generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

global existence and decay of smooth solution for the 2 d mhd equations without magnetic diffusion abstract we prove the global existence and the decay estimates of small smooth solution for the 2 d mhd equations without magnetic diffusion this confirms the numerical observation that the energy of the mhd equations is dissipated at a rate independent of the ohmic resistivity

riemannian geometry and matrix geometric means the geometric mean of two positive definite matrices has been defined in several ways and studied by several authors including pusz and woronowicz and ando the characterizations by these authors do not readily extend to three matrices and it has been a long standing problem to define a natural geometric mean of three positive definite matrices in some recent papers new understanding of the geometric mean of two positive definite matrices has been achieved by identifying the geometric mean of a and b as the midpoint of the geodesic with respect to a natural riemannian metric joining a and b this suggests some natural definitions for a geometric mean of three positive definite matrices we explain the necessary geometric background and explore the properties of some of these candidates

one sided cross validation abstract a new method of selecting the smoothing parameters of nonparametric regression estimators is introduced the method termed one sided cross validation oscv has the objectivity of cross validation and statistical properties comparable to those of a plug in rule the new method may be viewed as an application of the prequential model selection method of dawid as such our results identify a situation in which the prequential method is a more efficient model selector than cross validation an example simulations and theoretical results demonstrate the utility of oscv when used with local linear and kernel estimators

diagonality measures of hermitian positive definite matrices with application to the approximate joint diagonalization problem in this paper we introduce properly invariant diagonality measures of hermitian positive definite matrices these diagonality measures are defined as distances or divergences between a given positive definite matrix and its diagonal part we then give closed form expressions of these diagonality measures and discuss their invariance properties the diagonality measure based on the log determinant divergence is general enough as it includes a diagonality criterion used by the signal processing community as a special case these diagonality measures are then used to formulate minimization problems for finding the approximate joint diagonalizer of a given set of hermitian positive definite matrices numerical computations based on a modified newton method are presented and commented

breakdown of smoothness for the muskat problem in this paper we show that there exists analytic initial data in the stable regime for the muskat problem such that the solution turns to the unstable regime and later breaks down that is no longer belongs to c4

small scale creation for solutions of the incompressible two dimensional euler equation we construct an initial data for the two dimensional euler equation in a disk for which the gradient of vorticity exhibits double exponential growth in time for all times this estimate is known to be sharp the double exponential growth is the fastest possible growth rate

efficiency of a kernel density estimator under an autoregressive dependence model abstract the problem of estimating the probability density function of a strictly stationary process is considered to study the effect of a dependence structure on the efficiency of a kernel density estimator the mean integrated squared error mise of the fourier integral estimator fie is derived on the assumption that the observed data are generated by a first order autoregressive process numerical results for the normal and cauchy densities show that even moderate departures from independence can lead to a considerable loss in efficiency of the fie in addition to efficiency considerations the issue of determining an optimal smoothing parameter for the fie under the autoregressive model is addressed

global solutions for the gravity water waves equation in dimension 3 we show existence of global solutions for the gravity water waves equation in dimension 3 in the case of small data the proof combines energy estimates which yield control of l 2 related norms with dispersive estimates which give decay in l 8 to obtain these dispersive estimates we use an analysis in fourier space the study of space and time resonances is then the crucial point

global well posedness and long time dynamics for a higher order quasi geostrophic type equation abstract in this paper we study a higher order viscous quasi geostrophic type equation this equation was derived in 11 as the limit dynamics of a singularly perturbed navier stokes korteweg system with coriolis force when the mach rossby and weber numbers go to zero at the same rate the scope of the present paper is twofold first of all we investigate well posedness of such a model on the whole space r 2 we prove that it is well posed in h s for any s 3 globally in time interestingly enough we show that this equation owns two levels of energy estimates for which one gets existence and uniqueness of weak solutions with different regularities namely h 3 and h 4 regularities this fact can be viewed as a remainder of the so called bd entropy structure of the original system in the second part of the paper we investigate the long time behavior of these solutions we show that they converge to the solution of the corresponding linear parabolic type equation with same initial datum and external force our proof is based on dispersive estimates both for the solutions to the linear and non linear problems

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

detecting heteroscedasticity in nonparametric regression summary diagnostic tests and plots are proposed for detecting heteroscedasticity in nonparametric regression the large and small sample power properties are studied for a class of test statistics for the hypothesis of homogeneous variances new diagnostic plots are also developed and illustrated

score test for the first order autoregressive model with heteroscedasticity summary a score test is proposed for simultaneous testing of independence and homoscedasticity in the first order autoregressive model with nonconstant variance the relationships between the score test statistic and the local influence of minor perturbations on a statistical model are examined

global existence of quasi stratified solutions for the confined ipm equation in this paper we consider a confined physical scenario to prove the global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media ipm equation the result is proved using the stability of stratified solutions combined with an additional structure of our initial perturbation which allows us to get rid of the boundary terms in the energy estimates

smooth optimum kernel estimators near endpoints summary kernel estimators for smooth curves like density spectral density or regression functions require modifications when estimating near endpoints of the support both for practical and asymptotic reasons the construction of such boundary kernels as solutions of a variational problem is addressed and representations in orthogonal polynomials are given including explicit solutions for the most important cases based on explicit formulae for certain functionals of the kernels it is shown that local bandwidth variation might be indicated near boundaries various bandwidth variation schemes are discussed and

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

on landau damping going beyond the linearized study has been a longstanding problem in the theory of landau damping in this paper we establish exponential landau damping in analytic regularity the damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables rather than exchanges of energy phase mixing is the driving mechanism the analysis involves new families of analytic norms measuring regularity by comparison with solutions of the free transport equation new functional inequalities a control of non linear echoes sharp deflection estimates and a newton approximation scheme our results hold for any potential no more singular than coulomb or newton interaction the limit cases are included with specific technical effort as a side result the stability of homogeneous equilibria of the non linear vlasov equation is established under sharp assumptions we point out the strong analogy with the kam theory and discuss physical implications finally we extend these results to some gevrey non analytic distribution functions

matrix power means and the karcher mean we define a new family of matrix means pt a t 1 1 where and a vary over all positive probability vectors in rn and n tuples of positive definite matrices resp each of these means except t 0 arises as a unique positive definite solution of a non linear matrix equation satisfies all desirable properties of power means of positive real numbers and interpolates between the weighted harmonic and arithmetic means the main result is that the karcher mean coincides with the limit of power means as t 0 this provides not only a sequence of matrix means converging to the karcher mean but also a simple proof of the monotonicity of the karcher mean conjectured by bhatia and holbrook and other new properties which have recently been established by lawson and lim and also bhatia and karandikar using probabilistic methods on the metric structure of positive definite matrices equipped with the trace metric

optimization algorithms exploiting unitary constraints this paper presents novel algorithms that iteratively converge to a local minimum of a real valued function f x subject to the constraint that the columns of the complex valued matrix x are mutually orthogonal and have unit norm the algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold this significantly reduces the dimensionality of the optimization problem pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a hermitian matrix

a frequency domain selection criterion for regression with autocorrelated errors abstract we consider the regression model yt t e t t 0 1 n 1 where y t are scalar observations t is the unknown regression function and e t are unobservable errors generated by a zero mean weakly stationary process independent of t and with completely unknown autocorrelation structure we propose a data driven method for selecting a parametric or nonparametric estimator of t the method is based on cross validation in the frequency domain and requires no assumptions about the form of the estimator or the error correlations it does however require the discrete fourier transform dft of the signal t to be a smooth complex function of frequency as is the case for example with transient signals or growth and decay curves after giving some general motivations for the method we focus on the special case of linear estimators of a nonparametric regression function including both kernel and spline estimators for these estimators we develop efficient methods of evaluating t

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

smoothing parameter selection in nonparametric regression using an improved akaike information criterion summary many different methods have been proposed to construct nonparametric estimates of a smooth regression function including local polynomial convolution kernel and smoothing spline estimators each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set in this paper an improved version of a criterion based on the akaike information criterion aic termed aicc is derived and examined as a way to choose the smoothing parameter unlike plug in methods aicc can be used to choose smoothing parameters for any linear smoother including local quadratic and smoothing spline estimators the use of aicc avoids the large variability and tendency to undersmooth compared with the actual minimizer of average squared error seen when other classical approaches such as generalized cross validation or the aic are used to choose the smoothing parameter monte carlo simulations demonstrate that the aicc based smoothing parameter is competitive with a plug in method assuming that one exists when the plug in method works well but also performs well when the plug in approach fails or is unavailable

rayleigh taylor breakdown for the muskat problem with applications to water waves the muskat problem models the evolution of the interface between two different fluids in porous media the rayleigh taylor condition is natural to reach linear stability of the muskat problem we show that the rayleigh taylor condition may hold initially but break down in finite time as a consequence of the method used we prove the existence of water waves turning

global small solutions to an mhd type system the three dimensional case in this paper we consider the global well posedness of a three dimensional incompressible mhd type system with smooth initial data that is close to some nontrivial steady state it is a coupled system between the navier stokes equations and a free transport equation with a universal nonlinear coupling structure the main difficulty of the proof lies in exploring the dissipative mechanism of the system due to the fact that there is a free transport equation of in the coupled equations and only the horizontal derivatives of is dissipative with respect to time to achieve this we first employ anisotropic littlewood paley analysis to establish the key l1 lip 3 estimate to the third component of the velocity field then we prove the global well posedness to this system by the energy method which depends crucially on the divergence free condition of the velocity field 2014 wiley periodicals inc

finite time singularity for the modified sqg patch equation it is well known that the incompressible euler equations in two dimensions have globally regular solutions the inviscid surface quasi geostrophic sqg equation has a biot savart law which is one derivative less regular than in the euler case and the question of global regularity for its solutions is still open we study here the patch dynamics in the half plane for a family of active scalars which interpolates between these two equations via a parameter 0 12 appearing in the kernels of their biot savart laws the values 0 and 12 correspond to the 2d euler and sqg cases respectively we prove global in time regularity for the 2d euler patch model even if the patches initially touch the boundary of the half plane on the other hand for any sufficiently small 0 we exhibit initial data which lead to a singularity in finite time thus these results show a phase transition in the behavior of solutions to these equations and provide a rigorous foundation for classifying the 2d euler equations as critical department of mathematics rice university 6100 s main st houston tx 77005 1892 kiselev rice edu department of mathematics stanford university stanford ca 94305 ryzhik math stanford edu school of mathematics georgia institute of technology 686 cherry street atlanta ga 30332 0160 yaoyao math gatech edu department of mathematics university of wisconsin 480 lincoln dr madison wi 53706 1325 zlatos math wisc edu

common principal components in k groups abstract this article generalizes the method of principal components to so called common principal components as follows consider the hypothesis that the covariance matrices i for k populations are simultaneously diagonalizable that is there is an orthogonal matrix such that i is diagonal for i 1 k i derive the normal theory maximum likelihood estimates of the common component i matrices and the log likelihood ratio statistics for testing this hypothesis the solution has some favorable properties that do not depend on normality assumptions numerical examples illustrate the method applications to data reduction multiple regression and nonlinear discriminant analysis are sketched

fast approximate joint diagonalization incorporating weight matrices we propose a new low complexity approximate joint diagonalization ajd algorithm which incorporates nontrivial block diagonal weight matrices into a weighted least squares wls ajd criterion often in blind source separation bss when the sources are nearly separated the optimal weight matrix for wls based ajd takes a nearly block diagonal form based on this observation we show how the new algorithm can be utilized in an iteratively reweighted separation scheme thereby giving rise to fast implementation of asymptotically optimal bss algorithms in various scenarios in particular we consider three specific yet common scenarios involving stationary or block stationary gaussian sources for which the optimal weight matrices can be readily estimated from the sample covariance matrices which are also the target matrices for the ajd comparative simulation results demonstrate the advantages in both speed and accuracy as well as compliance with the theoretically predicted asymptotic optimality of the resulting bss algorithms based on the weighted ajd both on large scale problems with matrices of the size 100times100

nonparametric spline regression with autoregressive moving average errors summary we estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model unknown parameters are estimated by either maximum likelihood cross validation or generalized cross validation by expressing the problem in state space form we obtain 0 n algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross validation functions the finite sample properties of the function estimates are evaluated by an extensive simulation study and examples are given

a new algorithm for complex non orthogonal joint diagonalization based on shear and givens rotations this paper introduces a new algorithm to approximate non orthogonal joint diagonalization nojd of a set of complex matrices this algorithm is based on the frobenius norm formulation of the joint diagonalization jd problem and takes advantage from combining givens and shear rotations to attempt the approximate jd it represents a non trivial generalization of the jdi joint diagonalization algorithm souloumiac 2009 to the complex case the jdi is first slightly modified then generalized to the cjdi i e complex jdi using complex to real matrix transformation several methods already exist in the literature consequently we provide herein a brief overview of existing nojd algorithms then we provide an extensive comparative study to illustrate the effectiveness and stability of the cjdi with respect to various system parameters and application contexts

operator means of probability measures and generalized karcher equations abstract in this article we consider means of positive bounded linear operators on a hilbert space we present a complete theory that provides a framework which extends the theory of the karcher mean its approximating matrix power means and a large part of kubo ando theory to arbitrary many variables in fact to the case of probability measures with bounded support on the cone of positive definite operators this framework characterizes each operator mean extrinsically as unique solutions of generalized karcher equations which are obtained by exchanging the matrix logarithm function in the karcher equation to arbitrary operator monotone functions over the positive real half line if the underlying hilbert space is finite dimensional then these generalized karcher equations are riemannian gradients of convex combinations of strictly geodesically convex log determinant divergence functions hence these new means are their global minimizers in analogy to the case of the karcher mean as pointed out our framework is based on fundamental contraction results with respect to the thompson metric which provides us nonlinear contraction semigroups in the cone of positive definite operators that form a decreasing net approximating these operator means in the strong topology from above

score tests for the single index model the single index model is a generalization of the linear regression model with e y x g x where g is an unknown function the model provides a flexible alternative to the linear regression model while providing more structure than a fully nonparametric approach although the fitting of single index models does not require distributional assumptions on the error term the properties of the estimates depend on such assumptions as does practical application of the model in this article score tests are derived for three potential misspecifications of the single index model heteroscedasticity in the errors autocorrelation in the errors and the omission of an important variable in the linear index these tests have a similar structure to corresponding tests for nonlinear regression models monte carlo simulations demonstrate that the first two tests hold their nominal size well and have good power properties in identifying model violations often outperforming other tests testing for the need for ad

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

on the inviscid boussinesq system with rough initial data abstract we deal with the local well posedness theory for the two dimensional inviscid boussinesq system with rough initial data of yudovich type the problem is in some sense critical due to some terms involving riesz transforms in the vorticity density formulation we give a positive answer for a special sub class of yudovich data including smooth and singular vortex patches for the latter case we assume in addition that the initial density is constant around the singular part of the patch boundary

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

a fast algorithm for joint diagonalization with non orthogonal transformations and its application to blind source separation a new efficient algorithm is presented for joint diagonalization of several matrices the algorithm is based on the frobenius norm formulation of the joint diagonalization problem and addresses diagonalization with a general non orthogonal transformation the iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer the algorithm s efficiency stems from the special approximation of the cost function resulting in a sparse block diagonal hessian to be used in the computation of the quasi newton update step extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods the results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state of the art joint diagonalization algorithms the practical use of our algorithm is shown for blind source separation problems

means of hermitian positive definite matrices based on the log determinant α divergence function the set of hermitian positive definite matrices plays fundamental roles in many disciplines such as mathematics numerical analysis probability and statistics engineering and biological and social sciences in the last few years there has been a renewable interest in developing the theory of means for elements in this set this is due to theoretical and practical implications in this work we present a one parameter family of divergence functions for measuring distances between hermitian positive definite matrices we then study the invariance properties of these divergence functions as well as the matrix means based on them we also give globally convergent algorithms for computing these means

slicing regression a link free regression method slicing regression a link free regression m e t h o d author s naihua duan and k e r c h a u l i s o u r c e the annals of statistics v o l 19 n o 2 t u n 1991 p p 5 0 5 5 3 0 p u b l i s h e d b y institute of mathematical statistics s t a b l e u r l http www jstor org stable 2242072 accessed 16 05 2011 your use of the jstor archive indicates your acceptance of jstor s terms and conditions of use available at http www jstor org page info about policies terms jsp jstor s terms and conditions of use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the jstor archive only for your personal non commercial use please contact the publisher regarding any further use of this work publisher contact information may be obtained at http www jstor org action showpublisher publishercode ims each copy of any part of a jstor transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jstor is a not for profit service that helps scholars researchers and students discover use and build upon a wide range of content in a trusted digital archive we use information technology and tools to increase productivity and facilitate new forms of scholarship for more information about jstor please contact support jstor org http www jstor org

on the asymptotic stability of stationary solutions of the inviscid incompressible porous medium equation we study the stability of stationary solutions of the two dimensional inviscid incompressible porous medium equation ipm we show that solutions which are near certain stable stationary solutions must converge as t to a stationary solution of the ipm equation it turns out that linearizing the ipm equation about certain stable stationary solutions gives a non local partial damping mechanism on the torus the linearized problem has a very large set of stationary undamped modes this makes the problem of long time behavior more difficult since there is the possibility of a cascading non linear growth along the stationary modes of the linearized problem we solve this by more or less doing a second linearization around the undamped modes exploiting a special non linear structure and showing that the stationary modes can be controlled

choice of bandwidth for kernel regression when residuals are correlated summary standard techniques for selecting the bandwidth of a kernel estimator from the data in a nonparametric regression model perform badly when the errors are correlated in this paper we propose a modified version of an existing plug in bandwidth selector the method is generalized to stationary error variables by estimating a functional of the residual covariance function the proposed bandwidth selector shows good properties in asymptotic theory and in simulations without assuming a parametric model for the error process

divergence function duality and convex analysis from a smooth strictly convex function rn r a parametric family of divergence function d may be introduced d x y 4 1 2 1 2 x 1 2 y 1 2x 1 2y for x y int dom rn and for r with d 1 defined through taking the limit of each member is shown to induce an independent riemannian metric as well as a pair of dual connections which are generally nonflat except for 1 in the latter case d 1 reduces to the nonparametric bregman divergence which is representable using and its convex conjugate and becomes the canonical divergence for dually flat spaces amari 1982 1985 amari nagaoka 2000 this formulation based on convex analysis naturally extends the information geometric interpretation of divergence functions eguchi 1983 to allow the distinction between two different kinds of duality referential duality and representational duality when applied to not necessarily normalized probability densities the concept of conjugated representations of densities is introduced so that connections defined on probability densities embody both referential and representational duality and are hence themselves bidual when restricted to a finite dimensional affine submanifold the natural parameters of a certain representation of densities and the expectation parameters under its conjugate representation form biorthogonal coordinates the alpha representation indexed by now 1 1 is shown to be the only measure invariant representation the resulting two parameter family of divergence functionals d 1 1 1 1 induces identical fisher information but bidual alpha connection pairs it reduces in form to amari s alpha divergence family when 1 or when 1 but to the family of jensen difference rao 1987 when 1

existence and regularity of rotating global solutions for the generalized surface quasi geostrophic equations motivated by the recent work of hassainia and hmidi z hassainia t hmidi on the vstates for the generalized quasi geostrophic equations arxiv preprint arxiv 1405 0858 we close the question of the existence of convex global rotating solutions for the generalized surface quasigeostrophic equation for 2 1 2 we also show c 1 regularity of their boundary for all 2 0 2

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction

kernel regression when the boundary region is large with an application to testing the adequacy of polynomial models abstract it is well known that kernel regression estimators are subject to so called boundary or edge effects a phenomenon in which the bias of an estimator increases near the endpoints of the estimation interval when the regression curve is linear or nearly linear the requisite amount of smoothing is so great that the boundary region is effectively the entire estimation interval special boundary kernels are proposed here to deal with such cases it is shown that the proposed kernel estimator has a property also enjoyed by cubic smoothing splines namely as the estimator s smoothing parameter becomes large the estimator tends to a straight line the limiting straight line is essentially the least squares line when the design points are equally spaced a simple generalization of ideas in the linear case leads to kernel estimates that are polynomials of any given degree for large bandwidths such estimates are an important component of a proposed test for the adequacy of a polynomial model the test s