asymptotic normality of a nonparametric estimator of sample coverage this paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by good biometrica 40 1953 237 264 this new necessary and sufficient condition extends the validity of the asymptotic normality beyond the previously proven cases

information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

a bayesian approach to geometric subspace estimation this paper presents a geometric approach to estimating subspaces as elements of the complex grassmann manifold with each subspace represented by its unique complex projection matrix variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices elements of the unitary group u n subspace estimation or tracking then corresponds to inferences on u n taking a bayesian approach a posterior density is derived on u n and certain expectations under this posterior are empirically generated for the choice of the hilbert schmidt norm on u n to define estimation errors an optimal mmse estimator is derived it is shown that this estimator achieves a lower bound on the expected squared errors associated with all possible estimators the estimator and the bound are computed using metropolis adjusted langevin s diffusion algorithm for sampling from the posterior for use in subspace tracking a prior model on subspace rotation that utilizes newtonian dynamics is suggested

network tomography estimating source destination traffic intensities from link data abstract the problem of estimating the node to node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under poisson assumptions and two types of traffic routing regimens deterministic a fixed known path between each directed pair of nodes and markovian a random path between each directed pair of nodes determined according to a known markov chain fixed for that pair maximum likelihood estimation and related approximations are discussed and computational difficulties are pointed out a detailed methodology is presented for estimates based on the method of moments the estimates are derived algorithmically taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an em algorithm resulting in a particularly simple solution to a hard problem a small simulation study is carried out

pivotal bootstrap methods for k sample problems in directional statistics and shape analysis we propose a novel bootstrap hypothesis testing approach for the problem of testing a null hypothesis of a common mean direction mean polar axis or mean shape across several populations of real unit vectors the directional case or complex unit vectors the two dimensional shape case multisample testing problems of this type arise frequently in directional statistics and shape analysis as in other areas of statistics but to date there has been relatively little discussion of nonparametric bootstrap approaches to this problem the bootstrap approach described here is based on a statistic that can be expressed as the smallest eigenvalue of a certain positive definite matrix we prove that this statistic has a limiting chi squared distribution under the null hypothesis of equality of means across populations although we focus mainly on the version of the statistic in which neither isotropy within populations nor constant dispersion structure across populations is assumed we explain how to modify th

shape changes in the plane for landmark data this paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane we provide inference procedures on the complex projective plane for a basic measure of shape change in the plane on observing that shapes of configurations of k 1 landmarks in the plane may be represented as points on cp k 1 and that complex rotations are the only maps on cs k 1 which preserve the usual hermitian inner product specifically if u 1 u n are fixed points on cp k 1 represented as cs k 1 u 1 and v 1 v n are random points on cp k 1 such that the distribution of v j depends only on v j au j 2 for some unknown complex rotation matrix a then this paper provides asymptotic inference procedures for a it is demonstrated that shape changes of a kind not detectable as location shifts by standard euclidean analysis can be found by this frequency domain method a numerical example is given

rounding effects of quenched randomness on first order phase transitions frozen in disorder in an otherwise homogeneous system is modeled by interaction terms with random coefficients given by independent random variables with a translation invariant distribution for such systems it is proven that ind 2 dimensions there can be no first order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter discontinuities which would amount to a continuous symmetry breaking in systems which are stochastically invariant under the action of a continuous subgroup ofo n are suppressed by the randomness in dimensionsd 4 specific implications are found in the random field ising model for which we conclude that ind 2 dimensions at all h the gibbs state is unique for almost all field configurations and in the random bond potts model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point the results are explained by the argument of imry and ma 1 the proofs involve the analysis of fluctuations of free energy differences which are shown using martingale techniques to be gaussian on the suitable scale

estimation of a covariance matrix using the reference prior estimation of a covariance matrix sum is a notoriously difficult problem the standard unbiased estimator can be substantially suboptimal we approach the problem from a noninformative prior bayesian perspective developing the reference noninformative prior for a covariance matrix and obtaining expressions for the resulting bayes estimators these expressions involve the computation of high dimensional posterior expectations which is done using a recent markov chain simulation tool the hit and run sampler frequentist risk comparisons with previously suggested estimators are also given and determination of the accuracy of the estimators is addressed

shape activity a continuous state hmm for moving deforming shapes with application to abnormal activity detection the aim is to model activity performed by a group of moving and interacting objects which can be people cars or different rigid components of the human body and use the models for abnormal activity detection previous approaches to modeling group activity include co occurrence statistics individual and joint histograms and dynamic bayesian networks neither of which is applicable when the number of interacting objects is large we treat the objects as point objects referred to as landmarks and propose to model their changing configuration as a moving and deforming shape using kendall s shape theory for discrete landmarks a continuous state hidden markov model is defined for landmark shape dynamics in an activity the configuration of landmarks at a given time forms the observation vector and the corresponding shape and the scaled euclidean motion parameters form the hidden state vector an abnormal activity is then defined as a change in the shape activity model which could be slow or drastic and whose parameters are unknown results are shown on a real abnormal activity detection problem involving multiple moving objects

intrinsic analysis of statistical estimation the parametric statistical models with suitable regularity conditions have a natural riemannian manifold structure given by the information metric since the parameters are merely labels for the probability measures an inferential statement should be formulated through intrinsic objects invariant under reparametrizations in this context the estimators will be random objects valued on the manifold corresponding to the statistical model in spite of these considerations classical measures of an estimator s performance like the bias and the mean square error are clearly dependent on the statistical model parametrizations in this paper the authors work with extended notions of mean value and moments of random objects which take values on a hausdorff and connected manifold equipped with an affine connection in particular the riemannian manifold case is considered this extension is applied to the bias and the mean square error study in statistical point estimation theory under this approach an intrinsic version of the cramer rao lower bound is obtained a lower bound which depends on the intrinsic bias and the curvature of the statistical model for the mean square of the rao distance the invariant measure analogous to the mean square error further the behavior of the mean square of the rao distance of an estimator when conditioning with respect to a sufficient statistic is considered obtaining intrinsic versions of the rao blackwell and lehmann scheffe theorems asymptotic properties complete the study

the complex bingham quartic distribution and shape analysis summary the complex bingham distribution was introduced by kent as a tractable model for landmark based shape analysis it forms an exponential family with a sufficient statistic which is quadratic in the data however the distribution has too much symmetry to be widely useful in particular under high concentration it behaves asymptotically as a normal distribution but where the covariance matrix is constrained to have complex symmetry to overcome this limitation and to provide a full range of asymptotic normal behaviour we introduce a new complex bingham quartic distribution by adding a selection of quartic terms to the log density in the simplest case this new distribution corresponds to kent s fb5 distribution asymptotic and saddlepoint methods are developed for the normalizing constant to facilitate maximum likelihood estimation examples are given to show the usefulness of this new distribution

disclosure control of microdata abstract national statistical offices meet an increasing demand for the dissemination of microdata this trend can be at variance with the care taken not to disclose data about individuals therefore the risk of disclosure of each microdata set to be released should be assessed if this risk is too high measures have to be taken to protect the data set this article describes the disclosure problem and explains why it is a real problem using the concept of uniqueness some theory is developed that can help establish the risk of identification it turns out that useful microdata sets can only be released if some of the disclosure risks are dealt with by legal arrangements rather than by restrictions on the data to be released

large sample theory of intrinsic and extrinsic sample means on manifolds ii this article develops nonparametric inference procedures for estimation and testing problems for means on manifolds a central limit theorem for frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on riemannian manifolds central limit theorems are also obtained for extrinsic sample means w r t an arbitrary embedding of a differentiable manifold in a euclidean space bootstrap methods particularly suitable for these problems are presented applications are given to distributions on the sphere s d directional spaces real projective space rp n 1 axial spaces complex projective space cp k 2 planar shape spaces w r t veronese whitney embeddings and a three dimensional shape space 4 3

covariance subspace and intrinsic crame spl acute r rao bounds crame spl acute r rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists the frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail the set of subspaces called the grassmann manifold and the set of covariance positive definite hermitian matrices have no fixed coordinate system associated with them and do not possess a vector space structure both of which are required for deriving classical crame spl acute r rao bounds intrinsic versions of the crame spl acute r rao bound on manifolds utilizing an arbitrary affine connection with arbitrary geodesics are derived for both biased and unbiased estimators in the example of covariance matrix estimation closed form expressions for both the intrinsic and flat bounds are derived and compared with the root mean square error rmse of the sample covariance matrix scm estimator for varying sample support k the accuracy bound on unbiased covariance matrix estimators is shown to be about 10 log 10 n k sup 1 2 db where n is the matrix order remarkably it is shown that from an intrinsic perspective the scm is a biased and inefficient estimator and that the bias term reveals the dependency of estimation accuracy on sample support observed in theory and practice the rmse of the standard method of estimating subspaces using the singular value decomposition svd is compared with the intrinsic subspace crame spl acute r rao bound derived in closed form by varying both the signal to noise ratio snr of the unknown p dimensional subspace and the sample support in the simplest case the crame spl acute r rao bound on subspace estimation accuracy is shown to be about p n p sup 1 2 1 2 snr sup 1 2 rad for p dimensional subspaces it is seen that the svd based method yields accuracies very close to the crame spl acute r rao bound establishing that the principal invariant subspace of a random sample provides an excellent estimator of an unknown subspace the analysis approach developed is directly applicable to many other estimation problems on manifolds encountered in signal processing and elsewhere such as estimating rotation matrices in computer vision and estimating subspace basis vectors in blind source separation

rotation invariant kernels and their application to shape analysis shape analysis requires invariance under translation scale and rotation translation and scale invariance can be realized by normalizing shape vectors with respect to their mean and norm this maps the shape feature vectors onto the surface of a hypersphere after normalization the shape vectors can be made rotational invariant by modeling the resulting data using complex scalar rotation invariant distributions defined on the complex hypersphere e g using the complex bingham distribution however the use of these distributions is hampered by the difficulty in estimating their parameters and the nonlinear nature of their formulation in the present paper we show how a set of kernel functions that we refer to as rotation invariant kernels can be used to convert the original nonlinear problem into a linear one as their name implies these kernels are defined to provide the much needed rotation invariance property allowing one to bypass the difficulty of working with complex spherical distributions the resulting approach provides an easy fast mechanism for 2d 3d shape analysis extensive validation using a variety of shape modeling and classification problems demonstrates the accuracy of this proposed approach

bootstrap inference for mean reflection shape and size and shape with three dimensional landmark data working within the framework of a multi dimensional scaling approach to shape analysis we develop bootstrap methods for inference about mean reflection shape and size and shape based on labelled landmark data the approach is developed in general dimensions though we focus on the three dimensional case we consider two pivotal statistics which we use to construct bootstrap confidence regions for the mean reflection shape or size and shape and present simulation results which show that these statistics perform well in a variety of examples we also suggest regularized versions of the test statistics that are suitable for more challenging cases where sample size is not sufficiently large in relation to the number of landmarks and present numerical results confirming that regularization indeed leads to better performance an algorithm for producing a graphical representation of the confidence region for the mean reflection shape is presented and applied in an example involving molecular dynamics simulation data

energy entropy inequalities for classical lattice systems a new characterization of equilibrium states for classical lattice systems is given in terms of correlation inequalities their physical meaning is found to express thermodynamic stability we demonstrate the applicability of the inequalities in specific models

saddlepoint approximations for the bingham and fisher bingham normalising constants the fisher bingham distribution is obtained when a multivariate normal random vector is conditioned to have unit length its normalising constant can be expressed as an elementary function multiplied by the density evaluated at 1 of a linear combination of independent noncentral chi 1 2 random variables hence we may approximate the normalising constant by applying a saddlepoint approximation to this density three such approximations implementation of each of which is straightforward are investigated the first order saddlepoint density approximation the second order saddlepoint density approximation and a variant of the second order approximation which has proved slightly more accurate than the other two the numerical and theoretical results we present show that this approach provides highly accurate approximations in a broad spectrum of cases

estimation of sums of random variables examples and information bounds this paper concerns the estimation of sums of functions of observable and unobservable variables lower bounds for the asymptotic variance and a convolution theorem are derived in general finite and infinite dimensional models an explicit relationship is established between efficient influence functions for the estimation of sums of variables and the estimation of their means certain plug in estimators are proved to be asymptotically efficient in finite dimensional models while u v estimators of robbins are proved to be efficient in infinite dimensional mixture models examples include certain species network and data confidentiality problems

maximum likelihood detection in a four dimensional stokes space receiver the maximum likelihood detection rule for a four dimensional direct detection optical front end is derived the four dimensions are two intensities and two differential phases three different signal processing algorithms composed of symbol by symbol sequence and successive detection are discussed to remedy dealing with special functions in the detection rules an approximation for high signal to noise ratios snrs is provided simulation results show that despite the simpler structure of the successive algorithm the resulting performance loss in comparison with the other two algorithms is negligible for example for an 8 ring 8 ary phase constellation the complexity of detection reduces by a factor of 8 while the performance in terms of the symbol error rate degrades by 0 5 db it is shown that the high snr approximation is very accurate even at low snrs the achievable rates for different constellations are computed and compared by the monte carlo method for example for a 4 ring 8 ary phase constellation the achievable rate is 10 bits per channel use at an snr of 25 db while by using an 8 ring 8 ary phase constellation and an error correcting code of rate 5 6 this rate is achieved at an snr of 20 db

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

equilibrium conditions for coupled classical quantum systems systems with classical as well as quantal degrees of freedom are described this is done by means of a relative hamiltonian and a derivation satisfying a compatibility relation various equivalent equilibrium conditions are studied

what is the real size of a sampled network the case of the internet internet mapping projects generally consist in sampling the network from a limited set of sources by usingtraceroute probes this methodology akin to the merging of spanning trees from the different sources to a set of destinations leads necessarily to a partial incomplete map of the internet accordingly determination of internet topology characteristics from such sampled maps is in part a problem of statistical inference our contribution begins with the observation that the inference of many of the most basic topological quantities including network size and degree characteristics fromtraceroute measurements is in fact a version of the so called species problem in statistics this obse rvation has important implications since species problems are often quite challenging we focus here on the most fundamental example of atraceroute internet species the number of nodes in a network specifica lly

uniqueness of gibbs measures and absorption probabilities 1 introduction in studying uniqueness of gibbs measures it may be useful to make a comparison with a stochastic process we present a method connecting absorption probabilities of a simple markov chain at 0 with uniqueness our specific result theorem 1 1 is used for one dimensional systems it includes a well known result on uniqueness in ruelle 1968 and succeeds in section 6 to find a natural improvement of other results that needed refined estimates in our method the key role is played by a certain inequality comparison of processes is quite well known already in the literature duality see liggett 1985 is a nice technique based on an equality we hope that our comparison method using absorption probabilities is useful in more problems let us now describe our problem setting let s be a countable set and x a finite or countable set for a c s and a e xs write ga gj j ea we define gibbs measures on xs in terms of a given energy difference function ah a a for the energy difference between a and a in xs this function has to be properly defined only in case aa a o for the complement a of any finite set a assume that for any finite a c s this energy difference has the form

shape procrustes tangent projections and bilateral symmetry summary in shape analysis with concentrated data the procrustes tangent projection of shapes plays a fundamental role since this projection can be used to convert shape analysis to standard multivariate analysis in view of its importance a systematic and rigorous treatment of the procrustes tangent projection is developed here to facilitate its use in applications one important application involves an analytical description of bilateral symmetry of objects together with some related distributional results an explicit expression for the tangent projection is also derived

the complex watson distribution and shape analysis the complex watson distribution is an important simple distribution on the complex sphere which is used in statistical shape analysis we describe the density obtain the integrating constant and provide large sample approximations maximum likelihood estimation and hypothesis testing procedures for one and two samples are described the particular connection with shape analysis is discussed and we consider an application examining shape differences between normal and schizophrenic brains we make some observations about bayesian shape inference and finally we describe a more general rotationally symmetric family of distributions

estimation and inference of quantile regression for survival data under biased sampling abstractbiased sampling occurs frequently in economics epidemiology and medical studies either by design or due to data collecting mechanism failing to take into account the sampling bias usually leads to incorrect inference we propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes including but not limited to the length biased sampling the case cohort design and variants thereof we establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level we also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality we further propose a new resampling method for inference which differs from alternative procedures in that it does not require to repeatedly solve estimating equations it is proved that the resampling method consistently estimates the asymptoti

covariance and fisher information in quantum mechanics variance and fisher information are ingredients of the cramer rao inequality we regard fisher information as a riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and fisher information in this approach we show that there is a kind of dual one to one correspondence between the candidates of the two concepts we emphasize that fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold

quasi additive estimates on the hamiltonian for the one dimensional long range ising model in this work we study the problem of getting quasi additive bounds for the hamiltonian of the long range ising model when the two body interaction term decays proportionally to 1d2 0 1 we revisit the paper by cassandro et al j math phys 46 053305 2005 where they extend to the case 0 ln3ln2 1 the result of the existence of a phase transition by using a peierls argument given by frohlich and spencer commun math phys 84 87 101 1982 for 0 the main arguments of cassandro et al j math phys 46 053305 2005 are based in a quasi additive decomposition of the hamiltonian in terms of hierarchical structures called triangles and contours which are related to the original definition of contours introduced by frohlich and spencer commun math phys 84 87 101 1982 in this work we study the existence of a quasi additive decomposition of the hamiltonian in terms of the contours defined in the work of cassandro et al j math phys 46 053305 2005 the most relevant r

estimating a multiplicative treatment effect under biased allocation suppose that given x is poisson with mean while given y is poisson with mean or according as treatment 1 or treatment 2 is used moreover suppose that treatment 1 is used if x

saddlepoint approximations for the normalizing constant of fisher bingham distributions on products of spheres and stiefel manifolds in an earlier paper kume wood 2005 showed how the normalizing constant of the fisher bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation in this sequel we extend the approach to a more general setting and derive saddlepoint approximations for the normalizing constants of multicomponent fisher bingham distributions on cartesian products of spheres and fisher bingham distributions on stiefel manifolds in each case the approximation for the normalizing constant is essentially a multivariate saddlepoint density approximation for the joint distribution of a set of quadratic forms in normal variables both first order and second order saddlepoint approximations are considered computational algorithms numerical results and theoretical properties of the approximations are presented in the challenging high dimensional settings considered in this paper the saddlepoint approximations perform very well in all examples considered some key words directional data fisher matrix distribution kent distribution orientation statistics

optimal estimation under biased allocation of treatments summary this paper provides a semi parametric solution to a problem proposed by robbins zhang 1991 the solution is obtained utilizing the theory of optimum estimating functions godambe thompson 1989 our solution coincides with maximum likelihood estimation for the parametric model suggested by robbins zhang 1991 even for alternative models investigted in this paper the efficiency of our estimation appears very close to that of maximum likelihood estimation

detailed balance and equilibrium for classical lattice systems an infinite set of jump processes satisfying the condition of detailed balance is found it is proved that any state invariant for these processes is an equilibrium state providing a new characterization of dlr states by means of the notion of detailed balance this extends previous results proved in one and two dimensions

empirical likelihood methods for two dimensional shape analysis we consider empirical likelihood for the mean similarity shape of objects in two dimensions described by labelled landmarks the restriction to two dimensions permits the representation of preshapes as complex unit vectors we focus on the use of empirical likelihood techniques for the construction of confidence regions for the mean shape and for testing the hypothesis of a common mean shape across several populations theoretical properties and computational details are discussed and the results of a simulation study are presented our results show that bootstrap calibrated empirical likelihood performs well in practice in the planar shape setting

optimization criteria and geometric algorithms for motion and structure estimation prevailing efforts to study the standard formulation of motion and structure recovery have recently been focused on issues of sensitivity and robustness of existing techniques while many cogent observations have been made and verified experimentally many statements do not hold in general settings and make a comparison of existing techniques difficult with an ultimate goal of clarifying these issues we study the main aspects of motion and structure recovery the choice of objective function optimization techniques and sensitivity and robustness issues in the presence of noise we clearly reveal the relationship among different objective functions such as normalized epipolar constraints reprojection error or triangulation all of which can be unified in a new optimal triangulation procedure regardless of various choices of the objective function the optimization problems all inherit the same unknown parameter space the so called essential manifold based on recent developments of optimization techniques on riemannian manifolds in particular on stiefel or grassmann manifolds we propose a riemannian newton algorithm to solve the motion and structure recovery problem making use of the natural differential geometric structure of the essential manifold we provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analytical and practical equivalence of different objective functions the geometric characterization of critical points and the simulation results clarify the difference between the effect of bas relief ambiguity rotation and translation confounding and other types of local minima this leads to consistent interpretations of simulation results over a large range of signal to noise ratio and variety of configurations

on the absence of spontaneous symmetry breaking and of crystalline ordering in two dimensional systems we develop a unified approach based on araki s relative entropy concept to proving absence of spontaneous breaking of continuous internal symmetries and translation invariance in two dimensional statistical mechanical systems more precisely we show that under rather general assumptions on the interactions all equilibrium states of a two dimensional system have all the symmetries compact internal and spatial of the dynamics except possibly rotation invariance rotation invariance remains unbroken if connected correlations decay more rapidly than the inverse square distance we also prove that two dimensional systems with a non compact internal symmetry group like anharmonic crystals typically do not have gibbs states

multivariate aspects of shape theory sis and thus provide a comprehensive view of shape distributions when landmark coordinates are gaussian distributed this work allows the statistical analysis of shape to be carried out using standard techniques of multivariate analysis the paper includes some new results in all dimensions and a general gaussian approximation to the size and shape distribution we also discuss some inference problems and give a numerical example

estimating a treatment effect under biased sampling methods are presented for the estimation of a treatment effect based on before and after treatment values where for ethical reasons all and only those patients are treated whose before treatment values exceed a given constant

channel training for analog fdd repeaters optimal estimators and cramer rao bounds for frequency division duplex channels a simple pilot loop back procedure has been proposed that allows the estimation of the uplink ul and downlink dl channel subspaces between an antenna array and a fully analog repeater for this scheme we derive the maximum likelihood ml estimators for the ul and dl subspaces formulate the corresponding cramer rao bounds and show the asymptotic efficiency of both singular value decomposition svd based estimators by means of monte carlo simulations in addition we illustrate how to compute the underlying rank 1 svd with quadratic time complexity by employing the power iteration method to enable power control for the data transmission knowledge of the channel gains is needed assuming that the ul and dl channels have on average the same gain we formulate the ml estimator for the uplink channel vector norm and illustrate its robustness against strong noise perturbations by means of simulations

cramer rao bounds for deterministic modal analysis the accuracy with which deterministic modes can be identified from a finite record of noisy data is determined by computing the cramer rao bound on the error covariance matrix of any unbiased estimator of mode parameters the bound is computed for many of the standard parametric descriptions of a mode including autoregressive and moving average parameters poles and residues and poles and zeros asymptotic frequency domain versions of the cramer rao bound bring insight into the role played by poles and zeros application of the bound to second and fourth order systems illustrates the influence of mode locations on the ability to identify them application of the bound to the estimation of an energy spectrum illuminates the accuracy of estimators that presume to resolve spectral peaks

estimating the number of species in a stochastic abundance model consider a stochastic abundance model in which the species arrive in the sample according to independent poisson processes where the abundance parameters of the processes follow a gamma distribution we propose a new estimator of the number of species for this model the estimator takes the form of the number of duplicated species i e species represented by two or more individuals divided by an estimated duplication fraction the duplication fraction is estimated from all frequencies including singleton information the new estimator is closely related to the sample coverage estimator presented by chao and lee 1992 journal of the american statistical association 87 210 217 we illustrate the procedure using the malayan butterfly data discussed by fisher corbet and williams 1943 journal of animal ecology 12 42 58 and a 1989 christmas bird count dataset collected in florida u s a simulation studies show that this estimator compares well with maximum likelihood estimators i e empirical bayes estimators from the bayesian viewpoint for which an iterative numerical procedure is needed and may be infeasible

statistical analysis for the angular central gaussian distribution on the sphere summary the angular central gaussian distribution is an alternative to the bingham distribution for modeling antipodal symmetric directional data in this paper the statistical theory for the angular central gaussian model is presented some topics treated are maximum likelihood estimation of the parameters testing for uniformity and circularity and principal components analysis comparisons to methods based upon the sample second moments are made via an example

on the symmetry of the gibbs states in two dimensional lattice systems under fairly general conditions if a two dimensional classical lattice system has an internal symmetry groupg which is a compact connected lie group then all gibbs states areg invariant

on intrinsic cramer rao bounds for riemannian submanifolds and quotient manifolds we study cramer rao bounds crb s for estimation problems on riemannian manifolds in s t smith covariance subspace and intrinsic cramer rao bounds ieee trans signal process vol 53 no 5 1610 1630 2005 the author gives intrinsic crb s in the form of matrix inequalities relating the covariance of estimators and the fisher information of estimation problems we focus on estimation problems whose parameter space bar cal p is a riemannian submanifold or a riemannian quotient manifold of a parent space cal p that is estimation problems on manifolds with either deterministic constraints or ambiguities the crb s in the aforementioned reference would be expressed w r t bases of the tangent spaces to bar cal p in some cases though it is more convenient to express covariance and fisher information w r t bases of the tangent spaces to cal p we give crb s w r t such bases expressed in terms of the geodesic distances on the parameter space the bounds are valid even for singular fisher information matrices in two examples we show how the crb s for synchronization problems including a type of sensor network localization problem differ in the presence or absence of anchors leading to bounds for estimation on either submanifolds or quotient manifolds with very different interpretations

blind mimo eigenmode transmission based on the algebraic power method identification of the channel matrix is of main concern in wireless multiple input multiple output mimo systems to maximize the snr the best way to utilize a mimo system is to communicate on the top singular vectors of the channel matrix here we present a new approach for direct blind identification of the main independent singular modes without estimating the channel matrix itself the right and left singular vectors with maximum corresponding singular values are determined using payload data and are continuously updated while at the same time being used for communication the feasibility of the approach is demonstrated by simulating the performance over a noisy fading time varying channel mathematically the technique is related to the iterative numerical power method for finding eigenvalues of a matrix as well as the time reversal mirror technique developed within acoustics

dualistic differential geometry of positive definite matrices and its applications to related problems abstract analysis on the set of positive definite matrices is involved in many engineering problems we develop a differential geometric theory of the set of positive definite matrices by means of a specific class of connections introduced into it consequently various dualistic aspects of the set are elucidated next using the theory we derive new results and interesting geometrical interpretations for matrix approximation positive definite matrix completion and linear matrix inequality problems

euclidean invariance in statistical mechanics of classical continuous system it is shown that equilibrium states of classical particles with short range interactions are euclidean invariant whenever their correlation functions have a clustering which is integrable the relation between invariance and clustering is analysed for spatial rotations and internal rotational degrees of freedom the analysis is then extended to the case of long range interactions including the coulomb force and jellium systems

robust principal component analysis for power transformed compositional data geochemical surveys collect sediment or rock samples measure the concentration of chemical elements and report these typically either in weight percent or in parts per million ppm there are usually a large number of elements measured and the distributions are often skewed containing many potential outliers we present a new robust principal component analysis pca method for geochemical survey data that involves first transforming the compositional data onto a manifold using a relative power transformation a flexible set of moment assumptions are made which take the special geometry of the manifold into account the kent distribution moment structure arises as a special case when the chosen manifold is the hypersphere we derive simple moment and robust estimators ro of the parameters which are also applicable in high dimensional settings the resulting pca based on these estimators is done in the tangent space and is related to the power transformation method used in correspondence analysis t

absence of long range order in one dimensional spin systems for a one dimensional ising model with interaction energy e left mu right sum limits 1 leqslant i j leqslant n j j i mu iota mu j left j k geqslant 0 mu iota pm 1 right it is proved that there is no long range order at any temperature when s n sum limits k 1 n kj left k right o left log n 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right the same result is shown to hold for the corresponding plane rotator model when s n o left left log n mathord left vphantom log n log log n right kern nulldelimiterspace log log n right right

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

size and shape analysis of error prone shape data we consider the problem of comparing sizes and shapes of objects when landmark data are prone to measurement error we show that naive implementation of ordinary procrustes analysis that ignores measurement error can compromise inference to account for measurement error we propose the conditional score method for matching configurations which guarantees consistent inference under mild model assumptions the effects of measurement error on inference from naive procrustes analysis and the performance of the proposed method are illustrated via simulation and application in three real data examples supplementary materials for this article are available online

minimum mean square distance estimation of a subspace we consider the problem of subspace estimation in a bayesian setting since we are operating in the grassmann manifold the usual approach which consists of minimizing the mean square error mse between the true subspace u and its estimate u may not be adequate as the mse is not the natural metric in the grassmann manifold gn p i e the set of p dimensional subspaces in rn as an alternative we propose to carry out subspace estimation by minimizing the mean square distance between u and its estimate where the considered distance is a natural metric in the grassmann manifold viz the distance between the projection matrices we show that the resulting estimator is no longer the posterior mean of u but entails computing the principal eigenvectors of the posterior mean of uut derivation of the minimum mean square distance mmsd estimator is carried out in a few illustrative examples including a linear gaussian model for the data and bingham or von mises fisher prior distributions for u in all scenarios posterior distributions are derived and the mmsd estimator is obtained either analytically or implemented via a markov chain monte carlo simulation method the method is shown to provide accurate estimates even when the number of samples is lower than the dimension of u an application to hyperspectral imagery is anally investigated

the statistical analysis of shape data summary the paper deals with the statistical shape analysis of landmark data bookstein 1986 introduced a plausible model and obtained a useful normal approximation for three landmarks we use exact distribution theory and a normal approximation to consider maximum likelihood estimation the fisher information matrix for the normal approximation is given and we consider the hypothesis of shape change using these results we analyse a practical example based on digitized shapes this example motivated the work and the general direction for future work is indicated

the fisher bingham distribution on the sphere abstract the fisher distribution is the analogue on the sphere of the isotropic bivariate normal distribution in the plane the purpose of this paper is to propose and analyze a spherical analogue of the general bivariate normal distribution estimation hypothesis testing and confidence regions are also discussed author

statistical assessment of bilateral symmetry of shapes summary this paper formulates the problem of measuring bilateral symmetry of objects analytically for landmark data and develops various new testing procedures and exploratory data analyses the development is linked with the fundamental biological problem of measuring directional asymmetry and fluctuating asymmetry we distinguish two types of symmetry object symmetry and matching symmetry and provide tests under assumptions of isotropic landmark variability as well as non isotropy the tests require novel statistical and geometrical analyses of the procrustes shape manifold for describing components of symmetry and asymmetry within samples an extension of principal component analysis is introduced and illustrated by appropriate deformation techniques various real examples are used to illustrate the practical relevance of this work

on the product of independent complex gaussians in this paper we derive the joint amplitude phase distribution of the product of two independent non zero mean complex gaussian random variables we call this new distribution the complex double gaussian distribution this probability distribution function pdf is a doubly infinite summation over modified bessel functions of the first and second kind we analyze the behavior of this sum and show that the number of terms needed for accuracy is dependent upon the rician k factors of the two input variables we derive an upper bound on the truncation error and use this to present an adaptive computational approach that selects the minimum number of terms required for accuracy we also present the pdf for the special case where either one or both of the input complex gaussian random variables is zero mean we demonstrate the relevance of our results by deriving the optimal neyman pearson detector for a time reversal detection scheme and computing the receiver operating characteristics through monte carlo simulations and by computing the symbol error probability sep for a single channel m ary phase shift keying m psk communication system

quantum energy entropy inequalities a new method for proving the absence of symmetry breaking for quantum systems we develop a new method based on a general energy entropy inequality to rule out spontaneous breaking of symmetries the main advantage of our scheme consists in its clear cut physical significance and its new areas of applicability in particular we can handle discrete symmetry groups as well as continuous ones finally a few illustrations are discussed

nonparametric bayesian density estimation on manifolds with applications to planar shapes statistical analysis on landmark based shape spaces has diverse applications in morphometrics medical diagnostics machine vision and other areas these shape spaces are non euclidean quotient manifolds to conduct nonparametric inferences one may define notions of centre and spread on this manifold and work with their estimates however it is useful to consider full likelihood based methods which allow nonparametric estimation of the probability density this article proposes a broad class of mixture models constructed using suitable kernels on a general compact metric space and then on the planar shape space in particular following a bayesian approach with a nonparametric prior on the mixing distribution conditions are obtained under which the kullback leibler property holds implying large support and weak posterior consistency gibbs sampling methods are developed for posterior computation and the methods are applied to problems in density estimation and classification with shape based predictors simulation studies show improved estimation performance relative to existing approaches

efficiency of the u v method of estimation given a pool of motorists how do we estimate the total intensity of those who had a prespecified number of traffic accidents in the past year we previously have proposed the u v method as a solution to estimation problems of this type in this paper we prove that the u v method provides asymptotically efficient estimators in an important special case

estimating the number of species a review how many kinds are there suppose that a population is partitioned into c classes in many situations interest focuses not on estimation of the relative sizes of the classes but on estimation of c itself for example biologists and ecologists may be interested in estimating the number of species in a population of plants or animals numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue and linguists may be interested in estimating the size of an author s vocabulary in this article we review the problem of statistical estimation of c many approaches have been proposed some purely data analytic and others based in sampling theory in the latter case numerous variations have been considered the population may be finite or infinite if finite samples may be taken with replacement multinomial sampling or without replacement hypergeometric sampling or by bernoulli sampling if infinite sampling may be multinomial or bernoulli or the sample may be th

a multi dimensional scaling approach to shape analysis summary we propose an alternative to kendall s shape space for reflection shapes of configurations in rm with k labelled vertices where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations the proposed approach embeds the space of such shapes into the space p k 1 of k 1 x k 1 real symmetric positive semidefinite matrices which is the closure of an open subset of a euclidean space and defines mean shape as the natural projection of euclidean means in p k 1 on to the embedded copy of the shape space this approach has strong connections with multi dimensional scaling and the mean shape so defined gives good approximations to other commonly used definitions of mean shape we also use standard perturbation arguments for eigenvalues and eigenvectors to obtain a central limit theorem which then enables the application of standard statistical techniques to shape analysis in two or more dimensions

an informational measure of association and dimension reduction for multiple sets and groups with applications in morphometric analysis in this article we propose a new general index that measures relationships between multiple sets of random vectors this index is based on kullback leibler kl information which measures linear or nonlinear dependence between multiple sets using joint and marginal densities of affine transformations of the random vectors estimates of the matrixes are obtained by maximizing the kl information and are shown to be consistent the motivation for introducing such an index comes from morphological integration studies a topic in biological science as a special case of this index we define an overall measure of association and two other measures for dimension reduction the use of these measures is illustrated through real data analysis in morphometric studies and extensive simulations and their performance is compared with that of approaches based on canonical correlation analysis extensions of the aforementioned measures to multiple groups are also discussed in contrast to canonical correlation analysi

the complex bingham distribution and shape analysis summary a complex version of the bingham distribution is defined on the unit complex sphere in ck various statistical properties including asymptotic normality under high concentration are derived symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions strengths and weaknesses of this approach are investigated links and contrasts with bookstein co ordinates are discussed a hybrid approach to principal component analysis based on complex and real co ordinates is suggested

second order complex random vectors and normal distributions complex random vectors are usually described by their covariance matrix this is insufficient for a complete description of second order statistics and another matrix called the relation matrix is necessary some of its properties are analyzed and used to express the probability density function of normal complex vectors various consequences are presented

statistical analysis on high dimensional spheres and shape spaces we consider the statistical analysis of data on high dimensional spheres and shape spaces the work is of particular relevance to applications where high dimensional data are available a commonly encountered situation in many disciplines first the uniform measure on the infinite dimensional sphere is reviewed together with connections with wiener measure we then discuss densities of gaussian measures with respect to wiener measure some nonuniform distributions on infinite dimensional spheres and shape spaces are introduced and special cases which have important practical consequences are considered we focus on the high dimensional real and complex bingham uniform von mises fisher fisher bingham and the real and complex watson distributions asymptotic distributions in the cases where dimension and sample size are large are discussed approximations for practical maximum likelihood based inference are considered and in particular we discuss an application to brain shape modeling