higher order properties of the wild bootstrap under misspecification abstract we examine the higher order properties of the wild bootstrap wu 1986 in a linear regression model with stochastic regressors we find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them in the latter case the wild bootstrap may fail to match some of the terms in an edgeworth expansion of the full sample test statistic nonetheless we show that the wild bootstrap still has a lower maximal asymptotic risk as an estimator of the true distribution than a normal approximation in shrinking neighborhoods of properly specified models to assess the practical implications of this result we conduct a monte carlo study contrasting the performance of the wild bootstrap with a normal approximation and the traditional nonparametric bootstrap

wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

on the realizability of biorthogonal m dimensional two band filter banks we show an algebraic approach for the design of ladder structures for causal biorthogonal filter banks the key ingredient of the approach is known in literature as euclid s algorithm using this algorithm we derive some strong result on the design freedom for ladder structures in particular we show that the dimensionality of the problem plays an important role we end by with some conjectures concerning the extensions to multichannel and noncausal filter banks

perfect reconstruction fir filter banks some properties and factorizations perfect reconstruction finite impulse response fir filter banks are analyzed both in the z transform and time domains showing the alternatives between designs in the two domains various classes of perfect reconstruction schemes are indicated and relations between previously known systems are given windowed modulated filter banks with low computational complexity and perfect reconstruction are shown new factorizations of polyphase filter matrices leading in particular to linear phase filters are given the computational complexity and the architecture of the new structures are indicated

the role of linear semi infinite programming in signal adapted qmf bank design we consider the problem of designing a perfect reconstruction fir quadrature mirror filter qmf bank h g adapted to input signal statistics with the coding gain as the adaptation criterion maximization of the coding gain has so far been viewed as a difficult nonlinear constrained optimization problem it is shown that the coding gain depends only on the product filter p z h z h z sup 1 and this transformation leads to a stable class of linear optimization problems having finitely many variables and infinitely many constraints termed linear semi infinite programming sip problems the sought for original filter h z is obtained by deflation and spectral factorization of p z with the sip formulation every locally optimal solution is also globally optimal and can be computed using reliable numerical algorithms the natural regularity properties inherent in the sip formulation enhance the performance of these algorithms we present a comprehensive theoretical analysis of the sip problem and its dual characterize the optimal filters and analyze uniqueness and sensitivity issues all these properties are intimately related to those of the input signal and bring considerable insight into the nature of the adaptation process we present discretization and cutting plane algorithms and apply both methods to several examples

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

filters for distortion free two band multirate filter banks in this paper conditions are given for a two band multi rate filter bank to be alias free and to have a unity frequency response it is shown that the class of quadrature mirror filters qmf s that satisfies these conditions is quite limited a class of filters which does satisfy these conditions is given and a simple procedure for designing filters from this class is presented with an example

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

on line scheduling of jobs with fixed start and end times abstract we investigate an on line scheduling problem on a single machine where jobs have fixed start and end times if a job is not processed immediately after its arrival or if its processing is aborted the job is lost the goal is to maximize the total value of all processed jobs in general this problem does not allow on line approximations with finite worst case guarantee we give an approximation algorithm with worst case ratio four for large classes of special instances and we also prove that the factor four is best possible one of our classes contains the instances where the job values are proportional to the job lengths

on coefficient quantization and computational roundoff effects in lossless multirate filter banks it is shown that fir lossless transfer matrices in multirate analysis synthesis systems having the perfect reconstruction property can be implemented such that the lossless property and hence perfect reconstruction can be retained regardless of coefficient quantization such a result was previously shown to be true only for two channel filter banks a noise gain result is presented for lossless systems which finds application in analyzing roundoff noise in multirate filter banks

near perfect reconstruction pseudo qmf banks a novel approach to the design of m channel pseudo quadrature mirror filter qmf banks is presented in this approach the prototype filter is constrained to be a linear phase spectral factor of a 2mth band filter as a result the overall transfer function of the analysis synthesis system is a delay moreover the aliasing cancellation ac constraint is derived such that all the significant aliasing terms are canceled consequently the aliasing level at the output is comparable to the stopband attenuation of the prototype filter in other words the only error at the output of the analysis synthesis system is the aliasing error which is at the level of stopband attenuation using this approach it is possible to design a pseudo qmf bank where the stopband attenuation of the analysis and thus synthesis filters is on the order of spl minus 100 db moreover the resulting reconstruction error is also on the order of spl minus 100 db several examples are included

improved bounds for randomized preemptive online matching abstract preemptive online algorithms for the maximum matching problem maintain a valid matching m while edges of the underlying graph are presented one after the other when presented with an edge e the algorithm should decide whether to augment the matching m by adding e in which case e may be removed later on or to keep m in its current form without adding e in which case e is lost for good the objective is to eventually hold a matching m with maximum weight the main contribution of this paper is to establish new lower and upper bounds on the competitive ratio achievable by randomized preemptive online algorithms we provide a lower bound of 1 ln 2 1 693 on the competitive ratio of any randomized algorithm for the maximum cardinality matching problem we devise a randomized algorithm that achieves an expected competitive ratio of 5 356 for maximum weight matching

lattice structure for regular paraunitary linear phase filterbanks and m band orthogonal symmetric wavelets parauninary linear phase pulp m channel uniform filterbanks which are also known as the generalized lapped orthogonal transforms genlots can be designed and implemented using lattice structures this paper discusses how to impose regularity constraints onto the lattice structure of pulp filterbanks these conditions are expressed in term of the rotation angles of the lattice components by which the resulting filterbanks are guaranteed to have one or two degrees of regularity iterating these new regular filterbanks on the lowpass subband generates a large family of symmetric m band orthonormal wavelets design procedures with many design examples are presented smooth interpolation using regular pulp filterbanks is illustrated through image coding experiments where the novel m band wavelets consistently yield smoother reconstructed images and better perceptual quality

efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals this paper considers semiparametric efficient estimation ofconditional moment models with possibly nonsmooth residuals in unknown parametric components and unknown functions h of endogenous variables we show that 1 the penalized sieve minimum distance psmd estima tor can simultaneously achieve root n asymptotic normality ofand nonparametric optimal convergence rate of allowing for noncompact function parameter spaces 2 a simple weighted bootstrap procedure consistently estimates the limiting distribution of the psmd 3 the semi parametric efficiency bound formula of ai and chen 2003 remains valid for conditional models with nonsmooth residuals and the optimally weighted psmd estimator achieves the bound 4 the centered profiled optimally weighted psmd criterion is asymptotically chi square distributed we illustrate our theories using a partially linear quantile instrumental variables iv regression a monte carlo study and an empirical estimation of the shape invariant quantile iv engel curves

maximally decimated perfect reconstruction fir filter banks with pairwise mirror image analysis and synthesis frequency responses structures are presented for the perfect reconstruction quadrature mirror filter bank that are based on lossless building blocks these structures ensure that the frequency responses of the analysis and synthesis filters have pairwise symmetry with respect to pi 2 and require fewer parameters than recently reported structures also based on lossless building blocks the design time for the proposed structures is correspondingly much less than for the earlier methods which did not incorporate such symmetry

smooth minimum distance estimation and testing with conditional estimating equations uniform in bandwidth theory abstract to study the influence of a bandwidth parameter in inference with conditional moments we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth which can vary within a wide range including bandwidths independent of the sample size we study its behavior under misspecification we also propose an efficient version of our estimator we develop a procedure based on a distance metric statistic for testing restrictions on parameters as well as a bootstrap technique to account for the bandwidth s influence our new methods are simple to implement apply to non smooth problems and perform well in our simulations

hybrid wavelet support vector classification of waveforms the support vector machine svm represents a new and very promising technique for machine learning tasks involving classification regression or novelty detection improvements of its generalization ability can be achieved by incorporating prior knowledge of the task at hand we propose a new hybrid algorithm consisting of signal adapted wavelet decompositions and hard margin svms for waveform classification the adaptation of the wavelet decompositions is tailored for hard margin sv classifiers with radial basis functions as kernels it allows the optimization of the representation of the data before training the svm and does not suffer from computationally expensive validation techniques we assess the performance of our algorithm against the background of current concerns in medical diagnostics namely the classification of endocardial electrograms and the detection of otoacoustic emissions here the performance of hard margin svms can significantly be improved by our adapted preprocessing step

bootstrap confidence sets for spectral projectors of sample covariance let x 1 ldots x n be i i d sample in mathbb r p with zero mean and the covariance matrix varvec sigma the problem of recovering the projector onto an eigenspace of varvec sigma from these observations naturally arises in many applications recent technique from koltchinskii and lounici ann stat 45 1 121 157 2017 helps to study the asymptotic distribution of the distance in the frobenius norm left mathbf p r widehat mathbf p r right 2 between the true projector mathbf p r on the subspace of the rth eigenvalue and its empirical counterpart widehat mathbf p r in terms of the effective rank of varvec sigma this paper offers a bootstrap procedure for building sharp confidence sets for the true projector mathbf p r from the given data this procedure does not rely on the asymptotic distribution of left mathbf p r widehat mathbf p r right 2 and its moments it could be applied for small or moderate sample size n and large dimension p the main result states the validity of the proposed procedure for gaussian samples with an explicit error bound for the error of bootstrap approximation this bound involves some new sharp results on gaussian comparison and gaussian anti concentration in high dimensional spaces numeric results confirm a good performance of the method in realistic examples

on the performance of linear phase wavelet transforms in low bit rate image coding the behavior of linear phase wavelet transforms in low bit rate image coding is investigated the influence of certain characteristics of these transforms such as regularity number of vanishing moments filter length coding gain frequency selectivity and the shape of the wavelets on the coding performance is analyzed the wavelet transforms performance is assessed based on a first order markov source and on the image quality using subjective tests more than 20 wavelet transforms of a test image were coded with a product code lattice quantizer with the image quality rated by different viewers the results show that as long as the wavelet transforms perform reasonably well features like regularity and number of vanishing moments do not have any important impact on final image quality the influence of the coding gain by itself is also small on the other hand the shape of the synthesis wavelet which determines the visibility of coding errors on reconstructed images is very important analysis of the data obtained strongly suggests that the design of good wavelet transforms for low bit rate image coding should take into account chiefly the shape of the synthesis wavelet and to a lesser extent the coding

some nonasymptotic results on resampling in high dimension i confidence regions we study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure the random vector is supposed to be either gaussian or to have a symmetric and bounded distribution the dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non asymptotic control of the confidence level following ideas inspired by recent results in learning theory we consider two approaches the first based on a concentration principle valid for a large class of resampling weights and the second on a direct resampled quantile specifically using rademacher weights several intermediate results established in the approach based on concentration principles are of self interest we also discuss the question of accuracy when using monte carlo approximations of the resampled quantities we present an application of these results to the one sided and two sided multiple testing problem in which we derive several resampling based step down procedures providing a non asymptotic fwer control we compare our different procedures in a simulation study and we show that they can outperform bonferroni s or holm s procedures as soon as the observed vector has sufficiently correlated coordinates

the coding gain of multiplexed wavelet transforms evangelista 1994 1993 introduced the multiplexed wavelet transform mwt and pointed out its potential applications to the analysis synthesis processing and coding of pseudo periodic signals such as voiced speech and music coders based on the mwt have been shown to outperform the conventional subband coders when a reliable pitch parameter can be extracted from data in this paper we investigate the effects of uniform quantization of the mwt coefficients we compare the performance of the new coders with that of wt block dct and klt coders in terms of the coding gain achieved when optimal bit allocation schemes are adopted

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

how do bootstrap and permutation tests work resampling methods are frequently used in practice to adjust critical values of nonparametric tests in the present paper a comprehensive and unified approach for the conditional and unconditional analysis of linear resampling statistics is presented under fairly mild assumptions we prove tightness and an asymptotic series representation for their weak accumulation points from this series it becomes clear which part of the resampling statistic is responsible for asymptotic normality the results leads to a discussion of the asymptotic correctness of resampling methods as well as their applications in testing hypotheses they are conditionally correct iff a central limit theorem holds for the original test statistic we prove unconditional correctness iff the central limit theorem holds or when symmetric random variables are resampled by a scheme of asymptotically random signs special cases are the m n out of k n bootstrap the weighted bootstrap the wild bootstrap and all kinds of permutation statistics the program is carried out for convergent partial sums of rowwise independent infinitesimal triangular arrays in detail these results are used to compare power functions of conditional resampling tests and their unconditional counterparts the proof uses the method of random scores for permutation type statistics

signal adapted multiresolution transform for image coding the authors consider the problem of designing multiresolution transforms that are adapted to the given image signal in the sense that they maximize the coding gain at each resolution level a simple alternating optimization algorithm is derived for solving this problem in the framework of the lattice realization of para unitary quadrature mirror filters the resulting large coding scheme is discussed in some detail and its performance is compared with that of the discrete cosine transform jpeg technique and with that of some nonadapted multiresolution transforms

theory and design of m channel maximally decimated quadrature mirror filters with arbitrary m having the perfect reconstruction property based on the concept of losslessness in digital filter structures this paper derives a general class of maximally decimated m channel quadrature mirror filter banks that lead to perfect reconstruction the perfect reconstruction property guarantees that the reconstructed signal hat x n is a delayed version of the input signal x n i e hat x n x n n 0 it is shown that such a property can be satisfied if the alias component matrix ac matrix for short is unitary on the unit circle of the z plane the number of channels m is arbitrary and when m is two the results reduce to certain recently reported 2 channel perfect reconstruction qmf structures a procedure based on recently reported fir cascaded lattice structures is presented for optimal design of such fir m channel filter banks design examples are included

on the rate of convergence in the multivariate clt berry esseen theorems are proved in the multidimensional central limit theorem without using fourier methods an effective and simple estimate of the error in the clt for sums and convex sets using stein s method and induction is derived furthermore the error in the clt for multivariate functions of independent random elements is estimated extending results of van zwet and friedrich to the multivariate case

parametric estimation finite sample theory the paper aims at reconsidering the famous le cam lan theory the main features of the approach which make it different from the classical one are as follows 1 the study is nonasymptotic that is the sample size is fixed and does not tend to infinity 2 the parametric assumption is possibly misspecified and the underlying data distribution can lie beyond the given parametric family these two features enable to bridge the gap between parametric and nonparametric theory and to build a unified framework for statistical estimation the main results include large deviation bounds for the quasi maximum likelihood and the local quadratic bracketing of the log likelihood process the latter yields a number of important corollaries for statistical inference concentration confidence and risk bounds expansion of the maximum likelihood estimate etc all these corollaries are stated in a nonclassical way admitting a model misspecification and finite samples however the classical asymptotic results including the efficiency bounds can be easily derived as corollaries of the obtained nonasymptotic statements at the same time the new bracketing device works well in the situations with large or growing parameter dimension in which the classical parametric theory fails the general results are illustrated for the i i d setup as well as for generalized linear and median estimation the results apply for any dimension of the parameter space and provide a quantitative lower bound on the sample size yielding the root n accuracy

new quadrature mirror filter structures this paper introduces new quadrature mirror filter qmf structures for the frequency domain analysis and synthesis of digital signals the conventional qmf technique is first extended to cover complex quadrature mirror filters cqmf in which a digital signal is split into n adjacent complex subbands where the real and imaginary parts are subsampled by 1 2n with respect to the original signal the computational complexity of qmf banks is then analyzed and a new scheme which reduces the computational complexity by about a factor of two over conventional qmf implementations is proposed finally the filter design tradeoffs are discussed and the microprogramed implementation of qmf banks is evaluated

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

time varying lapped transforms and wavelet packets the perfect reconstruction conditions for a time varying lapped transform paraunitary filter bank are developed through the factorization of the transform matrix into sparse factors a general formulation is presented allowing one to switch between two paraunitary filter banks however the extended lapped transform elt is often used as an example furthermore an adaptive wavelet packet is developed employing a time varying tree association of elts in all cases perfect reconstruction is inherently assured

bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models abstract this paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear iv models under weak assumptions the method provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis the method is a non studentized version of the s test of stock and wright 2000 but is implemented and analyzed differently it does not require restrictive distributional assumptions linearity of the estimated model simultaneous equations or information about whether the instruments are strong or weak it can be applied to quantile iv models that may be nonlinear and can be used to test a parametric iv model against a nonparametric alternative it provides information about the relation between the degree of weakness of the instruments and the power of the test the bound presented here holds in finite samples regardless of the strength of the instruments

bootstrap confidence sets under model misspecification a multiplier bootstrap procedure for construction of likelihood based confidence sets is considered for finite samples and a possible model misspecification theoretical results justify the bootstrap consistency for a small or moderate sample size and allow to control the impact of the parameter dimension p the bootstrap approximation works if p n is small the main result about bootstrap consistency continues to apply even if the underlying parametric model is misspecified under the so called small modeling bias condition in the case when the true model deviates significantly from the considered parametric family the bootstrap procedure is still applicable but it becomes a bit conservative the size of the constructed confidence sets is increased by the modeling bias we illustrate the results with numerical examples for misspecified constant and logistic regressions jel classification codes c13 c15

on the statistics of fixed point roundoff error roundoff error after fixed point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal this paper presents a statistical analysis of fixed point roundoff error that identifies the conditions under which this model is valid and examines the statistical behavior of roundoff error when these conditions are not satisfied the results show that if the multiplier coefficient is expressed as a n m where m is a positive integral power of two and n is an odd integer then the errors generated by roundoff after multiplication can generally be modeled as uniformly distributed white and uncorrelated with the signal if the signal has sufficiently wide bandwidth and has a dynamic range that extends over approximately m quantum steps for narrow band low level signals the roundoff error statistics can differ significantly from the uniform white uncorrelated model in addition these results show that statistical behavior of roundoff error can differ significantly from that of the quantization error that is generated when a continuous random variable is quantized

on orthonormal wavelets and paraunitary filter banks the known result that a binary tree structured filter bank with the same paraunitary polyphase matrix on all levels generates an orthonormal basis is generalized to binary trees having different paraunitary matrices on each level a converse result that every orthonormal wavelet basis can be generated by a tree structured filter bank having paraunitary polyphase matrices is then proved the concept of orthonormal bases is extended to generalized nonbinary tree structures and it is seen that a close relationship exists between orthonormality and paraunitariness it is proved that a generalized tree structure with paraunitary polyphase matrices produces an orthonormal basis since not all phases can be generated by tree structured filter banks it is proved that if an orthonormal basis can be generated using a tree structure it can be generated specifically by a paraunitary tree

improved randomized results for the interval selection problem online interval selection is a problem in which intervals arrive one by one sorted by their left endpoints each interval has a length and a non negative weight associated with it the goal is to select a non overlapping set of intervals with maximal total weight and run them to completion the decision regarding a possible selection of an arriving interval must be done immediately upon its arrival the interval may be preempted later in favor of selecting an arriving overlapping interval in which case the weight of the preempted interval is lost we follow woeginger 1994 12 and study the same models the types of instances we consider are c benevolent instances where the weight of an interval is a monotonically increasing convex function of length and d benevolent instances where the weight of an interval is a monotonically decreasing function of length some of our results can be extended to the case of unit length intervals with arbitrary costs we significantly improve the previously known bounds on the performance of online randomized algorithms for the problem namely we introduce a new algorithm for the d benevolent case and for unit intervals which uses a parameter q and has a competitive ratio of at most q 2ln q q 1 2 this value is equal to approximately 2 4554 for q 3 513 being the solution of the equation x 1 2lnx we further design a lower bound of 1 ln2 1 693 on the competitive ratio of any randomized algorithm the lower bound is valid for any c benevolent instance some d benevolent functions and for unit intervals we further show a lower bound of 32 for a wider class of d benevolent instances this improves over previously known lower bounds we also design a barely random online algorithm for the d benevolent case and the case of unit intervals which uses a single random bit and has a competitive ratio of 3 22745

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

guarding against spurious discoveries in high dimensions many data mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable spurious discoveries can easily arise in high dimensional data analysis due to enormous possibilities of such selections how can we know statistically our discoveries better than those by chance in this paper we define a measure of goodness of spurious fit which shows how good a response variable can be fitted by an optimally selected subset of covariates under the null model and propose a simple and effective lamm algorithm to compute it it coincides with the maximum spurious correlation for linear models and can be regarded as a generalized maximum spurious correlation we derive the asymptotic distribution of such goodness of spurious fit for generalized linear models and l1 regression such an asymptotic distribution depends on the sample size ambient dimension the number of variables used in the fit and the covariance information it can be consistently estimated by multiplier bootstrapping and used as a benchmark to guard against spurious discoveries it can also be applied to model selection which considers only candidate models with goodness of fits better than those by spurious fits the theory and method are convincingly illustrated by simulated examples and an application to the binary outcomes from german neuroblastoma trials

recursive biorthogonal interpolating wavelets and signal adapted interpolating filter banks in this paper by combining the ideas of the recursive wavelets with second generation wavelets a family of recursive biorthogonal interpolating wavelets rbiws is developed the rbiws have simple shape parameter vectors on each level which allows a multichannel decomposition algorithm and provides a flexible structure for designing signal adapted interpolating filter banks in the single level case an efficient approach to design an optimum two channel biorthogonal interpolating filter bank is proposed which maximizes the coding gain under the traditional quantization noise assumption furthermore in the multilevel case using level wise optimization of the shape parameter vectors signal adapted tree structured recursive biorthogonal interpolating filter banks rbifbs are designed which are efficient in computation and can remarkedly improve the coding gain finally numerical results demonstrate the effectiveness of the proposed methods

structures for m channel perfect reconstruction fir qmf banks which yield linear phase analysis filters the authors develop structures for fir finite impulse response perfect reconstruction qmf quadrature mirror filter banks which cover a subclass of systems that yield linear phase analysis filters for arbitrary m the parameters of these structures can be optimized to design analysis filters with minimum stopband energy which at the same time have linear phase and satisfy the perfect reconstruction property if there are m subbands then depending on whether the coefficients h sub k n of each analysis filter are symmetric or antisymmetric several combinations of filter banks are possible some of these permit perfect reconstruction and some do not for a given m the authors develop a formula for the number of combinations for a subclass of linear phase perfect reconstruction structures as an example they elaborate on a perfect reconstruction linear phase lattice structure for three channels the lattice structure is such that regardless of the parameter values the qmf bank enjoys the perfect reconstruction property while at the same time the analysis filters have linear phase a design example is presented along with tables of impulse response coefficients

an integrated framework for adaptive subband image coding previous work on filter banks and related expansions has revealed an interesting insight different filter bank trees can be regarded as different ways of constructing orthonormal bases for linear signal expansion in particular fast algorithms for finding best bases in an operational rate distortion r d sense have been successfully used in image coding independently of this work other research has also explored the design of filter banks that optimize energy compaction for a single signal or a class of signals in this paper we integrate these two different but complementary approaches to best basis design and propose a coding paradigm in which subband filters tree structure and quantizers are chosen to optimize the r d performance these coder attributes represent side information they are selected from a codebook designed off line from training data using r d as the design criterion this approach provides a rational framework in which to explore alternatives to empirical design of filter banks quantizers and other coding parameters the on line coding algorithm is a relatively simple extension of current r d optimal coding algorithms that operate with fixed filter banks and empirically designed quantizer codebooks in particular it is shown that selection of the best adapted filter bank from the codebook is computationally elementary

one and two level filter bank convolvers in a recent paper it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results in this paper we further generalize the result we also derive the statistical coding gain for the generalized subband convolver as an application we derive a novel low sensitivity structure for fir filters from the convolution theorem we define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation this gain serves as a figure of merit for the low sensitivity structure several numerical examples are included to demonstrate the usefulness of these ideas by using the generalized polyphase representation we show that the subband convolvers linear periodically time varying systems and digital block filtering can be viewed in a unified manner furthermore the scheme called ifir filtering is shown to be a special case of the convolver

on the asymptotic performance of hierarchical transforms explicit formulas are derived for the coding gain of hierarchical transforms for a given number of stages and the asymptotic gain as this number goes to infinity the intuitive result that hierarchical transforms are not asymptotically optimal that is their coding gains do not approach the inverse of the spectral flatness measure as the number of stages goes to infinity is confirmed examples comparing the limits for hierarchical transforms and m band parallel systems filter banks for ar 1 signals are presented

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

digital filter bank design quadratic constrained formulation formulate the filter bank design problem as an quadratic constrained least squares minimization problem the solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters the formulations of the perfect reconstruction cosine modulated filter bank of the near perfect reconstruction pseudo qmf bank and of the two channel biorthogonal linear phase filter bank are derived using the proposed approach compared with other design methods the proposed technique yields pr filter banks with much higher stopband attenuation the proposed technique can also be extended to design multidimensional filter banks

partial spectrum reconstruction using digital filter banks the problem of reconstructing a part of the spectrum is reduced to designing the filter bank to satisfy a set of conditions for the case considered here these conditions cannot be satisfied simultaneously so perfect reconstruction is not possible the necessary and sufficient conditions on the filters so that the resulting filter bank cancels most alias components are found such filter banks are called partial alias cancellation filter banks the product of the polyphase transfer matrices of these filter banks must be a block pseudocirculant matrix an algorithm design procedure is discussed and examples are given to demonstrate the theory

quadrature mirror filter design in the time domain a new technique for designing quadrature mirror filters is described the formulation carried out in the time domain is shown to result in an optimization problem requiring minimization of a quartic multinomial an iterative solution is suggested which involves computation of the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps our experiments show that convergence to the optimum tap weights is stable and the accuracy of the final solution is limited only by the accuracy of the eigenvalue eigenvector routine as in an earlier technique the user can specify the stop band frequency the relative weights of the passband ripple energy and the stopband residual energy and of course the number of filter taps

a new design algorithm for two band orthonormal rational filter banks and orthonormal rational wavelets we present a new algorithm for the design of orthonormal two band rational filter banks owing to the connection between iterated rational filter banks and rational wavelets this is also a design algorithm for orthonormal rational wavelets it is basically a simple iterative procedure which explains its exponential convergence and adaptability under various linear constraints e g regularity although the filters obtained from this algorithm are suboptimally designed they show excellent frequency selectivity after an in depth account of the algorithm we discuss the properties of the rational wavelets generated by some designed filters in particular we stress the possibility to design almost shift error free wavelets which allows the implementation of a rational wavelet transform

subband coder design incorporating recursive quadrature filters and optimum adpcm coders this paper presents the results of an analytical and experimental study of the use of iir quadrature mirror filters and forward adapting adpcm with optimum quantizers for octave band subband coders for speech it is shown that the underlying analysis synthesis systems can be designed such that there is no interband aliasing distortion in the coded speech and such that the analysis synthesis transfer function has no frequency distortion or no phase distortion but not both the experimental study showed that subband coders based on a mixture of infinite impulse response iir and finite duration impulse response fir filters resulted in higher quality coding systems using fewer multiplies than for systems based on fir filters alone it was also found that a signal to noise ratio snr gain of about 4 db could be obtained using optimum quantizers for forward adapting adpcm coders over linear quantizers in backward adapting apcm codes but no perceptual quality gain was observed

a new approach to the realization of low sensitivity iir digital filters a new implementation of an iir digital filter transfer function is presented that is structurally passive and hence has extremely low pass band sensitivity the structure is based on a simple parallel interconnection of two all pass sections with each section implemented in a structurally lossless manner the structure shares a number of properties in common with wave lattice digital filters computer simulation results verifying the low sensitivity feature are included along with results on roundoff noise dynamic range interaction a large number of alternatives is available for the implementation of the all pass sections giving rise to the well known wave lattice digital filters as a specific instance of the implementation

quadrature mirror filter design for an arbitrary number of equal bandwidth channels the two channel quadrature mirror filter structure of croisier and esteban may be extended to an arbitrary number of equal bandwidth channels given certain restrictions on the bandpass filters the most serious restriction is that the stopband attenuation of eacli band pass filter must be high for all frequencies outside twice the nominal 3 db bandwidth of the filter this restriction is not really a limiting factor for speech subband waveform coding since high adjacent channel attenuation is a necessity for the confinement of quantization noise a key feature of our filter structure is that the number of multiplies adds and stored coefficients required for implementation is significantly less than those needed for the conventional qmf structure given the same number of channels fortran code for a 16 channel filter structure is listed as an example of efficient implementation