vector quantizers with direct sum codebooks the use of direct sum codebooks to minimize the memory requirements of vector quantizers is investigated assuming arbitrary fixed partitions necessary conditions for minimum distortion codebooks are derived first for scalar codebooks assuming mean squared error distortion and then for vector codebooks and a broader class of distortion measures an iterative procedure is described for designing locally optimal direct sum codebooks both optimal and computationally efficient suboptimal encoding schemes are considered it is shown that although an optimal encoding can be implemented by a sequential encoder the complexity of implementing optimal stagewise partitions generally exceeds the complexity of an exhaustive search of the direct sum codebook it is also shown that sequential nearest neighbor encoders can be extremely inefficient the m search method is explored as one method of improving the effectiveness of suboptimal sequential encoders representative results for simulated direct sum quantizers are presented

dynamic finite state vector quantization of digital images a vector quantization vq scheme with finite memory called dynamic finite state vector quantization dfsvq is presented the encoder consists of a large codebook so called super codebook where for each input vector a fixed number of its codevectors are chosen to generate a much smaller codebook sub codebook this sub codebook represents the best matching codevectors that could be found in the super codebook for encoding the current input vector the choice for the codevectors in the sub codebook is based on the information obtained from the previously encoded blocks where directional conditional block probability histogram matrices are used in the selection of the codevectors the index of the best matching codevector in the sub codebook is transmitted to the receiver an adaptive dfsvq scheme is also proposed in which when encoding an input vector first the sub codebook is searched for a matching codevector to satisfy a pre specified waveform distortion if such a codevector is not found in tile current sub codebook then the whole super codebook is checked for a better match if a better match is found then a signaling flag along with the corresponding index of the codevector is transmitted to the receiver both the dfsvq encoder and its adaptive version are implemented experimental results for several monochrome images with a super codebook size of 256 or 512 and different sub codebook sizes are presented

advances in residual vector quantization a review advances in residual vector quantization rvq are surveyed definitions of joint encoder optimality and joint decoder optimality are discussed design techniques for rvqs with large numbers of stages and generally different encoder and decoder codebooks are elaborated and extended fixed rate rvqs and variable rate rvqs that employ entropy coding are examined predictive and finite state rvqs designed and integrated into neural network based source coding structures are revisited successive approximation rvqs that achieve embedded and refinable coding are reviewed a new type of successive approximation rvq that varies the instantaneous block rate by using different numbers of stages on different blocks is introduced and applied to image waveforms and a scalar version of the new residual quantizer is applied to image subbands in an embedded wavelet transform coding system

editing and imputation for quantitative survey data abstract this article develops a three stage strategy for cleaning survey data with missing and outlying values a detection of outlying cases b detection of outlying values within outlying cases and c imputation of likely values for missing and or outlying and edited values methodological tools include distance measures graphical procedures and maximum likelihood and robust estimation for incomplete multivariate normal data data from the annual survey of manufactures asm are used to illustrate the method

bases for cohomology of local systems on hyperplane complements we study cohomology with coefficients in a rank one local system on the complement of an arrangement of hyperplanes a the cohomology plays an important role for the theory of generalized hy pergeometric functions we combine several known results to construct explicit bases of logarithmic forms for the only non vanishing cohomol ogy group under some nonresonance conditions on the local system for any arrangement a the bases are determined by a linear ordering of the hyperplanes and are indexed by certain no broken circuits bases of a the basic forms depend on the local system but any two bases con structed in this way are related by a matrix of integer constants which depend only on the linear orders and not on the local system in certain special cases we show the existence of bases of monomial logarithmic forms

multivariate student t regression models pitfalls and inference we consider likelihood based inference from multivariate regression models with independent student t errors some very intruiging pitfalls of both bayesian and classical methods on the basis of point observations are uncovered bayesian inference may be precluded as a consequence of the coarse nature of the data global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space a bayesian analysis on the basis of set observations is proposed and illustrated by several examples

a unified approach to robust estimation in finite population sampling we argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling we use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units under the model based approach to inference our proposed robust estimator is closely related to the well known estimator of chambers 1986 under the design based approach it possesses the desirable feature of being applicable with most sampling designs used in practice for stratified simple random sampling it is essentially equivalent to the estimator of kokic bell 1994 the proposed robust estimator depends on a tuning constant in this paper we propose a method for determining the tuning constant and show that the resulting estimator is consistent results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample

topological theory for selberg type integral associated with rigid fuchsian systems using the analytic realization of middle convolution due to dettweiler and reiter we show that any rigid fuchsian system can be obtained as a subsystem of some generating system which has an integral representation of solutions of selberg type twisted homology groups and twisted cohomology groups associated with such integrals are studied in particular contiguity relations and twisted cycles which realize local exponents are obtained

a fuzzy vector quantization approach to image compression the use of fuzzy clustering analysis in the early stages of a vector quantization process is able to make this process less sensitive to initialization this is justified by the fact that fuzzy clustering provides a framework for the quantitative formulation of the uncertainty typically involved in a training vector space this paper proposes a fuzzy clustering based vector quantization algorithm which employs an effective vector assignment strategy for the transition from fuzzy mode where each training vector is assigned to more than one clusters to crisp mode where each training vector is assigned to only one cluster this transition is controlled by analytical conditions that are obtained by minimizing a modified objective function for the fuzzy c means algorithm the application to image compression shows that the proposed approach is able to achieve a very efficient performance while maintaining the computational capabilities of other methods reported in the literature

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

predictive residual vector quantization image coding this paper presents a new vector quantization technique called predictive residual vector quantization prvq it combines the concepts of predictive vector quantization pvq and residual vector quantization rvq to implement a high performance vq scheme with low search complexity the proposed prvq consists of a vector predictor designed by a multilayer perceptron and an rvq that is designed by a multilayer competitive neural network a major task in our proposed prvq design is the joint optimization of the vector predictor and the rvq codebooks in order to achieve this a new design based on the neural network learning algorithm is introduced this technique is basically a nonlinear constrained optimization where each constituent component of the prvq scheme is optimized by minimizing an appropriate stage error function with a constraint on the overall error this technique makes use of a lagrangian formulation and iteratively solves a lagrangian error function to obtain a locally optimal solution this approach is then compared to a jointly designed and a closed loop design approach in the jointly designed approach the predictor and quantizers are jointly optimized by minimizing only the overall error in the closed loop design however a predictor is first implemented then the stage quantizers are optimized for this predictor in a stage by stage fashion simulation results show that the proposed prvq scheme outperforms the equivalent rvq operating at the same bit rate and the unconstrained vq by 2 and 1 7 db respectively furthermore the proposed prvq outperforms the pvq in the rate distortion sense with significantly lower codebook search complexity

outlier robust finite population estimation abstract outliers in sample data are a perennial problem for applied survey statisticians moreover it is a problem for which traditional sample survey theory offers no real solution beyond the sensible advice that such sample elements should not be weighted to their fullest extent in estimation sample outliers can be identified as of two basic types here we are concerned with the first type which may conveniently be termed representative outliers these are sample elements with values that have been correctly recorded and that cannot be assumed to be unique that is there is no good reason to assume there are no more similar outliers in the nonsampled part of the target population the remaining sample outliers which by default are termed nonrepresentative are sample elements whose data values are incorrect or unique in some sense methods for dealing with these nonrepresentative outliers lie basically within the scope of survey editing and imputation theory and are therefore not considered in

vector predictive coding of speech at 16 kbits s vector quantization in its simplest form may be regarded as a generalization of pcm independent quantization of each sample of a waveform to what might be called vector pcm where a block of consecutive samples a vector is simultaneously quantized as one unit in theory a performance arbitrarily close to the ultimate rate distortion limit is achievable with waveform vector quantization if the dimension of the vector k is large enough the main obstacle in effectively using vector quantization is complexity a vector quantizer of dimension k operating at a rate of r bits sample requires a number of computations on the order of k2 kr and a memory of the same order however a low dimensional vector quantizer dimensions 4 8 achieves a remarkable improvement over scalar quantization pcm consequently using the vector quantizer as a building block and imbedding it with other waveform data compression techniques may lead to the development of a new and powerful class of waveform coding systems this paper proposes and analyzes a waveform coding system adaptive vector predictive coding avpc in which a low dimensionality vector quantizer is used in an adaptive predictive coding scheme in the encoding process a locally generated prediction of the current input vector is subtracted from the current vector and the resulting error vector is coded by a vector quantizer each frame consisting of many vectors is classified into one of m statistical types this classification determines which one of m fixed predictors and of m vector quantizers will be used for encoding the current frame

bias calibrated estimation from sample surveys containing outliers we discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers we clarify the motivation for chambers s bias calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters we then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of chambers s estimator we also propose methodology based on the use of robust estimates and a bias calibrated form of the chambers and dunstan estimator of the population distribution function this proposal leads to a bias calibrated estimator of the population total which is an alternative to that of chambers we present a small simulation study to illustrate the utility of these estimators

bayesian robust multivariate linear regression with incomplete data abstract the multivariate t distribution and other normal independent multivariate distributions such as the multivariate slash distribution and the multivariate contaminated distribution are used for robust regression with complete or incomplete data most previous work focused on the method of maximum likelihood estimation for linear regression using normal independent distributions this article considers bayesian estimation of multivariate linear regression models using normal independent distributions with fully observed predictor variables and possible missing values from outcome variables a monotone data augmentation algorithm for posterior simulation of the parameters and missing data imputation is presented the posterior distributions of functions of the parameters can be obtained using monte carlo methods the monotone data augmentation algorithm can also be used for creating multiple imputations for incomplete data sets an illustrative example of using the multivariate t is also included

enhanced multistage vector quantization by joint codebook design multistage vector quantization msvq can achieve very low encoding and storage complexity in comparison to unstructured vector quantization however the conventional stage by stage design of the codebooks in msvq is suboptimal with respect to the overall performance measure the authors introduce an algorithm for the joint design of the stage codebooks to optimize the overall performance the performance improvement although modest is achieved with no effect on encoding or storage complexity and only a slight increase in design effort

gradient algorithms for designing predictive vector quantizers a predictive vector quantizer pvq is a vector extension of a predictive quantizer it consists of two parts a conventional memoryless vector quantizer vq and a vector predictor two gradient algorithms for designing a pvq are developed in this paper the steepest descent sd algorithm and the stochastic gradient sg algorithm both have the property of improving the quantizer and the predictor in the sense of minimizing the distortion as measured by the average mean squared error the differences between the two design approaches are the period and the step size used in each iteration to update the codebook and predictor the sg algorithm updates once for each input training vector and uses a small step size while the sd updates only once for a long period possibly one pass over the entire training sequence and uses a relatively large step size code designs and tests are simulated for both gauss markov sources and for sampled speech waveforms and the results are compared to codes designed using techniques that attempt to optimize only the quantizer for the predictor and not vice versa

downweighting influential clusters in surveys certain clusters may be extremely influential on survey estimates and consequently contribute disproportionately to their variance we propose a general approach to estimation that downweights highly influential clusters with the amount of downweighting based on m estimation applied to the empirical influence of the clusters the method is motivated by a problem in census coverage estimation and we illustrate it by using data from the 1990 post enumeration survey pes in this context an objective prespecified methodology for handling influential observations is essential to avoid having to justify judgmental post hoc adjustment of weights in 1990 both extreme weights and large errors in the census led to extreme influence we estimated influence by taylor linearization of the survey estimator and we applied m estimators based on the t distribution and the huber function as predicted by theory the robust procedures greatly reduced the estimated variance of estimated coverage rates more so tha

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

predictive vector quantization of images the purpose of this paper is to present new image coding schemes based on a predictive vector quantization pvq approach the predictive part of the encoder is used to partially remove redundancy and the vq part further removes the residual redundancy and selects good quantization levels for the global waveform two implementations of this coding approach have been devised namely sliding block pvq and block tree pvq simulations on real images show significant improvement over the conventional dpcm and tree codes using these new techniques the strong robustness property of these coding schemes is also experimentally demonstrated

influence functions and robust bayes and empirical bayes small area estimation we introduce new robust small area estimation procedures based on area level models we first find influence functions corresponding to each individual area level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation next based on these influence functions properly standardized we propose some new robust bayes and empirical bayes small area estimators the mean squared errors and estimated mean squared errors of these estimators are also found a small simulation study compares the performance of the robust and the regular empirical bayes estimators when the model variance is larger than the sample variance the proposed robust empirical bayes estimators are superior

outlier resistant alternatives to the ratio estimator abstract many techniques have been suggested to lower the impact of outliers on sample survey estimates outliers can be downweighted by winsorization that is by replacing extreme data points by a data dependent or a predetermined value before calculating estimates another approach is to reduce the weight of outliers from the inverse sampling fraction to 1 in the estimation of population characteristics in this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered a resistant version of the ratio estimator is introduced it is constructed with a m or a gm estimator of the slope of the regression model through the origin which is implicitly called on when considering the ratio estimator the asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan the selection of a resistant estimator is seen to involve a trade off betwee

ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data summary the general location model olkin tate 1961 krzanowski 1980 1982 little schluchter 1985 has categorical variables marginally distributed as a multinomial and continuous variables conditionally normally distributed with different means across cells defined by the categorical variables but a common covariance matrix across cells two extensions of the general location model are obtained the first replaces the common covariance matrix with different but proportional covariance matrices where the proportionality constants are to be estimated the second replaces the multivariate normal distributions of the first extension with multivariate t distributions where the degrees of freedom can also vary across cells and are to be estimated the t distribution is just one example of more general ellipsoidally symmetric distributions that can be used in place of the normal these extensions can provide more accurate fits to real data and can be viewed as tools for robust inference moreover the models can be very useful for multiple imputation of ignorable missing values maximum likelihood estimation using the aecm algorithm meng van dyk 1997 is presented as is a monotone data gibbs sampling scheme for drawing parameters and missing values from their posterior distributions to illustrate the techniques a numerical example is presented

some estimators of a population total from simple random samples containing large units abstract the problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations the effect of these large units in the sample is to distort the estimate of the population total it is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units in this paper three estimators that alter the usual sampling weights have been considered the efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators a numerical study of these estimators is also discussed

influence analysis for linear mixed effects models in this paper we extend several regression diagnostic techniques commonly used in linear regression such as leverage infinitesimal influence case deletion diagnostics cook s distance and local influence to the linear mixed effects model in each case the proposed new measure has a direct interpretation in terms of the effects on a parameter of interest and collapses to the familiar linear regression measure when there are no random effects the new measures are explicitly defined functions and do not necessitate re estimation of the model especially for cluster deletion diagnostics the basis for both the cluster deletion diagnostics and cook s distance is a generalization of miller s simple update formula for case deletion for linear models pregibon s infinitesimal case deletion diagnostics is adapted to the linear mixed effects model a simple compact matrix formula is derived to assess the local influence of the fixed effects regression coefficients finally a link between the local influence approach and cook s distance is established these influence measures are applied to an analysis of 5 year medicare reimbursements to colon cancer patients to identify the most influential observations and their effects on the fixed effects coefficients

adaptive entropy coded predictive vector quantization of images the authors consider 2 d predictive vector quantization pvq of images subject to an entropy constraint and demonstrate the substantial performance improvements over existing unconstrained approaches they describe a simple adaptive buffer instrumented implementation of this 2 d entropy coded pvq scheme which can accommodate the associated variable length entropy coding while completely eliminating buffer overflow underflow problems at the expense of only a slight degradation in performance this scheme called 2 d pvq aecq adaptive entropy coded quantization is shown to result in excellent rate distortion performance and impressive quality reconstructions of real world images indeed the real world coding results shown demonstrate little distortion at rates as low as 0 5 b pixel