the decay mode solutions for the cylindrical kp equation abstract the decay mode solutions for the cylindrical kadomtsev petviashvili equation can be obtained by the backlund transformation and hirota method

probabilistic measures of adequacy of a numerical search for a global maximum abstract measures of the probability of all unobserved species are applied to the problem of assessing the adequacy of a search for a global maximum using random starting points the measures as used here estimate the probability that an iterative algorithm using a randomly selected starting point will find a solution not observed in previous random starting points the probability of an unobserved global maximum is less than or equal to this probability we used these measures to evaluate the adequacy of our search procedure for the maximum likelihood estimates of the parameters of a mixture of two normals these measures indicated that for most problems generated there was little chance that there were unobserved domains of convergence occasional problems however had appreciable estimated probabilities in such problems examination of the data suggested regions where a more focused search for unobserved domains of convergence was warranted

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

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

distribution of the kurtosis statistic b2 for normal samples summary d agostino pearson 1973 gave percentage points of the distribution of b2 for independent observations from a common univariate normal distribution their results can be adequately approximated when the first three moments of the distribution of b2 have been determined by fitting a linear function of the reciprocal of a x2 variable and then using the wilson hilferty transformation evidence is presented suggesting that the same method of approximation is satisfactory for the b2 statistic calculated from any set of linear least squares residuals on the hypothesis of normal homoscedastic errors

rational solutions for a 2 1 dimensional nonlinear model in water waves generated by the jaulent miodek hierarchy abstract this paper deals with a 2 1 dimensional nonlinear evolution equation nlee generated by the jaulent miodek hierarchy for nonlinear water waves via the hirota s bilinear method and pfaffian first we construct rational solutions for general bilinear equations and then convert the target bilinear equations to the general ones to obtain their rational solutions the pfaffian plays a role to simplifying the computations compared with the determinant way in the existing literatures once the first and second order rational solutions have been obtained the higher order solutions can be derived by the same token figures for the first and second order rational solutions are plotted and analyzed as an application the rational solutions for the modified kadomtsev petviashvili equation have also been constructed the method might be used for some other nlees to construct their rational solutions

darboux and binary darboux transformations for the nonautonomous discrete kp equation it is shown how darboux and binary darboux transformations for a nonautonomous discrete kp equation can be obtained from fermion analysis this equation is obtained by considering a generalized miwa transformation it is also shown to be linked to the discrete kp equation by a special gauge transformation the darboux and binary darboux transformations are used to discuss general classes of solutions in the form of casorati and gramm type determinants n soliton solutions are discussed as well

optimal convergence properties of the feti domain decomposition method abstract the finite element tearing and interconnecting feti method is a practical and efficient domain decomposition dd algorithm for the solution of self adjoint elliptic partial differential equations for large scale structural problems discretized with shell and beam elements this method was found to outperform popular iterative algorithms and direct solvers on both serial and parallel computers and to compare favorably with leading dd methods in this paper we discuss some numerical properties of the feti method that were not addressed before in particular we show that the mathematical treatment of the floating subdomains and the specific conjugate projected gradient algorithm that characterize the feti method are equivalent to the construction and solution of a coarse problem that propagates the error globally accelerates convergence and ensures a performance that is independent of the number of subdomains we also show that when the interface problem is optimally preconditioned and the mesh is partitioned into well structured subdomains with good aspect ratios the performance of the feti method is also independent of the mesh size however we also argue that the feti and other leading dd methods for unstructured problems lose in practice these scalability properties when the mesh contains junctures with rotational degrees of freedom or the decomposition is irregular and characterized by arbitrary subdomain aspect ratios finally we report that for realistic problems optimal preconditioners are not necessarily computationally efficient and can be outperformed by non optimal ones

small sample tests for stock return predictability with possibly non stationary regressors and garch type effects we develop a simulation based procedure to test for stock return predictability with multiple regressors the process governing the regressors is left completely free and the test procedure remains valid in small samples even in the presence of non normalities and garch type effects in the stock returns

simulated percentage points for the null distribution of the likelihood ratio test for a mixture of two normals summary we find the percentage points of the likelihood ratio test of the null hypothesis that a sample of n observations is from a normal distribution with unknown mean and variance against the alternative that the sample is from a mixture of two distinct normal distributions each with unknown mean and unknown but equal variance the mixing proportion ir is also unknown under the alternative hypothesis for 2 500 samples of sizes n 15 20 25 40 50 70 75 80 100 150 250 500 and 1 000 we calculated the likelihood ratio statistic and from these values estimated the percentage points of the null distributions our algorithm for the calculation of the maximum likelihood estimates of the unknown parameters included precautions against convergence of the maximization algorithm to a local rather than global maximum investigations for convergence to an asymptotic distribution indicated that convergence was very slow and that stability was not apparent for samples as large as 1 000 comparisons of the percentage points to the commonly assumed chi squared distribution with 2 degrees of freedom indicated that this assumption is too liberal i e one s p value is greater than that indicated by x2 we conclude then that one would need what is usually an unfeasibly large sample size n 1 000 for the use of large sample approximations to be justified

schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations

quasiperiodic waves and asymptotic behavior for bogoyavlenskii s breaking soliton equation in 2 1 dimensions based on a multidimensional riemann theta function the hirota bilinear method is extended to explicitly construct multiperiodic quasiperiodic wave solutions for the 2 1 dimensional bogoyavlenskii breaking soliton equation among these periodic waves the one periodic waves are well known cnoidal waves their surface pattern is one dimensional and often they are used as one dimensional models of periodic waves in shallow water the two periodic biperiodic waves are a direct generalization of one periodic waves their surface pattern is two dimensional that is they have two independent spatial periods in two independent horizontal directions the two periodic waves may be considered to represent periodic waves in shallow water without the assumption of one dimensionality a limiting procedure is presented to analyze asymptotic behavior of the one and two periodic waves in details the exact relations between the periodic wave solutions and the well known soliton solutions are established it is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit

reduction of dispersionless coupled korteweg de vries equations to the euler darboux equation a quasilinear hyperbolic system of two first order equations is introduced the system is linearized by means of the hodograph transformation combined with riemann s method of characteristics in the process of linearization the main step is to explicitly express the characteristic velocities in terms of the riemann invariants the procedure is shown to be performed by quadrature only for specific combinations of the parameters in the system we then apply the method developed here to the dispersionless versions of the typical coupled korteweg de vries ckdv equations including the broer kaup ito hirota satsuma and bogoyavlenskii equations and show that these equations are transformed into the classical euler darboux equation a more general quasilinear system of equations is also considered with application to the dispersionless ckdv equations for the jaulent miodek and nutku oguz equations

hidden symmetries and exact solutions of integro differential jaulent miodek evolution equation use of the adjoint method to obtain optimal lie vectors a reduction of the jm equation to ordinary differential equations and detection of lie symmetries test if these symmetries are hidden analysis and plot of results comparison with previous work in the field analytical solutions of a 2 1 dimensional nonlinear model using the jaulent miodek hierarchy are investigated following a similarity reduction procedure for this adjoint lie matrices are first evaluated and an extensive list of optimal lie vectors is obtained the systematic reduction of jaulent miodek evolution equation to lower number of variables leads to hidden symmetries and new solutions

an interface strip domain decomposition preconditioner in this paper we consider domain decomposition preconditioners based on a vertex oriented vo decomposition of the computational domain in element oriented eo decompositions each element of the grid belongs to a different domain while in vo decompositions each vertex belongs to a different subdomain based on vo decompositions we present some preconditioners for the solution of the original system as well as for that of the schur complement system theoretical properties are investigated for a finite element approximation of an elliptic problem numerical results and comparison with state of the art preconditioners are also reported the numerical results presented here show the effectiveness of the proposed preconditioners and their good scalability properties

the likelihood ratio test for the two component normal mixture problem power and sample size analysis we find through simulation and modeling an approximation to the alternative distribution of the likelihood ratio test for two component mixtures in which the components have different means but equal variances we consider the range of mixing proportions from 0 5 through 95 our simulation results indicate a dependence of power on the mixing proportion when pi less than 2 and pi greater than 80 our model results indicated that the alternative distribution is approximately noncentral chi square possibly with 2 degrees of freedom using this model we estimate a sample of 40 is needed to have 50 power to detect a difference between means equal to 3 0 for mixing proportions between 2 and 8 the sample size increases to 50 when the mixing proportion is 90 or 1 and 82 when the mixing proportion is 95 or 05 this paper contains a complete table of sample sizes needed for 50 80 and 90 power

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

algebraic geometrical solutions of some multidimensional nonlinear evolution equations the known 2 1 dimensional breaking soliton equation the coupled kp equation with three potentials and a new 3 1 dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the 1 1 dimensional akns equations the abel jacobi coordinates are introduced to straighten out the associated flows from which algebraic geometrical solutions of the 2 1 dimensional breaking soliton equation the coupled kp equation and the 3 1 dimensional evolution equation are explicitly given in terms of the riemann theta functions

an aggregation based domain decomposition preconditioner for groundwater flow we consider theoretical and computational issues associated with an aggregation based domain decomposition preconditioner applied to a bi cgstab iterative solver used to solve both laplace s equation and an important nonlinear model from hydrology used to simulate unsaturated flow richards equation theoretical results for laplace s equation provide estimates of the condition number and the rate of convergence for a two level schwarz domain decomposition preconditioner computational results for laplace s equation and richards equation show excellent scalability although no theory is yet available to support the results for the difficult nonlinear problem

wronskian determinants the kp hierarchy and supersymmetric polynomials by using the wronskian representation of the solutions of the bilinear kp hierarchy a connection between hirota derivatives and supersymmetric polynomials is brought to light this correspondence is used in order to give an alternative construction of the hierarchy

computer algebra painleve analysis and the time dependent coefficient nonlinear schrodinger equation abstract the variable coefficient nonlinear schrodinger equations describe certain physical systems with nonuniform backgrounds in this paper the application of the painleve analysis and computer algebra leads to an auto backlund transformation and some special solutions to a general time dependent coefficient version of the nonlinear schrodinger equation

exact soliton solutions of coupled nonlinear schrodinger equations shape changing collisions logic gates and partially coherent solitons the different dynamical features underlying soliton interactions in coupled nonlinear schrodinger equations which model multimode wave propagation under varied physical situations in nonlinear optics are studied in this paper by explicitly constructing multisoliton solutions up to four soliton solutions for two coupled and arbitrary n coupled nonlinear schrodinger equations using the hirota bilinearization method we bring out clearly the various features underlying the fascinating shape changing intensity redistribution collisions of solitons including changes in amplitudes phases and relative separation distances and the very many possibilities of energy redistributions among the modes of solitons however in this multisoliton collision process the pairwise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons detailed asymptotic analysis also shows that when solitons undergo multiple collisions there exists the exciting possibility of shape restoration of at least one soliton during interactions of more than two solitons represented by three and higher order soliton solutions from an application point of view we have shown from the asymptotic expressions how the amplitude intensity redistribution can be written as a generalized linear fractional transformation for the n component case also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters leading to possible multistate logic in addition we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions thereby explaining their variable profile and shape variation in collision process

pfaffianization of the generalized variable coefficient kadomtsev petviashvili equation abstract in this paper the pfaffianization procedure is applied to the generalized variable coefficient kadomtsev petviashvili vckp equation which can describe the realistic nonlinear phenomena in the fluid dynamics and plasmas using the pfaffianization procedure the coupled system for the generalized vckp equation is derived together with the wronski type pfaffian solution for this generalized coupled vckp system under certain coefficient constraint furthermore the gramm type pfaffian solution for such a coupled system is presented and verified by virtue of the pfaffian identities

permutation tests for detecting and estimating mixtures in task performance within groups we propose a two sample permutation test incorporating mixture models as a general tool for detecting and quantifying effects on task performance we illustrate the proposed method with examples where the dependent measures under investigation are recorded for normal controls and relatives of patients with schizophrenia on a delayed response spatial and object working memory task our mixture modelling in relatives allows the component distributions to arise from different continuous parametric families we also investigate the effects of the within family correlation and the prior distribution of the mixing proportion on the test results the power of the test depends on sample sizes the mixing proportion the difference in component means and the ratio of component variances copyright 2002 john wiley sons ltd

on the 2 1 dimensional gardner equation determinant solutions and pfaffianization in this paper we first present the casorati and grammian determinant solutions to the 2 1 dimensional gardner equation then by using the pfaffianization procedure of hirota and ohta a new integrable coupled system is generated from the gardner equation moreover gramm type pfaffian solutions to the pfaffianized system are proposed

solitonic solutions and backlund transformation for the inhomogeneous n coupled nonlinear schrodinger equations abstract governing the simultaneous propagation of n fields in optical fibers and plasmas the inhomogeneous n coupled nonlinear schrodinger equations are with symbolic computation analytically investigated in this paper as one of the important integrable properties the explicit one and two solitonic solutions for the inhomogeneous n coupled nonlinear schrodinger equations are derived using the bilinear method with illustrated graphics additionally the backlund transformation in bilinear form is constructed

quantitative statistical assessment of conditional models for synthetic aperture radar many applications of object recognition in the presence of pose uncertainty rely on statistical models conditioned on pose for observations the image statistics of three dimensional 3 d objects are often assumed to belong to a family of distributions with unknown model parameters that vary with one or more continuous valued pose parameters many methods for statistical model assessment for example the tests of kolmogorov smirnov and k pearson require that all model parameters be fully specified or that sample sizes be large assessing pose dependent models from a finite number of observations over a variety of poses can violate these requirements however a large number of small samples corresponding to unique combinations of object pose and pixel location are often available we develop methods for model testing which assume a large number of small samples and apply them to the comparison of three models for synthetic aperture radar images of 3 d objects with varying pose each model is directly related to the gaussian distribution and is assessed both in terms of goodness of fit and underlying model assumptions such as independence known mean and homoscedasticity test results are presented in terms of the functional relationship between a given significance level and the percentage of samples that wold fail a test at that level

linkage between quantitative trait loci and marker loci resolution power of three statistical approaches in single marker analysis this paper presents a comparison of three methods of parameter estimation in analysis of linkage between a quantitative trait locus qtl and a marker locus maximum likelihood mean square for trait cumulative distribution function and method of moments employing simulated backcross data the sensitivity of estimates to violation of assumptions of normality and equal variances were also studied some measures of discrepancy between the trait distributions in the qtl groups are considered to evaluate the potential dependence of the resolution capacity of the qtl substitution effect with respect to trait mean value and variance

the use of backlund transformations in obtaining n soliton solutions in wronskian form the wronskian formulation of the n soliton solutions of various nonlinear evolution equations modified korteweg de vries with both zero and non zero asymptotic conditions sine gordon korteweg de vries kadomtsev petviashvili and boussinesq equations are obtained by inductive use of backlund transformations in hirota s 1980 bilinear notation

using bootstrap likelihood ratios in finite mixture models statistical inference using the likelihood ratio statistic for the number of components in a mixture model is complicated when the true number of components is less than that of the proposed model since this represents a non regular problem the true parameter is on the boundary of the parameter space and in some cases the true parameter is in a non identifiable subset of the parameter space the maximum likelihood estimator is shown to converge to the subset characterized by the same density function and connection is made to the bootstrap method proposed by aitkin and co workers and mclachlan for testing the number of components in a finite mixture and deriving confidence regions in a finite mixture

quasi periodic solutions for some 2 1 dimensional integrable models generated by the jaulent miodek hierarchy some 2 1 dimensional integrable models including the modified kadomtsev petviashvili equation generated by the jaulent miodek hierarchy are investigated with the help of the jaulent miodek eigenvalue problem these 2 1 dimensional integrable models are separated into compatible hamiltonian systems of ordinary differential equations using the generating function flow method the involutivity and the functional independence of the integrals are proved the abel jacobi coordinates are introduced from which the quasi periodic solutions for these 2 1 dimensional integrable models are derived by resorting to the riemann theta functions pacs number 0230j

where is the likelihood ratio test powerful for detecting two component normal mixtures we compare the power of the likelihood ratio test the engelman hartigan test two outlier tests four goodness of fit tests and eight tests of normality to detect a mixture consisting of two components that are normally distributed with different means but equal variances we consider the entire range of mixing proportions pi 0 85 or pi 15 overall fisher s skewness statistic is best with filliben s probability plot correlation coefficient test somewhat less powerful a combined skewness and kurtosis test the anderson darling test and the likelihood ratio test are also competitive for 35 pi 65 the engelman hartigan test is best for other mixing proportions the likelihood ratio test is best for situations in which the preferred test had power 50 or more the power of the likelihood ratio test is also above 50 and within 15 percentage points of the preferred test

some nonoverlapping domain decomposition methods the purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second order elliptic problems in two and three dimensions the methods under scrutiny fall into two major categories the substructuring type methods and the neumann neumann type methods the basic framework used for analysis is the parallel subspace correction method or additive schwarz method and other technical tools include local global and global local techniques the analyses for both two and three dimensional cases are carried out simultaneously some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived

general formulas for obtaining the mles and the asymptotic variance covariance matrix in mapping quantitative trait loci when using the em algorithm we present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance covariance matrix of the positions and effects of quantitative trait loci qtls in a finite normal mixture model when the em algorithm is used for mapping qtls the general formulas are based on two matrices d and q where d is the genetic design matrix characterizing the genetic effects of the qtls and q is the conditional probability matrix of qtl genotypes given flanking marker genotypes containing the information on qtl positions with the general formulas it is relatively easy to extend qtl mapping analysis to using multiple marker intervals simultaneously for mapping multiple qtls for analyzing qtl epistasis and for estimating the heritability of quantitative traits simulations were performed to evaluate the performance of the estimates of the asymptotic variances of qtl positions and effects

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

hybrid domain decomposition algorithms for compressible and almost incompressible elasticity overlapping schwarz methods are considered for mixed finite element approximations of linear elasticity with discontinuous pressure spaces as well as for compressible elasticity approximated by standard conforming finite elements the coarse components of the preconditioners are based on spaces with a number of degrees of freedom per subdomain which are uniformly bounded which are similar to those previously developed for scalar elliptic problems and domain decomposition methods of iterative substructuring type i e methods based on nonoverlapping decompositions of the domain the local components of the new preconditioners are based on solvers on a set of overlapping subdomains in the current study the dimension of the coarse spaces is smaller than in recently developed algorithms in the compressible case all independent face degrees of freedom have been eliminated while in the almost incompressible case five out of six are not needed in many cases this will result in a reduction of the dimension of the coarse space by about one half compared with that of the algorithm previously considered in addition in spite of using overlapping subdomains to define the local components of the preconditioner values of the residual and the approximate solution need only to be retained on the interface between the subdomains in the iteration of the new hybrid schwarz algorithm the use of discontinuous pressures makes it possible to work exclusively with symmetric positive definite problems and the standard preconditioned conjugate gradient method bounds are established for the condition number of the preconditioned operators the bound for the almost incompressible case grows in proportion to the square of the logarithm of the number of degrees of freedom of individual subdomains and the third power of the relative overlap between the overlapping subdomains and it is independent of the poisson ratio as well as jumps in the lame parameters across the interface between the subdomains numerical results illustrate the findings copyright 2009 john wiley sons ltd

solitons backlund transformation and lax pair for the 2 1 dimensional boiti leon pempinelli equation for the water waves under investigation in this paper is the 2 1 dimensional boiti leon pempinelli blp equation for the water waves by virtue of the binary bell polynomials and symbolic computation the bilinear form for the blp equation is obtained furthermore soliton solutions are presented and soliton interaction properties including the elastic inelastic and elastic inelastic collisions are discussed by the graphical analysis besides the backlund transformation in the form of the binary bell polynomials is derived via the backlund transformation the shock wave solutions and lax pair are both constructed

high frequency soliton like waves in a relaxing medium a nonlinear evolution equation is suggested to describe the propagation of waves in a relaxing medium it is shown that for low frequency approach this equation is reduced to the kdvb equation the high frequency perturbations are described by a new nonlinear equation this equation has ambiguous looplike solutions it is established that a dissipative term with a dissipation parameter less than some limit value does not destroy these looplike solutions

multi soliton and pfaffian solutions of a 2 1 dimensional nonlinear evolution equation via the jaulent miodek hierarchy abstract under investigation in this paper is a 2 1 dimensional nonlinear evolution equation generated by the jaulent miodek hierarchy via the hirota bilinear method multi soliton solutions of such equation are obtained soliton propagation and interactions are analyzed and both the elastic and inelastic interactions are seen with some parameters selected furthermore it is proved that the equation possesses the n soliton solutions expressed in terms of gramm type pfaffian and can be written in the form of a pfaffian identity

pfaffian solution of a semi discrete bkp type equation and its source generation version the pfaffian solution of a semi discrete bkp type equation is obtained at first then utilizing the source generation procedure this equation with self consistent sources bkpescs is presented and its pfaffian solutions are derived finally a bilinear backlund transformation for the semi discrete bkpescs is given

the n soliton solutions for the non isospectral mkdv equation the bilinear form of the non isospectral mkdv equation is given and the exact n soliton solutions are obtained through hirota method and wronskian technique respectively c

an overlapping domain decomposition preconditioner for a class of discontinuous galerkin approximations of advection diffusion problems we consider a scalar advection diffusion problem and a recently proposed discontinuous galerkin approximation which employs discontinuous finite element spaces and suitable bilinear forms containing interface terms that ensure consistency for the corresponding sparse non symmetric linear system we propose and study an additive two level overlapping schwarz preconditioner consisting of a coarse problem on a coarse triangulation and local solvers associated to suitable problems defined on a family of subdomains this is a generalization of the corresponding overlapping method for approximations on continuous finite element spaces related to the lack of continuity of our approximation spaces some interesting new features arise in our generalization which have no analog in the conforming case we prove an upper bound for the number of iterations obtained by using this preconditioner with gmres which is independent of the number of degrees of freedom of the original problem and the number of subdomains the performance of the method is illustrated by several numerical experiments for different test problems using linear finite elements in two dimensions

testing the number of components in a normal mixture we demonstrate that under a theorem proposed by vuong the likelihood ratio statistic based on the kullback leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi squared random variables with one degree of freedom under general regularity conditions we report simulation studies of two cases where we are testing a single normal versus a two component normal mixture and a two component normal mixture versus a three component normal mixture an empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution

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

sparse non gaussian component analysis non gaussian component analysis ngca introduced in offered a method for high dimensional data analysis allowing for identifying a low dimensional non gaussian component of the whole distribution in an iterative and structure adaptive way an important step of the ngca procedure is identification of the non gaussian subspace using principle component analysis pca method this article proposes a new approach to ngca called sparse ngca which replaces the pca based procedure with a new the algorithm we refer to as convex projection