efficient scalar quantization of exponential and laplacian random variables this paper presents solutions to the entropy constrained scalar quantizer ecsq design problem for two sources commonly encountered in image and speech compression applications sources having the exponential and laplacian probability density functions we use the memoryless property of the exponential distribution to develop a new noniterative algorithm for obtaining the optimal quantizer design we show how to obtain the optimal ecsq either with or without an additional constraint on the number of levels in the quantizer in contrast to prior methods which require a multidimensional iterative solution of a large number of nonlinear equations the new method needs only a single sequence of solutions to one dimensional nonlinear equations in some laplacian cases one additional two dimensional solution is needed as a result the new method is orders of magnitude faster than prior ones we show that as the constraint on the number of levels in the quantizer is relaxed the optimal ecsq becomes a uniform threshold quantizer utq for exponential but not for laplacian sources we then further examine the performance of the utq and optimal ecsq and also investigate some interesting alternatives to the utq including a uniform reconstruction quantizer urq and a constant dead zone ratio quantizer cdzrq

renaming in an asynchronous environment this paper is concerned with the solvability of the problem of processor renaming in unreliable completely asynchronous distributed systems fischer et al prove in 8 that nontrivial consensus cannot be attained in such systems even when only a single benign processor failure is possible in contrast this paper shows that problems of processor renaming can be solved even in the presence of up to t n 2 faulty processors contradicting the widely held belief that no nontrivial problem can be solved in such a system the problems deal with renaming processors so as to reduce the size of the initial name space when only uniqueness of the new names is required we present a lower bound of n 1 on the size of the new name space and a renaming algorithm that establishes an upper bound on n t if the new names are required also to preserve the original order a tight bound of 2 n t 1 1 is obtained

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

optimal byzantine resilient convergence in uni dimensional robot networks given a set of robots with arbitrary initial location and no agreement on a global coordinate system convergence requires that all robots asymptotically approach the exact same but unknown beforehand location robots are oblivious they do not recall the past computations and are allowed to move in a one dimensional space additionally robots cannot communicate directly instead they obtain system related information only via visual sensors even though convergence and the classical distributed approximate agreement problem that requires correct processes to decide for some constant e values distance e apart and within the range of initial proposed values are similar we provide evidence that solving convergence in robot networks requires specific assumptions about synchrony and byzantine resilience in more detail we prove necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being byzantine i e they can exhibit arbitrary behavior additionally we propose two deterministic convergence algorithms for robot networks and analyze their correctness and complexity in various atomicity and synchrony settings the first algorithm tolerates f byzantine robots for 2f 1 sized robot networks in fully synchronous atom networks while the second proposed algorithm tolerates f byzantine robots for 3f 1 sized robot networks in non atomic corda networks the resilience of these two algorithms is proved to be optimal

regression modeling in back propagation and projection pursuit learning we study and compare two types of connectionist learning methods for model free regression problems 1 the backpropagation learning bpl and 2 the projection pursuit learning ppl emerged in recent years in the statistical estimation literature both the bpl and the ppl are based on projections of the data in directions determined from interconnection weights however unlike the use of fixed nonlinear activations usually sigmoidal for the hidden neurons in bpl the ppl systematically approximates the unknown nonlinear activations moreover the bpl estimates all the weights simultaneously at each iteration while the ppl estimates the weights cyclically neuron by neuron and layer by layer at each iteration although the bpl and the ppl have comparable training speed when based on a gauss newton optimization algorithm the ppl proves more parsimonious in that the ppl requires a fewer hidden neurons to approximate the true function to further improve the statistical performance of the ppl an orthogonal polynomial approximation is used in place of the supersmoother method originally proposed for nonlinear activation approximation in the ppl

asymptotically optimal model estimation for quantization using high rate theory approximations we introduce flexible practical quantizers based on possibly non gaussian models in both the constrained resolution cr and the constrained entropy cases we derive model estimation criteria optimizing asymptotic with increasing rate quantizer performance we show that in the cr case the optimal criterion is different from the maximum likelihood criterion commonly used for that purpose and introduce a new criterion that we call constrained resolution minimum description length cr mdl we apply these principles to the generalized gaussian scaled mixture model which is accurate for many real world signals we provide an explanation of the reason why the cr mdl improves quantization performance in the cr case and show that cr mdl can compensate for a possible mismatch between model and data distribution thus this criterion is of a great interest for practical applications our experiments apply the new quantization method to controllable artificial data and to the commonly used modulated lapped transform representation of audio signals we show that both the cr mdl criterion and a non gaussian modeling have significant advantages

a semiparametric approach to canonical analysis summary classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables we propose a method called semiparametric canonical analysis to generalize canonical correlation analysis to incorporate the important non linear association semiparametric canonical analysis is easy to implement and interpret statistical properties are proved a consistent estimation method is developed selection of significant semiparametric canonical analysis components is discussed simulations suggest that the methods proposed have satisfactory performance in finite samples one environmental data set and one data set in social science are investigated in which non linear canonical associations are observed and interpreted

new combinatorial topology bounds for renaming the upper bound in the renaming task n 1 processes start with unique input names from a large space and must choose unique output names taken from a smaller name space 0 1 k to rule out trivial solutions a protocol must be anonymous the value chosen by a process can depend on its input name and on the execution but not on the specific process id attiya et al 1990 showed that renaming has a wait free solution when k 2n several algebraic topology proofs of a lower bound stating that no such protocol exists when k

a non topological proof for the impossibility of k set agreement in the k set agreement task each process proposes a value and each correct process has to decide a value which was proposed so that at most k distinct values are decided using topological arguments it has been proved that k set agreement is unsolvable in the asynchronous wait free read write shared memory model when k

a simple lemma on greedy approximation in hilbert space and convergence rates for projection pursuit regression and neural network training a general convergence criterion for certain iterative sequences in hilbert space is presented for an important subclass of these sequences estimates of the rate of convergence are given under very mild assumptions these results establish an 0 1 f4n nonsampling convergence rate for projection pursuit regression and neural network training where n represents the number of ridge functions neurons or coefficients in a greedy basis expansion

use of bias term in projection pursuit learning improves approximation and convergence properties in a regression problem one is given a multidimensional random vector x the components of which are called predictor variables and a random variable y called response a regression surface describes a general relationship between x and y a nonparametric regression technique that has been successfully applied to high dimensional data is projection pursuit regression ppr the regression surface is approximated by a sum of empirically determined univariate functions of linear combinations of the predictors projection pursuit learning ppl formulates ppr using a 2 layer feedforward neural network the smoothers in ppr are nonparametric whereas those in ppl are based on hermite functions of some predefined highest order r we demonstrate that ppl networks in the original form do not have the universal approximation property for any finite r and thus cannot converge to the desired function even with an arbitrarily large number of hidden units but by including a bias term in each linear projection of the predictor variables ppl networks can regain these capabilities independent of the exact choice of r experimentally it is shown in this paper that this modification increases the rate of convergence with respect to the number of hidden units improves the generalization performance and makes it less sensitive to the setting of r finally we apply ppl to chaotic time series prediction and obtain superior results compared with the cascade correlation architecture

optimal bit allocation via the generalized bfos algorithm p h westerink et al 1988 developed an optimal bit allocation algorithm that is simplified when all operational distortion rate functions which are referred to as quantizer functions are convex this algorithm is restated using the generalized breiman friedman olshen and stone bfos algorithm a recently developed technique for variable rate vector quantizer design for both cases of convex and nonconvex quantizer functions qfs and its complexity is analyzed the use of the generalized bfos algorithm for optimal bit allocation is analysed it is shown that if each source has a convex quantizer function then the complexity of the algorithm is low

an optimal quadtree based motion estimation and motion compensated interpolation scheme for video compression we propose an optimal quadtree qt based motion estimator for video compression it is optimal in the sense that for a given bit budget for encoding the displacement vector field dvf and the qt segmentation the scheme finds a dvf and a qt segmentation which minimizes the energy of the resulting displaced frame difference dfd we find the optimal qt decomposition and the optimal dvf jointly using the lagrangian multiplier method and a multilevel dynamic program we introduce a new very fast convex search for the optimal lagrangian multiplier spl lambda which results in a very fast convergence of the lagrangian multiplier method the resulting dvf is spatially inhomogeneous since large blocks are used in areas with simple motion and small blocks in areas with complex motion we also propose a novel motion compensated interpolation scheme which uses the same mathematical tools developed for the qt based motion estimator one of the advantages of this scheme is the globally optimal control of the tradeoff between the interpolation error energy and the dvf smoothness another advantage is that no interpolation of the dvf is required since we directly estimate the dvf and the qt segmentation for the frame which needs to be interpolated we present results with the proposed qt based motion estimator which show that for the same dfd energy the proposed estimator uses about 25 fewer bits than the commonly used block matching algorithm we also experimentally compare the interpolated frames using the proposed motion compensated interpolation scheme with the reconstructed original frames

a piecewise single index model for dimension reduction in this article we propose to use different single index models for observations in different regions of the sample space this approach inherits the estimation efficiency of the single index model in each region and at the same time allows the global model to have multidimensionality in the sense of conventional dimension reduction on the other hand the model can be seen as an extension of cart and a piecewise linear model proposed modeling procedures including identifying the region for every single index model and estimation of the single index models are developed simulation studies and real data analysis are employed to demonstrate the usefulness of the approach computer code and technical details of the method are provided as supplementary material online

application of projection pursuit learning to boundary detection and deblurring in images abstract projection pursuit learning networks pplns have been used in many fields of research but have not been widely used in image processing in this paper we demonstrate how this highly promising technique may be used to connect edges and produce continuous boundaries we also propose the application of ppln to deblurring a degraded image when little or no a priori information about the blur is available the ppln was successful at developing an inverse blur filter to enhance blurry images theory and background information on projection pursuit regression ppr and ppln are also presented

adaptive rate distortion optimal in loop quantization for matching pursuit in this paper an adaptive in loop quantization technique is proposed for quantizing inner product coefficients in matching pursuit for each matching pursuit mp stage a different quantizer is used based on the probability distribution of mp coefficients the quantizers are optimized for a given rate budget constraint additionally our proposed adaptive quantization scheme finds the optimal quantizers for each stage based on the already encoded inner product coefficients experimental results show that our proposed adaptive quantization scheme outperforms existing quantization methods used in matching pursuit image coding

progressive coding of a gaussian source using matching pursuit in this paper the application of matching pursuit mp in progressive coding of memoryless gaussian sources is studied in addition a detailed analysis of the rate distortion performance of our proposed mp encoder is presented and the distortion of the mp encoder is derived in terms of dictionary size and number of quantization levels and the optimum parameters are calculated our analysis is based on a probabilistic model for matching pursuit residual vectors our simulation results verify the accuracy of our analysis and show that matching pursuit can produce an embedded bitstream with comparable quality to existing quantizers the mp encoder outperforms quantizers that are capable of producing embedded bitstreams

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

reaching approximate agreement in the presence of faults this paper considers a variant of the byzantine generals problem in which processes start with arbitrary real values rather than boolean values or values from some bounded range and in which approximate rather than exact agreement is the desired goal algorithms are presented to reach approximate agreement in asynchronous as well as synchronous systems the asynchronous agreement algorithm is an interesting contrast to a result of fischer et al who show that exact agreement with guaranteed termination is not attainable in an asynchronous system with as few as one faulty process the algorithms work by successive approximation with a provable convergence rate that depends on the ratio between the number of faulty processes and the total number of processes lower bounds on the convergence rate for algorithms of this form are proved and the algorithms presented are shown to be optimal

the weak chebyshev x greedy algorithm in the unweighted bergman space we study a greedy algorithm called the weak chebyshev x greedy algorithm wcxga and investigate its application to unweighted bergman spaces we first show that the wcxga converges for a wide class of real and complex banach spaces and dictionaries we then prove that certain bergman spaces and their holomorphic monomial dictionaries belong to the class of banach spaces for which the wcxga converges

more choices allow more faults set consensus problems in totally asynchronous systems abstract we define the k set consensus problem as an extension of the consensus problem where each processor decides on a single value such that the set of decided values in any run is of size at most k we require the agreement condition that all values decided upon are initial values of some processor we show that the problem has a simple k 1 resilient protocol in a totally asynchronous system in an attempt to come up with a matching lower bound on the number of failures we study the uncertainty condition which requires that there must be some initial configuration from which all possible input values can be decided we prove using a combinatorial argument that any k resilient protocol for the k set agreement problem would satisfy the uncertainty condition while this is not true for any k 1 resilient protocol this result seems to strengthen the conjecture that there is no k resilient protocol for this problem we prove this result for a restricted class of protocols our motivation for studying this problem is to test whether the number of choices allowed to the processors is related to the number of faults we hope that this will provide intuition towards achieving better bounds for more practical problems that arise in distributed computing e g the renaming problem the larger goal is to characterize the boundary between possibility and impossibility in asynchronous systems given multiple faults

sparse identification of nonlinear functions and parametric set membership optimality analysis sparse identification can be relevant in the automatic control field to solve several problems for nonlinear systems such as identification control filtering fault detection however identifying a maximally sparse approximation of a nonlinear function is in general an np hard problem the common approach is to use relaxed or greedy algorithms that under certain conditions can provide sparsest solutions in this technical note a combined l1 relaxed greedy algorithm is proposed and conditions are given under which the approximation derived by the algorithm is a sparsest one differently from other conditions available in the literature the ones provided here can be actually verified for any choice of the basis functions defining the sparse approximation a set membership analysis is also carried out assuming that the function to approximate is a linear combination of unknown basis functions belonging to a known set of functions it is shown that the algorithm is able to exactly select the basis functions which define the unknown function and to provide an optimal estimate of their coefficients

linear mixed model selection for false discovery rate control in microarray data analysis in a microarray experiment one experimental design is used to obtain expression measures for all genes one popular analysis method involves fitting the same linear mixed model for each gene obtaining gene specific p values for tests of interest involving fixed effects and then choosing a threshold for significance that is intended to control false discovery rate fdr at a desired level when one or more random factors have zero variance components for some genes the standard practice of fitting the same full linear mixed model for all genes can result in failure to control fdr we propose a new method that combines results from the fit of full and selected linear mixed models to identify differentially expressed genes and provide fdr control at target levels when the true underlying random effects structure varies across genes

reaching approximate byzantine consensus with multi hop communication abstract we are interested in approximate byzantine consensus problem wherein all the fault free processes reach consensus asymptotically approximately in finite time in particular we focus on the algorithms under which each process communicates with other processes that are up to l hops away and maintains minimal states across iterations for a given l we identify a necessary and sufficient condition on the network structure for the existence of iterative algorithms of interest our necessary and sufficient condition generalizes the tight condition identified in prior work for l 1 for l l where l is the length of a longest cycle free path in the given network our condition is equivalent to the necessary and sufficient conditions for exact consensus in undirected and directed networks both

geometry based distributed scene representation with omnidirectional vision sensors this paper addresses the problem of efficient representation of scenes captured by distributed omnidirectional vision sensors we propose a novel geometric model to describe the correlation between different views of a 3 d scene we first approximate the camera images by sparse expansions over a dictionary of geometric atoms since the most important visual features are likely to be equivalently dominant in images from multiple cameras we model the correlation between corresponding features in different views by local geometric transforms for the particular case of omnidirectional images we define the multiview transforms between corresponding features based on shape and epipolar geometry constraints we apply this geometric framework in the design of a distributed coding scheme with side information which builds an efficient representation of the scene without communication between cameras the wyner ziv encoder partitions the dictionary into cosets of dissimilar atoms with respect to shape and position in the image the joint decoder then determines pairwise correspondences between atoms in the reference image and atoms in the cosets of the wyner ziv image in order to identify the most likely atoms to decode under epipolar geometry constraints experiments demonstrate that the proposed method leads to reliable estimation of the geometric transforms between views in particular the distributed coding scheme offers similar rate distortion performance as joint encoding at low bit rate and outperforms methods based on independent decoding of the different images

the combinatorial structure of wait free solvable tasks this paper presents a self contained study of wait free solvable tasks a new necessary condition for wait free solvability based on a restricted set of executions is proved this set of executions induces a very simple to understand structure which is used to prove tight bounds for k set consensus and renaming the framework is based on topology but uses only elementary combinatorics and in contrast to previous works does not rely on algebraic or geometric arguments

are wait free algorithms fast the time complexity of wait free algorithms in normal executions where no failures occur and processes operate at approximately the same speed is considered a lower bound of log n on the time complexity of any wait free algorithm that achieves approximate agreement among n processes is proved in contrast there exists a non wait free algorithm that solves this problem in constant time this implies an o log n time separation between the wait free and non wait free computation models on the positive side we present an o log n time wait free approximate agreement algorithm the complexity of this algorithm is within a small constant of the lower bound

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

harmonic decomposition of audio signals with matching pursuit we introduce a dictionary of elementary waveforms called harmonic atoms that extends the gabor dictionary and fits well the natural harmonic structures of audio signals by modifying the standard matching pursuit we define a new pursuit along with a fast algorithm namely the fast harmonic matching pursuit to approximate n dimensional audio signals with a linear combination of m harmonic atoms our algorithm has a computational complexity of o mkn where k is the number of partials in a given harmonic atom the decomposition method is demonstrated on musical recordings and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations e g very different note durations lots of reverberation and overlapping notes

a posteriori quantization of progressive matching pursuit streams this paper proposes a rate distortion optimal a posteriori quantization scheme for matching pursuit mp coefficients the a posteriori quantization applies to an mp expansion that has been generated offline and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise the redundancy of the mp dictionary provides an indicator of the relative importance of coefficients and atom indices and subsequently on the quantization error it is used to define a universal upper bound on the decay of the coefficients sorted in decreasing order of magnitude a new quantization scheme is then derived where this bound is used as an oracle for the design of an optimal a posteriori quantizer the latter turns the exponentially distributed coefficient entropy constrained quantization problem into a simple uniform quantization problem using simulations with random dictionaries we show that the proposed exponentially upper bounded quantization euq clearly outperforms classical schemes stepping on the ideal oracle based approach a suboptimal adaptive scheme is then designed that approximates the euq but still outperforms competing quantization methods in terms of rate distortion characteristics finally the proposed quantization method is studied in the context of image coding it performs similarly to state of the art coding methods and even better at low rates while interestingly providing a progressive stream that is very easy to transcode and adapt to changing rate constraints

sparse representations for image decompositions we are given an image i and a library of templates cal l such that cal l is an overcomplete basis for i the templates can represent objects faces features analytical functions or be single pixel templates canonical templates there are infinitely many ways to decompose i as a linear combination of the library templates each decomposition defines a representation for the image i given cal l what is an optimal representation for i given cal l and how to select it we are motivated to select a sparse compact representation for i and to account for occlusions and noise in the image we present a concave cost function criterion on the linear decomposition coefficients that satisfies our requirements more specifically we study a weighted l norm with 0 p 1 we prove a result that allows us to generate all local minima for the l norm and the global minimum is obtained by searching through the local ones due to the computational complexity i e the large number of local minima we also study a greedy and iterative weighted l matching pursuit strategy

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

optimized atom position and coefficient coding for matching pursuit based image compression in this paper we propose a new encoding algorithm for matching pursuit image coding we show that coding performance is improved when correlations between atom positions and atom coefficients are both used in encoding we find the optimum tradeoff between efficient atom position coding and efficient atom coefficient coding and optimize the encoder parameters our proposed algorithm outperforms the existing coding algorithms designed for matching pursuit image coding additionally we show that our algorithm results in better rate distortion performance than jpeg 2000 at low bit rates

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

local minimax learning of functions with best finite sample estimation error bounds applications to ridge and lasso regression boosting tree learning kernel machines and inverse problems optimal local estimation is formulated in the minimax sense for inverse problems and nonlinear regression this theory provides best mean squared finite sample error bounds for some popular statistical learning algorithms and also for several optimal improvements of other existing learning algorithms such as smoothing splines and kernel regularization the bounds and improved algorithms are not based on asymptotics or bayesian assumptions and are truly local for each query not depending on cross validating estimates at other queries to optimize modeling parameters results are given for optimal local learning of approximately linear functions with side information context using real algebraic geometry in particular finite sample error bounds are given for ridge regression and for a local version of lasso regression the new regression methods require only quadratic programming with linear or quadratic inequality constraints for implementation greedy additive expansions are then combined with local minimax learning via a change in metric an optimal strategy is presented for fusing the local minimax estimators of a class of experts providing optimal finite sample prediction error bounds from random forests local minimax learning is extended to kernel machines best local prediction error bounds for finite samples are given for tikhonov regularization the geometry of reproducing kernel hilbert space is used to derive improved estimators with finite sample mean squared error mse bounds for class membership probability in two class pattern classification problems a purely local cross validation free algorithm is proposed which uses fisher information with these bounds to determine best local kernel shape in vector machine learning finally a locally quadratic solution to the finite fourier moments problem is presented after reading the first three sections the reader may proceed directly to any of the subsequent applications sections

model checking in regression via dimension reduction lack of fit checking for parametric and semiparametric models is essential in reducing misspecification the efficiency of most existing model checking methods drops rapidly as the dimension of the covariates increases we propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern consistency of the method is proved for parametric and semiparametric regression models a bootstrap implementation is also discussed simulation comparisons with several existing methods are made suggesting that the proposed methods are more efficient than the existing methods when the dimension increases air pollution data from chicago are used to illustrate the procedure

in loop atom modulus quantization for matching pursuit and its application to video coding this paper provides a precise analytical study of the selection and modulus quantization of matching pursuit mp coefficients we demonstrate that an optimal rate distortion trade off is achieved by selecting the atoms up to a quality dependent threshold and by defining the modulus quantizer in terms of that threshold in doing so we take into account quantization error re injection resulting from inserting the modulus quantizer inside the mp atom computation loop in loop quantization not only improves coding performance but also affects the optimal quantizer design for both uniform and nonuniform quantization we measure the impact of our work in the context of video coding for both uniform and nonuniform quantization the precise understanding of the relation between atom selection and quantization results in significant improvements in terms of coding efficiency at high bitrates the proposed nonuniform quantization scheme results in 0 5 to 2 db improvement over the previous method

filter design with low complexity coefficients we introduce a heuristic for designing filters that have low complexity coefficients as measured by the total number of nonzeros digits in the binary or canonic signed digit csd representations of the filter coefficients while still meeting a set of design specifications such as limits on frequency response magnitude phase and group delay numerical examples show that the method is able to attain very low complexity designs with only modest relaxation of the specifications

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

order restricted score tests for homogeneity in generalised linear and nonlinear mixed models lin 1997 building on work by solomon cox 1992 and lin breslow 1996 introduced a score test for homogeneity in the generalised linear mixed model in this paper we propose an improvement to lin s test that exploits the fact that covariance parameters associated with random effects in the model are constrained so as to form a positive semidefinite covariance matrix therefore an omnibus score test will have power against alternatives that are known never to occur our improvement works by concentrating the score test into directions given by the positive semidefiniteness constraint we apply the same sort of modification to the bias corrected version of her score test in the generalised linear mixed model context and in a nonlinear mixed model context to a score test analogous to hers we show how to obtain the limiting distribution of our proposed test statistic we also argue via simulations and local alternative power calculations that the restricted test has better power than the unrestricted one

pattern classification using projection pursuit abstract this article discusses the adaptation of recently developed regression techniques to classifier design apart from finite sample effects projection pursuit pp regression may be used to model a desired response class as a sum of ridge functions according to a minimum expected squared error criterion this approach can be shown to furnish an optimal discriminant function which can satisfy the neyman pearson criterion over all possible thresholds basis function expansions are used instead of smoothed histograms to reduce computation since good approximation of a discriminant by a linear combination of moderate number of ridge functions may not be easy we introduce an improved method utilizing a nonlinear weighting function

on a conjecture of huber concerning the convergence of projection pursuit regression we generalize the projection pursuit procedure of friedman and stuetzle abstract version and prove strong convergence this answers a question of huber

random effects selection in linear mixed models nous presentons le probleme pratique important de la selection des effets aleatoires dans un modele lineaire mixte un modele bayesien hierarchique est utilise pour identifier tout effet aleatoire devariance nulle l approche proposee reparametrise le modele mixte de telle sorte que les fonctions des parametres de covariance de la distribution des effets aleatoires soient incorporees comme des coefficients de regression pour des variables latentes normales nous permettons aux effets aleatoires de sortir du modele en choisissant des melanges d a priori avec des masses ponctuelles en zero pour les variances des effets aleatoires du fait de la reparametrisation le modele prend une structure lineaire conditionnelle qui facilite l utilisation de lois a priori conjuguees et normales nous demontrons que les calculs a posteriori peuvent etre effectues via un algorithme simple et efficace de monte carlo par chaine de markov les methodes sont illustrees par des donnees simulees et par des donnees reelles d exposition prenatale au polychlorobiphenile et des donnees sur le developpement psychomoteur des enfants

a layered analysis of consensus this paper introduces a simple notion of layering as a tool for analyzing well behaved runs of a given model of distributed computation using layering a model independent analysis of the consensus problem is performed and then applied to proving lower bounds and impossibility results for consensus in a number of familiar and less familiar models the proofs are simpler and more direct than existing ones and they expose a unified structure to the difficulty of reaching consensus in particular the proofs for the classical synchronous and asynchronous models now follow the same outline a new notion of connectivity among states in runs of a consensus protocol called potence connectivity is introduced this notion is more general than previous notions of connectivity used for this purpose and plays a key role in the uniform analysis of consensus

fast matching pursuit with a multiscale dictionary of gaussian chirps we introduce a modified matching pursuit algorithm called fast ridge pursuit to approximate n dimensional signals with m gaussian chirps at a computational cost o mn instead of the expected o mn sup 2 logn at each iteration of the pursuit the best gabor atom is first selected and then its scale and chirp rate are locally optimized so as to get a good chirp atom i e one for which the correlation with the residual is locally maximized a ridge theorem of the gaussian chirp dictionary is proved from which an estimate of the locally optimal scale and chirp is built the procedure is restricted to a sub dictionary of local maxima of the gaussian gabor dictionary to accelerate the pursuit further the efficiency and speed of the method is demonstrated on a sound signal