new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

self dual maxwell chern simons theory on a cylinder in this paper we study the relativistic maxwell chern simons vortices on an asymptotically flat cylinder a topological multivortex solution is constructed by variational methods and the maxwell and the chern simons limits are verified

efficient empirical bayes variable selection and estimation in linear models we propose an empirical bayes method for variable selection and coefficient estimation in linear regression models the method is based on a particular hierarchical bayes formulation and the empirical bayes estimator is shown to be closely related to the lasso estimator such a connection allows us to take advantage of the recently developed quick lasso algorithm to compute the empirical bayes estimate and provides a new way to select the tuning parameter in the lasso method unlike previous empirical bayes variable selection methods which in most practical situations can be implemented only through a greedy stepwise algorithm our method gives a global solution efficiently simulations and real examples show that the proposed method is very competitive in terms of variable selection estimation accuracy and computation speed compared with other variable selection and estimation methods

enhancement of on orbit modal identification of large space structures through sensor placement abstract an iterative method called effective independence is used to place a small number of sensors on a large space structure for identification of a set of dynamically important mode shapes the work is important in the area of on orbit modal identification where a very limited number of sensors will be available the method ranks sensor locations based upon their contribution to the linear independence of the target modal partitions linear independence must be maintained to perform test analysis correlation to determine the accuracy of the analytical model with respect to the test data the derived sensor configuration maintains the spatial independence of the target modes and maximizes the determinant of the corresponding fisher information matrix the proposed sensor placement strategy also minimizes the size of the test data matrix used by a popular modal identification technique called the eigensystem realization algorithm a simple numerical example demonstrates the theory the eigensystem realization algorithm is used to extract mode shapes frequencies and damping from simulated response data for varying levels of noise and damping in all cases considered the effective independence sensor configuration accurately identified more target modes than sensor sets derived using other sensor placement techniques

one step local quasi likelihood estimation summary local quasi likelihood estimation is a useful extension of local least squares methods but its computational cost and algorithmic convergence problems make the procedure less appealing particularly when it is iteratively used in methods such as the back fitting algorithm cross validation and bootstrapping a one step local quasi likelihood estimator is introduced to overcome the computational drawbacks of the local quasi likelihood method we demonstrate that as long as the initial estimators are reasonably good the one step estimator has the same asymptotic behaviour as the local quasi likelihood method our simulation shows that the one step estimator performs at least as well as the local quasi likelihood method for a wide range of choices of bandwidths a data driven bandwidth selector is proposed for the one step estimator based on the pre asymptotic substitution method of fan and gijbels it is then demonstrated that the datadriven one step local quasi likelihood estimator performs as well as the maximum local quasilikelihood estimator by using the ideal optimal bandwidth

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

variable selection for multivariate failure time data in this paper we proposed a penalised pseudo partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients under certain regularity conditions we show the consistency and asymptotic normality of the penalised likelihood estimators we further demonstrate that for certain penalty functions with proper choices of regularisation parameters the resulting estimator can correctly identify the true model as if it were known in advance based on a simple approximation of the penalty function the proposed method can be easily carried out with the newton raphson algorithm we conduct extensive monte carlo simulation studies to assess the finite sample performance of the proposed procedures we illustrate the proposed method by analysing a dataset from the framingham heart study

blind high resolution localization and tracking of multiple frequency hopped signals this paper considers the problem of blind localization and tracking of multiple frequency hopped spread spectrum signals using a uniform linear antenna array without knowledge of hopping patterns or directions of arrival as a preprocessing step we propose to identify a hop free subset of data by discarding high entropy spectral slices from the spectrogram high resolution localization is then achieved via either quadrilinear regression of four way data generated by capitalizing on both spatial and temporal shift invariance or a new maximum likelihood ml based two dimensional 2 d harmonic retrieval algorithm the latter option achieves the best known model identifiability bound while remaining close to the cramer rao bound even at low signal to noise ratios snrs following beamforming using the recovered directions a dynamic programming approach is developed for joint ml estimation of signal frequencies and hop instants in single user tracking the efficacy of the proposed algorithms is illustrated in pertinent simulations

nonparametric independence screening in sparse ultra high dimensional varying coefficient models the varying coefficient model is an important class of nonparametric statistical model which allows us to examine how the effects of covariates vary with exposure variables when the number of covariates is large the issue of variable selection arises in this article we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra high dimensional varying coefficient models the proposed nonparametric independence screening nis selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable the sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order and the dimensionality reduction of nis is quantified to enhance the practical utility and finite sample performance two data driven iterative nis inis methods are proposed for selecting thresholding parameters and variables conditional permutation and greedy metho

multivariate statistical process control using lasso this article develops a new multivariate statistical process control spc methodology based on adapting the lasso variable selection method to the spc problem the lasso method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling which is especially useful in cases where the number of nonzero coefficients is small in multivariate spc applications process mean vectors often shift in a small number of components our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components using this connection between the two problems we propose a lasso based multivariate test statistic and then integrate this statistic into the multivariate ewma charting scheme for phase ii multivariate process monitoring we show that this approach balances protection against various shift levels and shift directions and thus provides an effective tool for multivariate spc applications this article

hop timing estimation for noncoherent frequency hopped m fsk intercept receivers the optimum hop timing estimator based on classical likelihood ratio lr theory is derived for noncoherent slow and fast frequency hopped m fsk intercept receivers such receivers have no a priori knowledge of the hopping code and thus the solution to this estimation problem differs considerably from the more commonly considered case of the friendly receiver the implementation and performance of the lr hop timing structures are presented and compared with that of other previously documented suboptimum schemes in particular when compared to the multiple hop autocorrelation mhac approach and the ping pong approach the average likelihood ratio alr and maximum likelihood ratio mlr optimum estimators offer an improvement in performance of several db in input snr robustness issues for the optimal estimator are examined and alternative configurations are proposed that offer enhanced insensitivity to unknown frequency offsets

sampling piecewise sinusoidal signals with finite rate of innovation methods we consider the problem of sampling piecewise sinusoidal signals classical sampling theory does not enable perfect reconstruction of such signals since they are not band limited however they can be characterized by a finite number of parameters namely the frequency amplitude and phase of the sinusoids and the location of the discontinuities in this paper we show that under certain hypotheses on the sampling kernel it is possible to perfectly recover the parameters that define the piecewise sinusoidal signal from its sampled version in particular we show that at least theoretically it is possible to recover piecewise sine waves with arbitrarily high frequencies and arbitrarily close switching points extensions of the method are also presented such as the recovery of combinations of piecewise sine waves and polynomials finally we study the effect of noise and present a robust reconstruction algorithm that is stable down to snr levels of 7 db

outlier models and prior distributions in bayesian linear regression summary bayesian inference in regression models is considered using heavy tailed error distri butions to accommodate outliers the particular class of distributions that can be con structed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in bayesian linear modelling includ ing simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters the modelling of outliers in nominally normal linear regression models using alternative error distributions which are heavy tailed relative to the normal provides an automatic means of both detecting and accommodating possibly aberrant observations such realistic models do however often lead to analytically intractable analyses with complex posterior distributions in several dimensions that are difficult to summarize and understand in this paper we consider a special yet rather wide class of heavy tailed unimodal and symmetric error distributions for which the analyses though apparently intractable can be examined in some depth by exploiting certain properties of the assumed error form the distributions concerned are those that can be con structed as scale mixtures of normal distributions in his paper concerning location parameters de finetti 1961 discusses such distributions and suggests the hypothetical interpretation that each observation is taken using an instrument with normal error but each time chosen at random from a collection of instruments of different precisions the distribution of the

high dimensional variable selection via tilting the paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations high dimensionality of the data brings in many complications such as possibly spurious high correlations between the variables which result in marginal correlation being unreliable as a measure of association between the variables and the response we propose a new way of measuring the contribution of each variable to the response which takes into account high correlations between the variables in a data driven way the proposed tilting procedure provides an adaptive choice between the use of marginal correlation and tilted correlation for each variable where the choice is made depending on the values of the hard thresholded sample correlation of the design matrix we study the conditions under which this measure can successfully discriminate between the relevant and the irrelevant variables and thus be used as a tool for variable selection finally an iterative variable screening algorithm is constructed to exploit the theoretical properties of tilted correlation and its good practical performance is demonstrated in a comparative simulation study

the existence of chern simons vortices a new type of vortices called chern simons vortices is considered and the existence is established

nonconcave penalized likelihood with a diverging number of parameters a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by fan and li to simultaneously estimate parameters and select important variables they demonstrated that this class of procedures has an oracle property when the number of parameters is finite however in most model selection problems the number of parameters should be large and grow with the sample size in this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators furthermore the consistency of the sandwich formula of the covariance matrix is demonstrated nonconcave penalized likelihood ratio statistics are discussed and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions the asymptotic results are augmented by a simulation study and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

topological multivortex solutions of the self dual maxwell chern simons higgs system abstract we study the existence and various behaviors of topological multivortex solutions of the relativistic self dual maxwell chern simons higgs system we first prove the existence of general topological solutions by applying variational methods to the newly discovered minimizing functional then by an iteration method we prove the existence of topological solutions satisfying some extra conditions which we call admissible solutions we establish asymptotic exponential decay estimates for these topological solutions we also investigate the limiting behavior of the admissible solutions as parameters in our system go to some limits for the abelian higgs limit we obtain strong convergence result while for the chern simons limit we only obtained that our admissible solutions weakly approximate one of the chern simons solutions

existence and uniqueness of topological multivortex solutions of the self dual chern simons cp 1 model abstract in this paper we study the existence and uniqueness of the topological chern simons vortices in the cp 1 model in r 2 after reducing the self dual equations to semilinear elliptic partial differential equations we show that a topological solution exists and it is unique up to a real smooth function if the chern simons coupling constant is sufficiently small

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

identification of external structural loads from measured harmonic responses abstract in many practical situations it is difficult to perform direct measurements or calculations of the external forces acting on an existing vibrating structure instead the structural response may than be measured and the position and magnitude of the exciting forces be calculated from the measured response unfortunately the results from this inverse process are often highly sensitive to noise in the measurements of the response and errors in the model of the structure the present study is focussed on this sensitivity under the assumption of a linear relation between the unknown harmonic force amplitudes and the response at discrete measurement positions a scalar measure of the sensitivity is suggested numerical examples that illustrate the sensitivity and its correlation to the proposed sensitivity measure are given the present sensitivity measure can be calculated for different candidate experimental configurations prior to any actual measurements and hence assist in the experimental design

the solution structure of the o 3 sigma model in a maxwell chern simons theory in this paper a system of semilinear elliptic equations arising from a relativistic self dual maxwell chern simons o 3 sigma model is considered we reveal the uniqueness aspect of the topological solutions for the model the uniqueness result is associated with a clear solution structure of the equations of the radially symmetric case we locate each solution set denoted by a planar diagram

estimating multiple frequency hopping signal parameters via sparse linear regression frequency hopping fh signals have well documented merits for commercial and military applications due to their near far resistance and robustness to jamming estimating fh signal parameters e g hopping instants carriers and amplitudes is an important and challenging task but optimum estimation incurs an unrealistic computational burden the spectrogram has long been the starting non parametric estimator in this context followed by line spectra refinements the problem is that hop timing estimates derived from the spectrogram are coarse and unreliable thus severely limiting performance a novel approach is developed in this paper based on sparse linear regression slr using a dense frequency grid the problem is formulated as one of under determined linear regression with a dual sparsity penalty and its exact solution is obtained using the alternating direction method of multipliers admom the slr based approach is further broadened to encompass polynomial phase hopping pph signals encountered in chirp spread spectrum modulation simulations demonstrate that the developed estimator outperforms spectrogram based alternatives especially with regard to hop timing estimation which is the crux of the problem

one step sparse estimates in nonconcave penalized likelihood models fan and li propose a family of variable selection methods via penalized likelihood using concave penalty functions the nonconcave penalized likelihood estimators enjoy the oracle properties but maximizing the penalized likelihood function is computationally challenging because the objective function is nondifferentiable and nonconcave in this article we propose a new unified algorithm based on the local linear approximation lla for maximizing the penalized likelihood for a broad class of concave penalty functions convergence and other theoretical properties of the lla algorithm are established a distinguished feature of the lla algorithm is that at each lla step the lla estimator can naturally adopt a sparse representation thus we suggest using the one step lla estimator from the lla algorithm as the final estimates statistically we show that if the regularization parameter is appropriately chosen the one step lla estimates enjoy the oracle properties with good initial estimators computationally the one step lla estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood we conduct some monte carlo simulation to assess the finite sample performance of the one step sparse estimation methods the results are very encouraging

piecewise linear regularized solution paths we consider the generic regularized optimization problem argmin l y x j efron hastie johnstone and tibshirani ann statist 32 2004 407 499 have shown that for the lasso that is if l is squared error loss and j 1 is the l 1 norm of the optimal coefficient path is piecewise linear that is is piecewise constant we derive a general characterization of the properties of loss l penalty j pairs which give piecewise linear coefficient paths such pairs allow for efficient generation of the full regularized coefficient paths we investigate the nature of efficient path following algorithms which arise we use our results to suggest robust versions of the lasso for regression and classification and to develop new efficient algorithms for existing problems in the literature including mammen and van de geer s locally adaptive regression splines

variable selection using mm algorithms variable selection is fundamental to high dimensional statistical modeling many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and or nonconcave this article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions these algorithms operate by perturbing the penalty function slightly to render it differentiable then optimizing this differentiable function using a minorize maximize mm algorithm mm algorithms are useful extensions of the well known class of em algorithms a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for em algorithms in particular we prove that when our mm algorithms converge they must converge to a desirable point we also discuss conditions under which this convergence may be guaranteed we exploit the newton raphson like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators our method performs well in numerical tests

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

the problem of vibration field reconstruction statement and general properties abstract the paper addresses the problem of reconstructing the vibration field of a structure or the acoustic field of a bounded fluid from limited data the problem relates to practical situations when there is a need to know the dynamic stress and displacement distribution over the entire structure e g for estimating its remaining service life but the vibration may be measured only on accessible parts of the structure surface in the paper this problem is mathematically formulated and its general properties solvability uniqueness and continuity are studied most attention is paid to the analysis of the error of reconstruction one of the main results obtained is the proof of existence of the optimal vibration model of the structure which renders minimum to the reconstruction error the application of the results to discrete systems is discussed

shrinkage estimation of the varying coefficient model the varying coefficient model is a useful extension of the linear regression model nevertheless how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood to solve the problem we propose here a novel method which combines the ideas of the local polynomial smoothing and the least absolute shrinkage and selection operator lasso the new method can do nonparametric estimation and variable selection simultaneously with a local constant estimator and the adaptive lasso penalty the new method can identify the true model consistently and that the resulting estimator can be as efficient as the oracle estimator numerical studies clearly confirm our theories extension to other shrinkage methods e g the scad i e the smoothly clipped absolute deviation and other smoothing methods is straightforward

hazard models with varying coefficients for multivariate failure time data statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis a local pseudo partial likelihood procedure is proposed for estimating the unknown coefficient functions a weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator the consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested to reduce the computational burden of the maximum local pseudo partial likelihood estimator a simple and useful one step estimator is proposed statistical properties of the one step estimator are established and simulation studies are conducted to compare the performance of the one step estimator to that of the maximum local pseudo partial likelihood estimator the results show that the one step estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudo partial likelihood estimator a data set from the busselton population health surveys is analyzed to illustrate our proposed methodology

on the choice of expansion functions in the helmholtz equation least squares method this paper examines the performance of helmholtz equation least squares hels method in reconstructing acoustic radiation from an arbitrary source by using three different expansions namely localized spherical waves lsw distributed spherical waves dsw and distributed point sources dps under the same set of measurements the reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 hz reconstruction is obtained by using tikhonov regularization or its modification with the regularization parameter selected by error free parameter choice methods the impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated results demonstrate that dsw leads to a better conditioned transfer matrix yields more accurate reconstruction than both lsw and dps and is not affected as much by the change in measurement points also it is possible to obtain optimal locations of the auxiliary sources for dsw lsw and dps by taking an independent layer of measurements use of these auxiliary sources and an optimal combination of regularization and error free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost effective manner

i lamm for sparse learning simultaneous control of algorithmic complexity and statistical error we propose a computational framework named iterative local adaptive majorize minimization i lamm to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models i lamm is a two stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi likelihood the first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator which is further refined in the second stage by iteratively solving a sequence of convex programs with smaller precision tolerances theoretically we establish a phase transition the first stage has a sublinear iteration complexity while the second stage achieves an improved linear rate of convergence though this framework is completely algorithmic it provides solutions with optimal statistical performances and controlled algorithmic complexity for a large family of nonconvex optimization problems the iteration effects on statistical errors are clearly demonstrated via a contraction property our theory relies on a localized version of the sparse restricted eigenvalue condition which allows us to analyze a large family of loss and penalty functions and provide optimality guarantees under very weak assumptions for example i lamm requires much weaker minimal signal strength than other procedures thorough numerical results are provided to support the obtained theory

generalized high dimensional trace regression via nuclear norm regularization abstract we study the generalized trace regression with a near low rank regression coefficient matrix which extends notion of sparsity for regression coefficient vectors specifically given a matrix covariate x the probability density function of the response y is f y x c y exp 1 y b where tr t x this model accommodates various types of responses and embraces many important problem setups such as reduced rank regression matrix regression that accommodates a panel of regressors matrix completion among others we estimate through minimizing empirical negative log likelihood plus nuclear norm penalty we first establish a general theory and then for each specific problem we derive explicitly the statistical rate of the proposed estimator they all match the minimax rates in the linear trace regression up to logarithmic factors numerical studies confirm the rates we established and demonstrate the advantage of generalized trace regression over linear trace regression when the response is dichotomous we also show the benefit of incorporating nuclear norm regularization in dynamic stock return prediction and in image classification

nontopological solutions in the self dual maxwell chern simons gauged o 3 sigma model abstract in this paper we prove the existence of nontopological solutions in the self dual maxwell chern simons gauged o 3 sigma model in the plane if the scaling parameter is small enough the reduced equation can be regarded as a perturbation of the liouville equation then we use the generalized implicit function theorem to prove the existence of solutions with nontopological boundary conditions using this result we show the existence of symmetrically topological solutions and nontopological solutions for the original self dual equations whose magnetic fluxes are slightly bigger than the critical value moreover we also compute the topological charge and the degree of the spin vectors

global existence and nonrelativistic limit for the vlasov maxwell chern simons system the vlasov maxwell chern simons system is studied global existence of classical solutions is proved and then its nonrelativistic limit is investigated when the speed of light tends to infinity it is proved that solutions of the vlasov maxwell chern simons system converge to solutions of the vlasov yukawa system in a suitable sense

helmholtz equation least squares method for reconstructing the acoustic pressure field a method using spherical wave expansion theory to reconstruct acoustic pressure field from a vibrating object is developed the radiated acoustic pressures are obtained by means of an expansion of independent functions generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation on the vibrating surface under consideration the coefficients associated with these independent functions are determined by requiring the assumed form of solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method once these coefficients are specified the acoustic pressure at any point including the source surface is completely determined in this paper this method is used to reconstruct the surface acoustic pressures based on the measured acoustic pressure signals in the field it is shown that this method can be applied to both separable and nonseparable geometries and the

a gradient algorithm locally equivalent to the em algorithm in many problems of maximum likelihood estimation it is impossible to carry out either the e step or the m step of the em algorithm the present paper introduces a gradient algorithm that is closely related to the em algorithm this em gradient algorithm approximately solves the m step of the em algorithm by one iteration of newton s method since newton s method converges quickly the local properties of the em gradient algorithm are almost identical with those of the em algorithm any strict local maximum point of the observed likelihood locally attracts the em and em gradient algorithm at the same rate of convergence and near the maximum point the em gradient algorithm always produces an increase in the likelihood with proper modification the em gradient algorithm also exhibits global convergence properties that are similar to those of the em algorithm our proof of global convergence applies and improves existing theory for the em algorithm these theoretical points are reinforced by a discussion of three realistic examples illustrating how the em gradient algorithm can succeed where the em algorithm is intractable

penalized high dimensional empirical likelihood we propose penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models by using an appropriate penalty function we showthat penalized empirical likelihood has the oracle property that is with probability tending to 1 penalized empirical likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance the advantage of penalized empirical likelihood as a nonparametric likelihood approach is illustrated by testing hypotheses and constructing confidence regions numerical simulations confirm our theoretical findings

a unified framework for mode filtering and the maximum a posteriori mode filter a unified framework is presented for examining the performance of linear mode filtering algorithms two common mode filters samples of the mode shapes and the pseudo inverse of the mode shapes are presented in this framework as a tradeoff between sensitivity to other modes and sensitivity to white noise the maximum a posteriori mode filter is presented as an alternative which gracefully transitions between these extremes and attains the minimum mean squared error when the modes to be estimated are well modeled as samples of a gaussian random process numerical simulations in both shallow and deep water environments confirm the analytically derived properties of these mode filters

existence and asymptotics of topological solutions in the self dual maxwell chern simons o 3 sigma model we are concerned with the topological vortex equations arising in the self dual maxwell chern simons o 3 sigma model we prove the existence of solutions for any parameters and q by a variational method we also verify both the maxwell limit and the chern simons limit for the variational solutions

compensation for discarded singular values in vibro acoustic inverse methods the paper addresses the inverse problem where source strengths are back calculated from a sound pressure field sampled at several points regularization techniques such as singular value discarding or tikhonov regularization are commonly used to improve estimates of source strength in such situations however over regularization can result in even worse errors a simple procedure is proposed here to compensate for errors of over regularization the basis is to constrain the solution such that the spatial mean of the measured and reconstructed sound pressure are equal in other words to set the overall sound power of the equivalent calculated sources equal to that of the real source it is argued that the overall sound power is the most stable and reliable quantity on which to base source strength estimates examples of both singular value discarding and tikhonov regularization are given

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

regularization parameter selections via generalized information criterion we apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators this approach relies heavily on the choice of regularization parameter which controls the model complexity in this paper we propose employing the generalized information criterion encompassing the commonly used akaike information criterion aic and bayesian information criterion bic for selecting the regularization parameter our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches we show that the bic type selector enables identification of the true model consistently and the resulting estimator possesses the oracle property in the terminology of fan and li 2001 in contrast however the aic type selector tends to overfit with positive probability we further show that the aic type selector is asymptotically loss efficient while the bic type selector is not

method of superposition applied to patch near field acoustic holography the method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface unlike conformal near field holography where the measurement surface surrounds the entire structure in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required using the method of superposition the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure the source strengths are evaluated by applying boundary conditions on the measurement surface the algorithm requires the inversion of the green s function matrix which may be ill conditioned truncated singular value decomposition is used to invert it the field on the structure surface is then approximated by the field produced by the source distribution the algorithm is easier to implement than the

consensus in ad hoc wsns with noisy links part i distributed estimation of deterministic signals we deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks wsns we cast the decentralized estimation problem as the solution of multiple constrained convex optimization subproblems using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation different from existing alternatives our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages thus allowing for decentralized computation even of nonlinear estimators including maximum likelihood estimators mle in nonlinear and non gaussian data models we prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal furthermore our decentralized algorithms exhibit resilience in the presence of receiver and or quantization noise in particular we introduce a decentralized scheme for least squares and best linear unbiased estimation blue and establish its convergence in the presence of communication noise our algorithms also exhibit potential for higher convergence rate with respect to existing schemes corroborating simulations demonstrate the merits of the novel distributed estimation algorithms

variable selection in semiparametric regression modeling in this paper we are concerned with how to select significant variables in semiparametric modeling variable selection for semiparametric regression models consists of two components model selection for nonparametric components and select significant variables for parametric portion thus it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel this leads to very heavy computational burden in this paper we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood the newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously this allows us to establish the sampling properties of the resulting estimate we first establish the rate of convergence of the resulting estimate with proper choices of penalty functions and regularization parameters we then establish the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component we investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi squared distribution which is independent of the nuisance parameters extensive monte carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures