analytic formulation and numerical implementation of an acoustic pressure gradient prediction two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the psu wopwop rotor noise prediction code the pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems the first formulation is derived from the gradient of the ffowcs williams hawkings fw h equation this formulation has a form involving the observer time differentiation outside the integrals in the second formulation the time differentiation is taken inside the integrals analytically this formulation avoids the numerical time differentiation with respect to the observer time which is computationally more efficient the acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources the agreement between the predictions and exact solutions is excellent the formulations are applied to the rotor noise problems for two model rotors a purely numerical approach is compared with the analytical formulations the agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases

an improvement to the bit stuffing algorithm the bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence this approach was previously introduced and applied to d k constrained codes results show that the maximum average rate of the bit stuffing code achieves capacity when k d 1 or k spl infin while it is suboptimal for all other d k pairs furthermore this technique was generalized to produce codes with an average rate that achieves capacity for all d k pairs however this extension results in a more complicated scheme this correspondence proposes a modification to the bit stuffing algorithm that maintains its simplicity we show analytically that the proposed algorithm achieves improved average rates over bit stuffing for most d k constraints we further determine all constraints for which this scheme produces codes with an average rate equal to the shannon capacity

an efficient coding system for long source sequences the elias source coding scheme is modified to permit a source sequence of practically unlimited length to be coded as a single codeword using arithmetic of only limited precision the result is shown to be a nonblock arithmetic code of the first in first out fifo type source symbols are decoded in the same order as they were encoded codeword lengths which are near optimum for the specified statistical properties of the source can be achieved explicit encoding and decoding algorithms are provided which effectively implement the coding scheme applications to data compression and cryptography are suggested

derivation and implementation of the boundary integral formula for the convective acoustic wave equation in time domain kirchhoff s formula for the convective wave equation is derived using the generalized function theory the generalized convective wave equation for a stationary surface is obtained and the integral formulation the convective kirchhoff s formula is derived the formula has a similar form to the classical kirchhoff s formula but an additional term appears due to a moving medium effect for convenience the additional term is manipulated to a final form as the classical kirchhoff s formula the frequency domain boundary integral can be obtained from the current time domain boundary integral form the derived formula is verified by comparison with the analytic solution of source in the uniform flow the formula is also utilized as a boundary integral equation time domain boundary element method bem analysis using the boundary integral equation is conducted and the results show good agreement with the analytical solution the formula derived here can be useful for sound radiation and scattering by arbitrary bodies in a moving medium in the time domain

testing the order of a model using locally conic parametrization population mixtures and stationary arma processes in this paper we address the problem of testing hypotheses using the likelihood ratio test statistic in nonidentifiable models with application to model selection in situations where the parametrization for the larger model leads to nonidentifiability in the smaller model we give two major applications the case where the number of populations has to be tested in a mixture and the case of stationary arma p q processes where the order p q has to be tested we give the asymptotic distribution for the likelihood ratio test statistic when testing the order of the model in the case of order selection for armas the asymptotic distribution is invariant with respect to the parameters generating the process a locally conic parametrization is a key tool in deriving the limiting distributions it allows one to discover the deep similarity between the two problems

computation of acoustic scattering from a moving rigid surface application of the kirchhoff formula for subsonically moving surfaces to scattering of sound from a moving rigid body is described the formulation leads to a singular integral equation that yields surface values of the field the integral equation is solved using a boundary element technique in conjunction with the galerkin method several checks on the accuracy and validity of the scheme are discussed numerical results are obtained for scattering of sound from a harmonic point source co moving with a thin winglike body

nonparametric estimation of roc curves in the absence of a gold standard in the evaluation of diagnostic accuracy of tests a gold standard on the disease status is required however in many complex diseases it is impossible or unethical to obtain such a gold standard if an imperfect standard is used the estimated accuracy of the tests would be biased this type of bias is called imperfect gold standard bias in this article we develop a nonparametric maximum likelihood method for estimating roc curves and their areas of ordinal scale tests in the absence of a gold standard our simulation study shows that the proposed estimators for the roc curve areas have good finite sample properties in terms of bias and mean squared error further simulation studies show that our nonparametric approach is comparable to the binormal parametric method and is easier to implement finally we illustrate the application of the proposed method in a real clinical study on assessing the accuracy of seven specific pathologists in detecting carcinoma in situ of the uterine cervix

on the complexity of nonnegative matrix factorization nonnegative matrix factorization nmf has become a prominent technique for the analysis of image databases text databases and other information retrieval and clustering applications the problem is most naturally posed as continuous optimization in this report we define an exact version of nmf then we establish several results about exact nmf i that it is equivalent to a problem in polyhedral combinatorics ii that it is np hard and iii that a polynomial time local search heuristic exists

nonparametric bayes modeling of multivariate categorical data modeling of multivariate unordered categorical nominal data is a challenging problem particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure commonly used approaches rely on the incorporation of latent gaussian random variables or parametric latent class models the goal of this article is to develop a nonparametric bayes approach which defines a prior with full support on the space of distributions for multiple unordered categorical variables this support condition ensures that we are not restricting the dependence structure a priori we show this can be accomplished through a dirichlet process mixture of product multinomial distributions which is also a convenient form for posterior computation methods for nonparametric testing of violations of independence are proposed and the methods are applied to model positional dependence within transcription factor binding motifs

nonparametric estimation of non exchangeable latent variable models we propose a two step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable applications include microeconometric models with unobserved types of agents regime switching models and models with misclassification error in the first step we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable in the second step these conditional moments are estimated as weighted sample averages we illustrate the method by estimating a model of wages with unobserved heterogeneity on psid data

generalized reduced rank tests using the singular value decomposition we propose a novel statistic to test the rank of a matrix the rank statistic overcomes deficiencies of existing rank statistics like a kronecker covariance matrix for the canonical correlation rank statistic of anderson annals of mathematical statistics 1951 22 327 351 sensitivity to the ordering of the variables for the ldu rank statistic of cragg and donald journal of the american statistical association 1996 91 1301 1309 and gill and lewbel journal of the american statistical association 1992 87 766 776 a limiting distribution that is not a standard chi squared distribution for the rank statistic of robin and smith econometric theory 2000 16 151 175 usage of numerical optimization for the objective function statistic of cragg and donald journal of econometrics 1997 76 223 250 and ignoring the non negativity restriction on the singular values in ratsimalahelo 2002 rank test based on matrix perturbation theory unpublished working paper u f r science economique university de franche comte in the non stationary cointegration case the limiting distribution of the new rank statistic is identical to that of the johansen trace statistic

robust estimation of mixture complexity in many applications it is important to find the mixture with fewest number of components known as the mixture complexity that provides a satisfactory fit to the data this article focuses on developing an estimator of mixture complexity that is consistent when the form of component densities are unknown but are postulated to be members of some parametric family and is simultaneously robust against model misspecification we treat the estimation of mixture complexity as a model selection problem and construct an estimator of mixture complexity as a byproduct of minimizing a hellinger information criterion this estimator is shown to be consistent for any parametric family of mixtures when the model is correctly specified monte carlo simulations for a wide variety of normal mixtures show that our estimator is very competitive with several others in the literature in correctly identifying the true mixture complexity the basic construction being firmly rooted in the minimum hellinger distance approach

estimating latent distributions consider vectors of item responses obtained from a sample of subjects from a population in which ability is distributed with densityg where the are unknown parameters assuming the responses depend on through a fully specified item response model this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses i e without estimating an ability parameter for each subject also provided are asymptotic standard errors and tests of fit computing approximations and details of four special cases a non parametric approximation a normal solution a resolution of normal components and a beta binomial solution

non parametric estimation of finite mixtures from repeated measurements this paper provides methods to estimate finite mixtures from data with repeated measurements non parametrically we present a constructive identification argument and use it to develop simple two step estimators of the component distributions and all their functionals we discuss a computationally efficient method for estimation and derive asymptotic theory simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples

nonparametric estimation of multivariate mixtures a multivariate mixture model is determined by three elements the number of components the mixing proportions and the component distributions assuming that the number of components is given and

simplex factor models for multivariate unordered categorical data gaussian latent factor models are routinely used for modeling of dependence in continuous binary and ordered categorical data for unordered categorical variables gaussian latent factor models lead to challenging computation and complex modeling structures as an alternative we propose a novel class of simplex factor models in the single factor case the model treats the different categorical outcomes as independent with unknown marginals the model can characterize flexible dependence structures parsimoniously with few factors and as factors are added any multivariate categorical data distribution can be accurately approximated using a bayesian approach for computation and inferences a markov chain monte carlo mcmc algorithm is proposed that scales well with increasing dimension with the number of factors treated as unknown we develop an efficient proposal for updating the base probability vector in hierarchical dirichlet models theoretical properties are described and we evaluate the appr

almost nonparametric inference for repeated measures in mixture models summary we consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions we require a vector of observations on each subject this vector is mapped into a vector of os and 1 s and summed the resulting distribution of sums can be modelled as a mixture of binomials we then work with the binomial mixture the efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when typically the true underlying mixture distribution is different it is shown that in many cases the approach based on simple binomial mixtures is superior let pi x and p2 x be probability distributions with ai and a2 positive real numbers that sum to 1 then p x al pi x a2 p2 x defines a two component mixture distribution with com ponents pl x and p2 x and mixture weights al and a2 mixture distributions arise when observations come from different populations each with a different distribution and the population sampled is unobserved interesting examples include those in the social sciences in which important variables are latent and unobserved as an example consider the problem of trying to infer the solution strategies which young children employ in solving a cognitive task when different solution strategies can be employed a group of same age children can be considered a sample from a mixture distribution in which the components correspond to the various strategies see thomas and horton 1997 recently there has been an expanding interest in mixtures and there is now a large literature examples and theory may be found in many sources including lindsay 1995 mclachlan and basford 1988 titterington et al 1985 and everitt and hand 1981 computational issues in estimating the model parameters rely mainly on the em algorithm see mclachlan and krishnan 1997 for a detailed account two main issues remain unresolved in applications of mixtures one is the specification of the number of components although there may sometimes be substantive theory to guide this specification in exploratory settings

non parametric identification and estimation of the number of components in multivariate mixtures this article analyzes the identiability of the number of components in k variate mcomponent nite mixture models in which each component distribution has independent marginals including models in latent class analysis without making parametric assumptions on the component distributions we investigate how one can identify the number of components from the distribution function of the observed data when k 2 a lower bound on the number of components m is nonparametrically identiable from the rank of a matrix constructed from the distribution function of the observed variables building on this identication condition we develop a procedure to consistently estimate a lower bound on the number of components

nonnegative ranks decompositions and factorizations of nonnegative matrices the nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank one matrices into which the matrix can be decomposed additively such decompositions are useful in diverse scientific disciplines we obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm

residual diagnostics for mixture models abstract a sample is commonly modeled by a mixture distribution if the observations follow a common distribution but the parameter of interest differs between observations for example we observe the lengths but not the ages of a sample offish it may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish provided there is more than one age class in the sample then the data are distributed as a mixture of normals in this article we assume that the data are a random sample from a mixture of exponential family distributions and that for each observation the parameter of interest is sampled independently from an unknown mixing distribution q the adequacy of a fitted mixture model can be assessed by examining residuals based on the ratio of the observed to expected fit residuals based on the homogeneity model in which q is a one point distribution display a convexity property when the data follow a mixture model this becomes the basis fo

nonparametric inference in multivariate mixtures summary we consider mixture models in which the components of data vectors from any given subpopulation are statistically independent or independent in blocks we argue that if under this condition of independence we take a nonparametric view of the problem and allow the number of subpopulations to be quite general the distributions and mixing proportions can often be estimated root n consistently indeed we show that if the data are k variate and there are p subpopulations then for each p 2 there is a minimal value of k kp say such that the mixture problem is always nonparametrically identifiable and all distributions and mixture proportions are nonparametrically identifiable when k kp we treat the case p 2 in detail and there we show how to construct explicit distribution density and mixture proportion estimators converging at conventional rates other values of p can be addressed using a similar approach although the methodology becomes rapidly more complex as p increases

maximum smoothed likelihood for multivariate mixtures summary we introduce an algorithm for estimating the parameters in a finite mixture of completely unspecified multivariate components in at least three dimensions under the assumption of conditionally independent coordinate dimensions we prove that this algorithm based on a majorization minimization idea possesses a desirable descent property just as any em algorithm does we discuss the similarities between our algorithm and a related one the so called nonlinearly smoothed em algorithm for the non mixture setting we also demonstrate via simulation studies that the new algorithm gives very similar results to another algorithm that has been shown empirically to be effective but that does not satisfy any descent property we provide code for implementing the new algorithm in a publicly available r package

universal modeling and coding the problems arising in the modeling and coding of strings for compression purposes are discussed the notion of an information source that simplifies and sharpens the traditional one is axiomatized and adaptive and nonadaptive models are defined with a measure of complexity assigned to the models a fundamental theorem is proved which states that models that use any kind of alphabet extension are inferior to the best models using no alphabet extensions at all a general class of so called first in first out fifo arithmetic codes is described which require no alphabet extension devices and which therefore can be used in conjunction with the best models because the coding parameters are the probabilities that define the model their design is easy and the application of the code is straightforward even with adaptively changing source models

identifiability of parameters in latent structure models with many observed variables while hidden class models of various types arise in many statistical applications it is often difficult to establish the identifiability of their parameters focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones we demonstrate a general approach for establishing identifiability utilizing algebraic arguments a theorem of j kruskal for a simple latent class model with finite state space lies at the core of our results though we apply it to a diverse set of models these include mixtures of both finite and nonparametric product distributions hidden markov models and random graph mixture models and lead to a number of new results and improvements to old ones in the parametric setting this approach indicates that for such models the classical definition of identifiability is typically too strong instead generic identifiability holds which implies that the set of nonidentifiable parameters has measure zero so that parameter inference is still meaningful in particular this sheds light on the properties of finite mixtures of bernoulli products which have been used for decades despite being known to have nonidentifiable parameters in the nonparametric setting we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed but we explicitly describe the conditions

modified wald tests under nonregular conditions abstract under nonregular conditions wald tests are known to have incorrect size even asymptotically in part of the parameter space modifications are discussed which ensure an asymptotic 2 distribution of the wald statistic under h0 as an example wald tests for multi step causality are considered a variable yt is h step causal for another variable xt if the information in yt helps improving the j step forecasts of xt for some j 1 2 h if more than two variables are involved and are generated by a finite order vector autoregressive var process this type of multi step noncausality implies a set of highly nonlinear restrictions on the var coefficient matrices for this type of nonlinear restrictions standard wald tests fail to have limiting 2 distributions in general

nonparametric estimation of component distributions in a multivariate mixture suppose k variate data are drawn from a mixture of two distributions each having independent components it is desired to estimate the univariate marginal distributions in each of the products as well as the mixing proportion this is the setting of two class fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable the problem is one of inference in a mixture of distributions without training data and until now it has been tackled only in a fully parametric setting we investigate the possibility of using nonparametric methods of course when k 1 the problem is not identifiable from a nonparametric viewpoint we show that the problem is almost identifiable when k 2 there the set of all possible representations can be expressed in terms of any one of those representations as a two parameter family furthermore it is proved that when k geq3 the problem is nonparametrically identifiable under particularly mild regularity conditions in this case we introduce root n consistent nonparametric estimators of the 2k univariate marginal distributions and the mixing proportion finite sample and asymptotic properties of the estimators are described

nonparametric identification of finite mixture models of dynamic discrete choices in dynamic discrete choice analysis controlling for unobserved heterogeneity is an important issue and finite mixture models provide flexible ways to account for it this paper studies nonparametric identifiability of type probabilities and type specific component distributions in finite mixture models of dynamic discrete choices we derive sucient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under dierent assumptions on the markov property stationarity and type invariance in the transition process three elements emerge as the important determinants of identification the time dimension of panel data the number of values the covariates can take and the heterogeneity of the response of dierent types to changes in the co

a semi nonparametric estimator of regression discontinuity design with discrete duration outcomes abstract we consider the regression discontinuity rd design with the duration outcome which has discrete support the parameters of policy interest are treatment effects on unconditional duration effect and conditional hazard effect exiting probabilities for each discrete level we propose a novel semi nonparametric estimator which exploits a flexible separability structure of the underlying continuous time duration process simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank the peculiarity is delivered by the nature of the rd estimand and we provide solutions random censoring and competing risks can also be allowed in our framework

pressure field permeable surface integral formulations for sound scattered by moving bodies abstract this paper presents two novel integral formulations for the prediction of sound scattered by moving bodies derived from the lighthill and the ffowcs williams and hawkings equations for the pressure field these are expressed in the frequency domain over a permeable fictitious surface surrounding the scatterer s and are numerically evaluated through application of a boundary element technique the aims of the paper are the assessment of the influence of the nonlinear terms of lighthill and ffowcs williams and hawkings equations on sound scattering prediction in the presence of nonuniform mean flow due to scatterer motion the assessment of the corresponding limits of applicability of the widely used linear formulations for solid wall boundaries and the development of integral formulations capable to predict accurately and efficiently the noise scattered in the far field by moving bodies the numerical investigation concerns a non lifting wing in uniform translation impinged by an acoustic disturbance generated by a co moving source and includes the comparison of the results obtained through the proposed scattering formulations with those provided by a boundary field velocity potential approach recently validated for moving body problems its main outcomes reveal that when the proposed pressure field formulations include the nonlinear terms through application of a suitable permeable surface their predictions match those provided by the boundary field velocity potential solver whereas the fully linear versions of both pressure field approaches yield underestimated scattered noise predictions significantly less accurate than those given by the linear version of the velocity potential formulation

a graphical technique for determining the number of components in a mixture of normals abstract when a population is assumed to be composed of a finite number of subpopulations a natural model to choose is the finite mixture model it will often be the case however that the number of component distributions is unknown and must be estimated this problem can be difficult for instance the density of two mixed normals is not bimodal unless the means are separated by at least 2 standard deviations hence modality of the data per se can be an insensitive approach to component estimation we demonstrate that a mixture of two normals divided by a normal density having the same mean and variance as the mixed density is always bimodal this analytic result and other related results form the basis for a diagnostic and a test for the number of components in a mixture of normals the density is estimated using a kernel density estimator under the null hypothesis the proposed diagnostic can be approximated by a stationary gaussian process under the alternative hypothesis components in the mixtu

consistent estimation of mixture complexity the consistent estimation of mixture complexity is of fundamental importance in many applications of finite mixture models an enormous body of literature exists regarding the application computational issues and theoretical aspects of mixture models when the number of components is known but estimating the unknown number of components remains an area of intense research effort this article presents a semiparametric methodology yielding almost sure convergence of the estimated number of components to the true but unknown number of components the scope of application is vast as mixture models are routinely employed across the entire diverse application range of statistics including nearly all of the social and experimental sciences

information ratios for validating mixture analyses abstract determining the number of components in a mixture of distributions is an important but difficult problem this article introduces a procedure called minimum information ratio estimation and validation mirev which is based on a ratio of fisher information matrices the smallest eigenvalue of the information ratio matrix is used to determine the number of components a measure of uncertainty may be obtained using a bootstrap technique simulations illustrate the effectiveness of the procedure for mixtures of exponential families an expression for the observed information ratio matrix provides insight to the success of the procedure cluster analysis attempts to identify and characterize subpopulations believed to be present in a population a wide variety of methods are available including criterion optimization hierarchical methods and various heuristic methods criterion optimization techniques such as mixture analysis fuzzy clustering and partitioning methods are popular because they