively curved manifold a horosphere in m is the projection to m of a limit of metric spheres in the universal cover m see 2 a horospherical foliation h is a foliation of the unit tangent bundle t 1m whose leaves consist of unit normal vector fields to horospheres 1 while regularity of horospherical foliations has been studied extensively for negatively curved manifolds m considerably less is known in the nonpositively curved case the most general result is due to p eberlein if m is complete and nonpositively curved then horospheres are c2 which implies that the individual leaves of h are c1 further the tangent distribution th depends continuously the basepoint v t 1m see 9 beyond eberlein s theorem smoothness results have consisted mainly of counterexamples 2 5 in particular the best one could hope for in the case of a general compact nonpositively curved m is for th to be holdercontinuous in this paper we prove

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

darboux transformation and hamiltonian structure for the jaulent miodek hierarchy abstract starting from the jaulent miodek spectral problem we derive the associated hierarchy of nonlinear evolution equations in this paper it is shown that this hierarchy is completely integrable in the liouville sense and possesses the hamiltonian structure moreover by virtue of symbolic computation two types of darboux transformations for the whole hierarchy are explicitly constructed which enables us to find the new soliton like shock and anti shock solutions for the jaulent miodek hierarchy figures are presented to discuss the properties of the new soliton like solutions

the analysis of repeated categorical measurements subject to nonignorable nonresponse abstract conditional likelihood methods have been proposed for analyzing the repeated measurement of categorical responses this article extends the methods to include partially classified subjects the extension allows for an ignorable or nonignorable nonresponse mechanism and uses standard statistical software for the computations two examples of incomplete longitudinal categorical data illustrate the method

maximum likelihood narrow band direction finding and the em algorithm generalized em expectation maximization algorithms have been derived for the maximum likelihood estimation of the direction of arrival of multiple narrowband signals in noise both deterministic and stochastic signal models are considered the algorithm for the deterministic model yields estimates of the signal amplitudes while that for the stochastic model yields estimates of the powers of the signal both algorithms have the properties that their limit points are stable and satisfy the necessary maximizer conditions for maximum likelihood estimators it is shown via simulation that the maximum likelihood method allows for the resolution of the directions of arrival of signals at angular separation and noise levels for which other high resolution methods will not work algorithm convergence does depend on initial conditions however convergence to a global maximum has been observed in simulation when the initial estimates are within a significant fraction if one beamwidth componentwise of this maximum simulations also show that the deterministic model has a significant impact on the angle estimator performance

double bootstrap for shrinkage estimators computer intensive bootstrap methods are potentially problematic when applied to biased estimators similar to ridge regression because biased estimators may lack a pivot we propose a modification for efron s bias corrected percentiles and suggest an approximate pivoting transformation for ridge regression we indicate practical aspects of beran s double bootstrap designed specifically for situations where there is nonnormality and a lack of a pivot econometric applications to estimating consumption functions a simulation with multicollinear data and new graphical tools are included

symmetry group and exact solutions for the 2 1 dimensional ablowitz kaup newell segur equation a 2 1 dimensional ablowitz kaup newell segur akns system is obtained from the potential boiti leon manna pempinelli equation by means of an asymptotically exact reduction method based on fourier expansion and spatiotemporal rescaling furthermore applying the modified direct method to the 2 1 dimensional akns system we get its symmetry and the relationship between the new solution and the old one based on the relationship a new solution can be obtained by using a given solution of the equation

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

estimating the power of the two sample wilcoxon test for location shift summary traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution the distribution shape however may be unknown this paper describes a bootstrap method for using observed data or pilot data to approximate the power no assumptions need be made about the shape of the underlying continuous probability distribution simulation evidence shows that when applied to the wilcoxon two sample test for location shift the suggested method is reliable the evidence also shows that it is more accurate than a benchmark traditional approach the bootstrap method is applied to a real data example the analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift

a sensitivity analysis of the music algorithm a first order analysis of the sensitivity of the music algorithm to system errors which cause differences between the array manifold used by music and the true array manifold is presented the effect of such errors on the direction of arrival estimates is investigated the ability of the music algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or the receivers or errors in the element locations is analyzed a formula for computing the failure threshold of music as a function of source separation and other system parameters is derived and tested by simulation the analysis assumes that the exact covariance matrix of array element outputs is known the infinite data case

backlund transformations for the schrodinger equation with a spectral dependence in the potential the schrodinger equation on the line with a potential depending linearly on the spectral parameter is considered it is shown that this spectral problem admits one parameter called elementary backlund transformations and two parameter called full backlund transformations the transformations of the spectral data under all these backlund transformations bts are explicitly computed different nonlinear superposition formulae for the different bts considered are given and used to obtain soliton solutions of the evolution equations associated with the spectral problem

dynamics and zeta functions on conformally compact manifolds in this note we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures we begin with a discussion of a larger class of manifolds known as convex co compact manifolds with variable negative curvature applying results from dynamics on these spaces we obtain optimal meromorphic extensions of weighted dynamical zeta functions and asymptotic counting estimates for the number of weighted closed geodesics a meromorphic extension of the standard dynamical zeta function and the prime orbit theorem follow as corollaries finally we investigate interactions between the dynamics and spectral theory of these spaces

evaluating screening for the early detection and treatment of cancer without using a randomized control group abstract sometimes the only data available for evaluating screening for the early detection and treatment of cancer come from studies lacking a randomized control group to evaluate these data various approaches have been proposed they include constructing a model to estimate the duration of preclinical cancer and the sensitivity of the screen formulating a model to estimate rates of cancer mortality and using a nonrandomized control group to estimate age specific incidence and mortality rates these methods have various limitations either the estimated quantities are insufficient for a complete evaluation strong parametric assumptions are required or an assumption must be made that the nonrandomized control group yields unbiased estimates of cancer incidence to bypass some of these limitations a new method has been developed for analyzing screening data without a randomized control group the method is called periodic screening evaluation pse because it requires data from periodic screens rath

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

loop soliton interaction in an integrable nonlinear telegraphy model reciprocal and backlund transformations an integrable telegraphy equation linked in turn to the geometry of pseudospherical surfaces and a class of model nonlinear elastic stress strain laws descriptive of ideally hard material response is investigated a constant coefficient ideal formalism is introduced which leads to a reciprocal transformation between this nonlinear telegraphy equation and a system compatible with the classical sine gordon equation a backlund transformation is then constructed which is used to analyse two loop soliton interaction the latter exhibits a novel exchange particle phenomenon

asymptotic performance of optimal gain and phase estimators of sensor arrays for estimating angles of arrival there are three well known algorithms weighted noise subspace fitting wnsf unconditional maximum likelihood uml and conditional maximum likelihood cml these algorithms can also be used for estimating calibrating the gains and phases of sensor arrays assuming the angles of arrival are known we show that the wnsf algorithm with an optimal weight has the same statistical efficiency as the uml algorithm but more efficient than the cml algorithm this conclusion was known for angles of arrival estimation and is now confirmed for gains and phases calibration computationally the wnsf algorithm is shown to be more attractive than the other two as it can be implemented via a quadratic minimization procedure for arbitrarily shaped arrays

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

nondata aided i q mismatch and dc offset compensation for direct conversion receivers a digital signal processing technique is presented that can compensate for the frequency independent inphase quadrature i q mismatch and dc offset in zero intermediate frequency direct conversion receivers the proposed compensator consists of dc offset and i q mismatch estimators followed by a dc offset canceller and self image suppressor the estimators are nondata aided nda schemes that are derived by assuming that the desired signal is a random variable having an arbitrary circular symmetric distribution the cramer rao lower bounds crlbs for nda estimation are derived and the characteristics of the estimators are analyzed in terms of mean square errors in particular it is shown that for white gaussian distributed signals the accuracy of the estimates approaches the crlbs as the number of observed samples increases the characteristics of the proposed method as well as the validity of the analytical results are demonstrated through computer simulation

anosov flows and dynamical zeta functions we study the ruelle and selberg zeta functions for c r anosov ows r 2 on a compact smooth manifold we prove several results the most remarkable being a for c 1 ows the zeta function is meromorphic on the entire complex plane b for contact ows satisfying a bunching condition e g geodesic ows on manifolds of negative curvature better than 1 9 pinched the zeta function has a pole at the topological entropy and is analytic in a strip to its left c under the same hypotheses as in b we obtain sharp results on the number of periodic orbits our arguments are based on the study of the spectral properties of a transfer operator acting on suitable banach spaces of anisotropic currents

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

quadrature receiver mismatch calibration this article introduces nonlinear regression techniques to estimate gain and phase mismatches between the in phase i and quadrature q branches of a quadrature receiver under modest assumptions the system intrinsically follows a nonlinear regression model the algorithm is effective easily implemented customizable and requires few assumptions large sample jackknife and bootstrap techniques provide on line error assessment and parameter inference

robust predictive distributions for exponential families summary the bootstrap predictive distribution considered by harris 1989 is modified by replacing the maximum likelihood estimator of the unknown parameter by its minimum hellinger distance estimator the predictive distribution thus obtained is asymptotically superior to the corresponding estimative distribution in terms of the average kullback leibler divergence when the true distribution is in the natural exponential family simulation results are provided for the binomial and normal distributions which suggest that the proposed predictive distributions are robust and can perform better than the likelihood based methods under data contamination

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

estimation of sensor gain and phase the problem of estimating the direction independent gain and phase characteristics of an array of sensors using knowledge of the true field covariance at the sensor locations is considered a concise expression for the log likelihood function is derived and several mathematical properties of this objective function are given the cramer rao c r lower bounds on the variances of gain and phase estimates are derived with the plane wave in isotropic noise considered as a special case the maximum likelihood estimates are shown to be consistent asymptotically efficient and asymptotically normal a simple estimator is proposed which is consistent and which gives good initial estimates for a newton algorithm for finding the maximum likelihood solution comparison of the maximum likelihood estimates and the c r bounds is given for the plane wave in isotropic noise example

cross validation the jackknife and the bootstrap excess error estimation in forward logistic regression abstract given a prediction rule based on a set of patients what is the probability of incorrectly predicting the outcome of a new patient call this probability the true error an optimistic estimate is the apparent error or the proportion of incorrect predictions on the original set of patients and it is the goal of this article to study estimates of the excess error or the difference between the true and apparent errors i consider three estimates of the excess error cross validation the jackknife and the bootstrap using simulations and real data the three estimates for a specific prediction rule are compared when the prediction rule is allowed to be complicated overfitting becomes a real danger and excess error estimation becomes important the prediction rule chosen here is moderately complicated involving a variable selection procedure based on forward logistic regression

n soliton solutions of the kdv6 and mkdv6 equations the kdv6 and mkdv6 equations are solved through darboux matrix method by constructing darboux transformations for the deformed kdv and mkdv equations n soliton solutions of the kdv6 and mkdv6 equations are presented by using the darboux transformations and selecting nonconstant seed solutions of the kdv6 and mkdv6 equations

evaluating prediction rules for t year survivors with censored regression models suppose that we are interested in establishing simple but reliable rules for predicting future t year survivors through censored regression models in this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate sensitivity and specificity and positive and negative predictive values specifically under various working models we derive consistent estimators for the above measures through substitution and cross validation estimation procedures furthermore we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified confidence intervals for example for the difference of the precision measures between two competing rules can then be constructed all of the proposals are illustrated with real examples and their finite sample properties are evaluated through a simulation study

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

inference from stratified samples second order analysis of three methods for nonlinear statistics abstract for stratified samples and nonlinear statistics that can be expressed as functions of estimated totals second order asymptotic expansions of the linearization jackknife and balanced repeated replication variance estimators are obtained based on these comparisons are made in terms of their biases some higher order asymptotic equivalence results are also established the special case of a combined ratio estimator is investigated in detail some results on bias reduction achieved by the jack knife and balanced repeated replication estimators of a nonlinear function of totals are also given

a simulation study of cross validation for selecting an optimal cutpoint in univariate survival analysis continuous measurements are often dichotomized for classification of subjects this paper evaluates two procedures for determining a best cutpoint for a continuous prognostic factor with right censored outcome data one procedure selects the cutpoint that minimizes the significance level of a logrank test with comparison of the two groups defined by the cutpoint this procedure adjusts the significance level for maximal selection the other procedure uses a cross validation approach the latter easily extends to accommodate multiple other prognostic factors we compare the methods in terms of statistical power and bias in estimation of the true relative risk associated with the prognostic factor both procedures produce approximately the correct type i error rate use of a maximally selected cutpoint without adjustment of the significance level however results in a substantially elevated type i error rate the cross validation procedure unbiasedly estimated the relative risk under the null hypothesis while the procedure based on the maximally selected test resulted in an upward bias when the relative risk for the two groups defined by the covariate and true changepoint was small the cross validation procedure provided greater power than the maximally selected test the cross validation based estimate of relative risk was unbiased while the procedure based on the maximally selected test produced a biased estimate as the true relative risk increased the power of the maximally selected test was about 10 per cent greater than the power obtained using cross validation the maximally selected test overestimated the relative risk by about 10 per cent the cross validation procedure produced at most 5 per cent underestimation of the true relative risk finally we report the effect of dichotomizing a continuous non linear relationship between covariate and risk we compare using a linear proportional hazard model to using models based on optimally selected cutpoints our simulation study indicates that we can have a substantial loss of statistical power when we use cutpoint models in cases where there is a continuous relationship between covariate and risk

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

on bootstrap resampling and iteration summary we propose a single unifying approach to bootstrap resampling applicable to a very wide range of statistical problems it enables attention to be focused sharply on one or more characteristics which are of major importance in any particular problem such as coverage error or length for confidence intervals or bias for point estimation our approach leads easily and directly to a very general form of bootstrap iteration unifying and generalizing present disparate accounts of this subject it also provides simple solutions to relatively complex problems such as a suggestion by lehmann 1986 for conditionally short confidence intervals we set out a single unifying principle guiding the operation of bootstrap resampling applicable to a very wide range of statistical problems including bias reduction shrinkage hypothesis testing and confidence interval construction our principle differs from other approaches in that it focuses attention directly on a measure of quality or accuracy expressed in the form of an equation whose solution is sought a very general form of bootstrap iteration is an immediate consequence of iterating the empirical solution to this equation so as to improve accuracy when employed for bias reduction iteration of the resampling principle yields a competitor to the generalized jackknife enabling bias to be reduced to arbitrarily low levels when applied to confidence intervals it produces the techniques of hall 1986 and beran 1987 the resampling principle leads easily to solutions of new complex problems such as empirical versions of confidence intervals proposed by lehmann 1986 lehmann argued that an ideal confidence interval is one which is short when it covers the true parameter value but not necessarily otherwise the resampling principle suggests a simple empirical means of constructing such intervals section 2 describes the general principle and 3 shows how it leads naturally to bootstrap iteration there we show that in many problems of practical interest such as bias reduction and coverage error reduction in two sided confidence intervals each iteration reduces error by the factor n 1 where n is sample size in the case of confidence intervals our result sharpens one of beran 1987 who showed that coverage error is reduced by the factor n 2 in two sided intervals the main exception to our n 1 rule is coverage error of one sided intervals where error is reduced by the factor n a at each iteration our approach to bootstrap iteration serves to unify not just the philosophy of iteration for different statistical problems but also different techniques of iteration for the same

numerically stable and efficient algorithm for vector channel parameter and frequency offset estimation in this paper we present a novel and numerically efficient algorithm for vector channel and calibration vector estimation which works when frequency offset error caused by either unstable oscillator or doppler effect is present in spread spectrum antenna system we propose an estimation algorithm based on gauss seidal algorithm rather than using eigen decomposition or svd in computing eigenvalues and eigenvectors at each iteration the algorithm is based on the two step procedures one for estimating both channel and frequency offset and the other for estimating the unknown array gain and phase consequently estimates of the doas the multi path impulse response of the reference signal source and the carrier frequency offset as well as the calibration of antenna array are provided the analytic performance improvement in multiplications number is presented the performance of the proposed algorithm is investigated by means of computer simulations throughout the analytic and computer simulation we show that the proposed algorithm reduces the number of multiplications by order of one

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

bootstrap model selection abstract in a regression problem typically there are p explanatory variables possibly related to a response variable and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response a bootstrap variable model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error where the bootstrap estimates are constructed based on a data set of size n although the bootstrap estimates have good properties this bootstrap selection procedure is inconsistent in the sense that the probability of selecting the optimal subset of variables does not converge to 1 as n this inconsistency can be rectified by modifying the sampling method used in drawing bootstrap observations for bootstrapping pairs response explanatory variable it is found that instead of drawing n bootstrap observations a customary bootstrap sampling plan much less bootstrap observations should be sampled the bootstrap selection p

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

classification of gene expression data the manifold based metric learning way classification of microarray gene expression data can potentially help medical diagnosis and becomes an important topic in bioinformatics however microarray data sets are usually of small sample size relative to an overwhelming number of genes this makes the classification problem fairly challenging instance based learning ibl algorithms such as nearest neighbor k nn are usually the baseline algorithm due to their simplicity however practices show that k nn performs not very well in this field this paper introduces manifold based metric learning to improve the performance of ibl methods a novel metric learning algorithm is proposed by utilizing both local manifold structural information and local discriminant information in addition a random subspace extension is also presented we apply the proposed algorithm to the gene classification problem in three ways one in the original feature space another in the reduced feature space and the third via the random subspace extension statistical evaluation shows that the proposed algorithm can achieve promising results and gain significant performance improvement over traditional ibl algorithms

estimating the asymptotic covariance matrix for quantile regression models a monte carlo study abstract this monte carlo study examines several estimation procedures of the asymptotic covariance matrix in the quantile and censored quantile regression models design matrix bootstrap error bootstrapping order statistic sigma bootstrap homoskedastic kernel and heteroskedastic kernel the monte carlo samples are drawn from two alternative data sets 1 a the unaltered current population survey cps for 1987 and 2 b this cps data with independence between error term and regressors imposed this special setup allows one to evaluate the estimators under various realistic scenarios the results favor the design bootstrap for the general case but also support the order statistic when the error term is independent of the regressors

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

a new approach to critical exponents in phase transitions of spin systems abstract we investigate a method to obtain critical exponents using standard numerical simulation techniques for spin systems we show that by analyzing the inverse of the logarithmic derivative of the susceptibility with respect to temperature the accuracy in determining can be increased significantly the method is tested on the two and three dimensional ising models but this alternative approach is thought to be most useful for spin systems on non periodic structures like quasi crystals and fractal lattices where the finite size scaling method is difficult to apply

soliton solutions for two nonlinear partial differential equations using a darboux transformation of the lax pairs two darboux transformations of the 1 1 dimensional wu zhang wz equation and the two component camassa holm 2ch system with the reciprocal transformation are obtained one loop and two loop soliton solutions and multisoliton like solutions of the 2ch system are obtained by using the darboux transformations and selecting different seed solutions of the corresponding equations the bidirectional soliton solutions of the 1 1 dimensional wz equation are also obtained the interactions of two soliton head on and overtaking collisions for the wz equation and the evolution of the two soliton like solutions for the 2ch system are studied

the relationship between hadamard and conventional multiplication for positive definite matrices abstract it is known that if a is positive definite hermitian then a a 1 i in the positive semidefinite ordering our principal new result is a converse to this inequality under certain weak regularity assumptions about a function f on the positive definite matrices a f a af a for all positive definite a if and only if f a is a positive multiple of a 1 in addition to the inequality a a 1 i it is known that a a 1 t i and stronger that min a b min ab t for a b positive definite hermitian we also show that min a b min ab and note that min ab and min ab t can be quite different for a b positive definite hermitian we utilize a simple technique for dealing with the hadamard product which relates it to the conventional product and which allows us to give especially simple proofs of the closure of the positive definites under hadamard multiplication and of the inequalities mentioned

a note on the jackknife the bootstrap and the delta method estimators of bias and variance three methods for the nonparametric reduction of bias and estimation of variance are in common use the jackknife the delta method i e the method of statistical differentials and the bootstrap in recent work efron 1981 a b 1982 has compared these three methods numerically for the case of the sample correlation coefficient for present purposes we define the procedures as follows consider a statistic tn thought of as an estimator of an unknown parameter 0 we wish to study the possibility of bias reduction by estimating the bias and subtracting off the estimate and variance estimation for g tj considered as an estimator of g 0 throughout we assume that we observe x1 xn independent and identically distributed with common cumulative distribution function f let tn denote the abovementioned statistic computed based on x1 xn we assume tn to be symmetric in its arguments furthermore let t 1 denote the above mentioned statistic computed based upon the sample of size n 1 consisting of x1 xi1 xi 1 xn the jackknife estimator of the bias of g tn is then given as b n n 1 1 g t 1 g tn n and the jackknife variance estimator is just

estimation of multiresponse simulation metamodels using control variates this paper provides a unified development of the method of control variates for simulation experiments in which the objective is estimation of a multiresponse metamodel that is a linear model for an output vector of simulation performance measures expressed in terms of an input vector of decision variables for the target system in contrast to previous treatments of this topic we allow both the input and output of the metamodel to be multidimensional so that control variates can be applied to multipopulation multiresponse simulation experiments assuming that the responses and controls are jointly normal with a homogeneous covariance structure across the points of the experimental design we develop control variates procedures for point and confidence region estimation and for hypothesis testing on the coefficients of a postulated metamodel we derive a generalized minimum variance ratio to quantify the maximum efficiency that is achievable with a given set of controls and we formulate a generalized l

analysis of cusum and other markov type control schemes by using empirical distributions the run length distribution of a cumulative sum control scheme when the underlying distribution of the incoming observations is unknown is discussed given a sample of size n from this distribution the estimators related to various characteristics of the run length can be obtained by using the empirical cdf instead of the true cdf in the standard analysis procedure the article discusses the properties of the resulting point estimators as well as interval estimators obtained by using resampling techniques applications of the technique for the purpose of design and analysis of control schemes are also discussed the proposed methodology can be easily adapted for other markov type control schemes

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

three state potts antiferromagnet on the triangular lattice the three state potts antiferromagnetic model on the triangular lattice 3paft has a weak first order transition in the pure case the first order nature follows from analytic arguments and while it has been observed in some simulations the precision of and internal disagreement between these observations has left much to be desired the 3paft is the only two dimensional nearest neighbour potts model with an ordered phase that does not have an infinite degeneracy that remains without an exact value for its critical point this model is expected to exhibit interesting glassy behaviour and a possible crossover to a second order transition upon dilution a careful characterization of the nature of the pure transition is needed in order to explore the physics of the dilute model we find clear indication of a first order transition at tt 0 62731 or 0 00006 using a cluster method that can be extended to the dilute case and histogram reweighting analysis our estimate is two orders of magnitude more precise than previous simulations and falls within the error bounds of a reanalysis of existing series expansion tt 0 628 or 0 004 reported on herein

on solutions of the two component camassa holm system following the approach of chen et al lett math phys 75 1 15 2006 we continue the study of the two component camassa holm system by using its relation with the first negative flow of the akns hierarchy we obtain a more general class of particular solutions including the multisoliton ones

an approximate analytical approach to resampling averages using a novel reformulation we develop a framework to compute approximate resampling data averages analytically the method avoids multiple retraining of statistical models on the samples our approach uses a combination of the replica trick of statistical physics and the tap approach for approximate bayesian inference we demonstrate our approach on regression with gaussian processes a comparison with averages obtained by monte carlo sampling shows that our method achieves good accuracy

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

application of the bootstrap methods in factor analysis a monte carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied and unsatisfied the parameters and their functions of interest include unrotated loadings analytically rotated loadings and unique variances the results reveal that a bootstrap bias estimation performs sometimes poorly for factor loadings and nonstandardized unique variances b bootstrap variance estimation performs well even when the distributional assumption is violated c bootstrap confidence intervals based on the studentized statistics are recommended d if structural hypothesis about the population covariance matrix is taken into account then the bootstrap distribution of the normal theory likelihood ratio test statistic is close to the corresponding sampling distribution with slightly heavier right tail

latent change classes in dichotomous data changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra the llra does not require observable criteria representing a single underlying latent trait but it postulates the generalizability of the treatment effects over criteria and subjects to test this latter crucial assumption the mixture llra was proposed that allows directly unobservable types of subjects to have different treatment effects as the earlier methods for estimating the parameters of the mixture llra have specific drawbacks a further method based on the conditional maximum likelihood principle will be presented here in contrast to the earlier conditional methods it uses all of the dichotomous change data while having fewer parameters further its goodness of fit tests become more sensitive to a falsely specified number of change types even though the treatment effects are biased for typically occurring small to moderate sample sizes however parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests finally three applications of the new method to empirical data are described first about the effect of the so called trager psychophysical integration second about the effect of autogenic therapy on patients with psychosomatic symptoms and third about the effect of religious education on the attitude towards sects

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

the bootstrap to smooth or not to smooth summary the bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals by linear functionals consideration of an example the estimation of the standard error in the variance stabilized sample correlation coefficient elucidates previously published simulation results and also illustrates the use of computer algebraic manipulation as a useful technique in asymptotic statistics finally the various approximations used are vindicated by a simulation study

factorisation of energy dependent schrodinger operators miura maps and modified systems we consider the energy dependent schrodinger operator mathbb l sum limits i 0 n lambda i varepsilon i partial 2 u i which we have previously shown to be associated with multi hamiltonian structures 2 in this paper we use an unusual form of the lax approach to derive by asingle construction the time evolutions of the eigenfunctions of mathbb l the associated hamiltonian operators and the hamiltonian functionals we then generalise the well known factorisation of standard lax operators to the case of energy dependent operators the simple product of linear factors is replaced by a dependent quadratic form we thus generalise the resulting construction of miura maps and modified equations we show that for some of our systems there exists a sequence ofn such modifications therth modification possessing n r 1 hamiltonian structures

painleve property soliton like solutions and complexitons for a coupled variable coefficient modified korteweg de vries system in a two layer fluid model abstract as a model derived from a two layer fluid system which describes the atmospheric and oceanic phenomena a coupled variable coefficient modified korteweg de vries system is concerned in this paper with the help of symbolic computation its integrability in the painleve sense is investigated furthermore hirota s bilinear method is employed to construct the bilinear forms through the dependent variable transformations and soliton like solutions and complexitons are derived finally effects of variable coefficients are discussed graphically and it is concluded that the variable coefficients control the propagation trajectories of solitons and complexitons