concolor constrained non convex low rank model for image deblocking due to independent and coarse quantization of transform coefficients in each block block based transform coding usually introduces visually annoying blocking artifacts at low bitrates which greatly prevents further bit reduction to alleviate the conflict between bit reduction and quality preservation deblocking as a post processing strategy is an attractive and promising solution without changing existing codec in this paper in order to reduce blocking artifacts and obtain high quality image image deblocking is formulated as an optimization problem within maximum a posteriori framework and a novel algorithm for image deblocking using constrained non convex low rank model is proposed the l p 0 penalty function is extended on singular values of a matrix to characterize low rank prior model rather than the nuclear norm while the quantization constraint is explicitly transformed into the feasible solution space to constrain the non convex low rank optimization moreover a new quantization noise model is developed and an alternatively minimizing strategy with adaptive parameter adjustment is developed to solve the proposed optimization problem this parameter free advantage enables the whole algorithm more attractive and practical experiments demonstrate that the proposed image deblocking algorithm outperforms the current state of the art methods in both the objective quality and the perceptual quality

residual maximum likelihood reml estimation of a neighbour model for field experiments a spatial analysis of field experiments is proposed which takes account of association between neighbouring plots the residual maximum likelihood reml method of patterson and thompson 1971 biometrika 58 545 554 is used to estimate parameters of a general neighbour model which can be expressed as an autoregressive moving average arma model three data sets are analysed to i highlight the need for a model selection procedure ii illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design and iii illustrate the environmental variation within an experiment using prediction of trend

analysis of longitudinal data random coefficient regression modelling we review random coefficient regression rcr models and methods for fitting these models from an applications perspective methods for data with exponential family distributions are presented with the gaussian distribution as a special case attention is given to interpretation of fixed effects and the correlation structures implied by rcr models estimation methods are presented wtih computational approaches problems associated with testing fixed effects include accurate variance estimation and robustness to misspecification of the covariance structure methods for model selection and assessment are presented an example is used to demonstrate recommended approaches

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

an h likelihood method for spatial mixed linear models based on intrinsic auto regressions summary we consider sparse spatial mixed linear models particularly those described by besag and higdon and develop an h likelihood method for their statistical inference the method proposed allows for singular precision matrices as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model furthermore we generalize the h likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between gaussian intrinsic markov random fields on regular arrays and the de wijs process keeping various applications of spatial mixed linear models in mind we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix free statistical computations we provide two applications the first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation the second application concerns an analysis of a large cotton field which gives a focus to matrix free computations the paper closes with some further considerations such as applications to irregularly spaced data use of the parametric bootstrap and some generalizations to the gaussian matern mixed effect models

splitting np complete sets we show that a set is m autoreducible if and only if it is m mitotic this solves a long standing open question in a surprising way as a consequence of this unconditional result and recent work by glaser et al complete sets for all of the following complexity classes are m mitotic mathrm np mathrm conp oplus mathrm p mathrm pspace and mathrm nexp as well as all levels of mathrm ph mathrm modph and the boolean hierarchy over mathrm np in the cases of mathrm np mathrm pspace mathrm nexp and mathrm ph this at once answers several well studied open questions these results tell us that complete sets share a redundancy that was not known before in particular every mathrm np complete set a splits into two mathrm np complete sets a 1 and a 2 we disprove the equivalence between autoreducibility and mitoticity for all polynomial time bounded reducibilities between 3 tt reducibility and turing reducibility there exists a sparse set in mathrm exp that is polynomial time 3 tt autoreducible but not weakly polynomial time t mitotic in particular polynomial time t autoreducibility does not imply polynomial time weak t mitoticity which solves an open question by buhrman and torenvliet

efficient experimental designs when most treatments are unreplicated in early generation variety trials large numbers of new breeders lines varieties may be compared with each having little seed available a so called unreplicated trial has each new variety on just one plot at a site but includes several replicated control varieties making up around 10 and 20 of the trial the aim of the trial is to choose some usually around one third good performing new varieties to go on for further testing rather than precise estimation of their mean yields now that spatial analyses of data from field experiments are becoming more common there is interest in an efficient layout of an experiment given a proposed spatial analysis and an efficiency criterion common optimal design criteria values depend on the usual c matrix which is very large and hence it is time consuming to calculate its inverse since most varieties are unreplicated the variety incidence matrix has a simple form and some matrix manipulations can dramatically reduce the computation needed however there are many designs to compare and numerical optimisation lacks insight into good design features some possible design criteria are discussed and approximations to their values considered these allow the features of efficient layouts under spatial dependence to be given and compared c 2006 elsevier inc all rights reserved

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

diagnostics for a cumulative multinomial generalized linear model with applications to grouped toxicological mortality data abstract toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment in this article we develop and extend a number of diagnostic tools for the detection of mean misspecification or systematic departures of the mean link specification in cumulative multinomial generalized linear models fit to such data several real data sets are used to illustrate these diagnostics these tools help the analyst to differentiate between two sources of lack of fit in such models mean misspecification and extra multinomial variation or overdispersion

assessing local influence for specific restricted likelihood application to factor analysis in restricted statistical models since the first derivatives of the likelihood displacement are often nonzero the commonly adopted formulation for local influence analysis is not appropriate however there are two kinds of model restrictions in which the first derivatives of the likelihood displacement are still zero general formulas for assessing local influence under these restrictions are derived and applied to factor analysis as the usually used restriction in factor analysis satisfies the conditions various influence schemes are introduced and a comparison to the influence function approach is discussed it is also shown that local influence for factor analysis is invariant to the scale of the data and is independent of the rotation of the factor loadings

local influence in principal components analysis summary based on the definition of generalised influence function and generalised cook statistic local influence of small perturbations on the eigenvalues and eigenvectors of a covariance matrix are studied for population and sample versions the results based on the correlation matrix are also derived and some related topics are discussed finally an example is used for illustration bations although this method has been applied to many models beckman nachtsheim cook 1987 lawrance 1988 thomas cook 1990 assessing the local influence for multivariate data is still an unexplored area in this paper a method based on a generalised influence function and generalised cook statistic is introduced to assess the local influence of small perturbations on a statistic of interest and we prove that this method is equivalent to cook s work based on normal curvature in the likelihood framework since local influence on some statistics in multivariate analysis is not easy to study using the likelihood displacement of cook 1986 this method is expected to have wider applications in this paper we employ the generalised cook statistic to assess local influence in principal components analysis in 2 we introduce the definition of the generalised influ ence function and generalised cook statistic in 3 the perturbation theory of eigenvalues and eigenvectors of a real symmetric matrix is studied in 4 the local influence of small perturbations of observations on eigenvalues and the eigenvectors of sample covariance

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

recursive block coding a new approach to transform coding the concept of fast kl transform coding introduced earlier 7 8 for first order markov processes and certain random fields has been extended to higher order autoregressive ar sequences and practical images yielding what we call recursive block coding rbc algorithms in general the rate distortion performance for these algorithms is significantly superior to that of the conventional block kl transform algorithm moreover these algorithms permit the use of small size transforms thereby removing the need for fast transforms and making the hardware implementation of such coders more appealing this improved performance has been verified for practical image data and results in suppression of the block boundary effect commonly observed in traditional transform coding techniques this is illustrated by comparing rbc with cosine transform coding using both one and twodimensional algorithms examples of rbc encoded images at various rates are given

postprocessing of low bit rate block dct coded images based on a fields of experts prior transform coding using the discrete cosine transform dct has been widely used in image and video coding standards but at low bit rates the coded images suffer from severe visual distortions which prevent further bit reduction postprocessing can reduce these distortions and alleviate the conflict between bit rate reduction and quality preservation viewing postprocessing as an inverse problem we propose to solve it by the maximum a posteriori criterion the distortion caused by coding is modeled as additive spatially correlated gaussian noise while the original image is modeled as a high order markov random field based on the fields of experts framework experimental results show that the proposed method in most cases achieves higher psnr gain than other methods and the processed images possess good visual quality in addition we examine the noise model used and its parameter setting the noise model assumes that the dct coefficients and their quantization errors are independent this assumption is no longer valid when the coefficients are truncated we explain how this problem can be rectified using the current parameter setting

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

a note on the relationship between parameter collinearity and local influence in this note we demonstrate the close relationship between the concepts of parameter collinearity and local influence an important consequence of this relationship is that it suggests a modification of cook s 1986 measure for the local influence of model perturbations which is invariant over reparameterizations of the perturbation scheme this removes a serious theoretical and practical shortcoming of cook s measure of local influence

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

the analysis of multistratum and spatially correlated repeated measures data summary in repeated measures experiments on animals the animals are often housed in pens and as well as the correlation between measurements over time the induced correlation due to the pen effect must be taken into account current research in the analysis of field experiments is focused on the use of spatial methods if in addition we have repeated measurements over time we need to take into account both the temporal and spatial dependence an approach is presented for the analysis of repeated measures data when an additional level of dependence exists we consider both the complete and incomplete data situations and discuss estimation based on residual maximum likelihood the procedures are illustrated using data from two experiments

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

statistical quality control of variety trial data summary i propose detection criteria for identifying an abnormal or erroneous data vector provided by a single variety trial in a longer series of variety trials the test criteria are based on the linear effects estimated separately for each studied trial using global variance components estimated from the whole series of variety trials the criteria comprise three mutually independent test statistics the first one is a quadratic form in the estimated fixed effects the second one is a quadratic form in the estimated realized linear random effects not including the residual effects and the third one is a quadratic form in the estimated realized residual effects under the null hypothesis defining a valid data vector the three quadratics have independent x2 distributions under natural alternative hypotheses they have noncentral x2 distributions decomposing the total variation of the data vector studied into quadratic forms due to different types of the realized linear effects intuitively justifies the resulting test criteria the decomposition may also be used to show that the resulting tests are likelihood ratio tests i further present computational procedures that allow us to dispense with the need for prior estimation of the linear effects

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

on local influence analysis of full information item factor models the full information item factor fiif model is very useful for analyzing relations of dichotomous variables in this article we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the fiif model the development is based on a q displacement function which is closely related with the monte carlo em algorithm in the ml estimation in the e step of this algorithm the conditional expectations are approximated by sample means of observations simulated by the gibbs sampler from the appropriate conditional distributions it turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures the diagnoses are based on the conformal normal curvature that can be computed easily a number of interesting perturbation schemes are considered the methodology is illustrated with two real examples

average information reml an efficient algorithm for variance parameter estimation in linear mixed models a strategy of using an average information matrix is shown to be computationally convenient and efficient for estimating variance components by restricted maximum likelihood reml in the mixed linear model three applications are described the motivation for the algorithm was the estimation of variance components in the analysis of wheat variety means from 1 071 experiments representing 10 years and 60 locations in new south wales we also apply the algorithm to the analysis of designed experiments by incomplete block analysis and spatial analysis of field experiments

weak mitoticity of bounded disjunctive and conjunctive truth table autoreducible sets abstract glaser et al siamjcomp 2008 and tcs 2009 2 proved existence of two sparse sets a and b in exp where a is 3 tt truth table polynomial time autoreducible but not weakly polynomial time turing mitotic and b is polynomial time 2 tt autoreducible but not weakly polynomial time 2 tt mitotic we unify and strengthen both of those results by showing that there is a sparse set in exp that is polynomial time 2 tt autoreducible but not even weakly polynomial time turing mitotic all these results indicate that polynomial time autoreducibilities in general do not imply polynomial time mitoticity at all with the only exceptions of the many one and 1 tt reductions on the other hand however we proved that every autoreducible set for the polynomial time bounded disjunctive or conjunctive tt reductions is weakly mitotic for the polynomial time tt reduction that makes logarithmically many queries only this shows that autoreducible sets for reductions making more than one query could still be mitotic in some way if they possess certain special properties

separating complexity classes using autoreducibility a set is autoreducible if it can be reduced to itself by a turing machine that does not ask its own input to the oracle we use autoreducibility to separate the polynomial time hierarchy from exponential space by showing that all turing complete sets for certain levels of the exponential time hierarchy are autoreducible but there exists some turing complete set for doubly exponential space that is not although we already knew how to separate these classes using diagonalization our proofs separate classes solely by showing they have different structural properties thus applying post s program to complexity theory we feel such techniques may prove unknown separations in the future in particular if we could settle the question as to whether all turing complete sets for doubly exponential time are autoreducible we would separate either polynomial time from polynomial space and nondeterministic logarithmic space from nondeterministic polynomial time or else the polynomial time hierarchy from exponential time we also look at the autoreducibility of complete sets under nonadaptive bounded query probabilistic and nonuniform reductions we show how settling some of these autoreducibility questions will also lead to new complexity class separations

local influence for incomplete data models this paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data the idea is to utilize cook s approach to the conditional expectation of the complete data log likelihood function in the em algorithm it is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods an application to the generalized linear mixed model is investigated some illustrative artificial and real examples are presented

case deletion diagnostics for linear mixed models based on the q function the conditional expectation of the logarithm of the joint likelihood between responses and random effects we propose a case deletion approach to identify influential subjects and influential observations in linear mixed models the models considered here are very broad in the sense that any covariance structures can be specified in the covariance matrices of the random effects and random errors analytically explicit forms of diagnostic measures for the fixed effects and variance components are provided comparisons with existing methods including likelihood based case deletion and local influence methods are made numerical results including real data analysis and simulation studies are presented for both illustration and comparison this article has supplementary material online

projection based spatially adaptive reconstruction of block transform compressed images at the present time block transform coding is probably the most popular approach for image compression for this approach the compressed images are decoded using only the transmitted transform data we formulate image decoding as an image recovery problem according to this approach the decoded image is reconstructed using not only the transmitted data but in addition the prior knowledge that images before compression do not display between block discontinuities a spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets apart from the data constraint set this algorithm uses another new constraint set that enforces between block smoothness the novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics a simplified spatially adaptive recovery algorithm is also proposed and the analysis of its computational complexity is presented numerical experiments are shown that demonstrate that the proposed algorithms work better than both the jpeg deblocking recommendation and our previous projection based image decoding approach

influence analysis of structural equation models with polytomous variables the estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures however sensitivity or influence analysis of the model is not well studied we demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables and we develop appropriate procedures based on the local influence approach of cook 1986 the proposed procedures are computationally efficient the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model we consider the influence of an individual cell frequency with respect to three cases when all parameters in an unstructured model are of interest when the unstructured polychoric correlations are of interest and when the structural parameters are of interest we also consider the sensitivity of the parameters estimates two examples based on real data are presented for illustration

assessing influence in regression analysis with censored data in this paper we show how to evaluate the effect that perturbations to the model data or case weights have on maximum likelihood estimates from censored survival data the ideas and methods also apply to other nonlinear estimation problems we review the ideas behind using log likelihood displacement and local influence methods we describe new interpretations for some local influence statistics and show how these statistics extend and complement traditional case deletion influence statistics for linear least squares these statistics identify individual and combinations of cases that have important influence on estimates of parameters and functions of these parameters we illustrate the methods by reanalyzing the stanford heart transplant data with a parametric regression model

a random field approach to the analysis of field plot experiments and other spatial experiments several nearest neighbor methods for the analysis of data from spatial experiments e g agricultural field experiments have recently been proposed these methods attempt to account for the effect of spatial heterogeneity on the estimation of treatment contrasts typically this is accomplished indirectly by differencing or by using residuals from neighboring plots to construct covariates we examine an alternative approach in which the spatial heterogeneity is modeled directly the model underlying our approach is similar to the model underlying a geostatistical kriging analysis and as in the latter model the observations are regarded collectively as a partial realization of a random field a randomization study of uniformity trial data suggests that the random field approach often provides more accurate estimates of treatment contrasts than nearest neighbor approaches in addition the random field approach is devoid of ambiguities as to the handling of border plots and is generally more flexible than nearest neighbor approaches

influence on confidence regions for regression coefficients in generalized linear models abstract influence on confidence regions has received less attention than the problem of influence on regression coefficients in generalized linear models diagnostics are given for examining influence on confidence intervals or the confidence region for all of the regression coefficients these diagnostics permit one to check whether the standard errors of the coefficients are sensitive to the exact specification of case weights or the observed values of the explanatory variables or the response the diagnostics are illustrated with an example and compared to standard diagnostic methods

principal components regression and r k class predictions in linear mixed models abstract in this article we propose the principal components regression and r k class predictors which combine the techniques of the ridge and principal components regressions in the linear mixed models we demonstrate that the henderson s predictors the ridge predictors and the principal components regression predictors are special cases of the r k class predictors we also research assumption that the variance parameters are not known and get estimators of variance parameters the necessary and sufficient conditions for the superiorities of the r k class predictors over each of these three predictors are obtained by the criterion of mean square error matrix furthermore we suggest tests to approve if these conditions are indeed satisfied finally real data analysis and a simulation study are used to illustrate the findings

conformal normal curvature and assessment of local influence in 1986 r d cook proposed differential geometry to assess local influence of minor perturbations of statistical models we construct a conformally invariant curvature the conformal normal curvature for the same purpose this curvature provides a measure of local influence ranging from 0 to 1 with objective bench marks to judge largeness we study various approaches to using the conformal normal curvature and the relationships between these approaches

non mitotic sets we study the question of the existence of non mitotic sets in np we show under various hypotheses that 1 tt mitoticity and m mitoticity differ on np t autoreducibility and t mitoticity differ on np this contrasts the situation in the recursion theoretic setting where ladner showed that autoreducibility and mitoticity coincide 2 tt autoreducibility does not imply weak 2 tt mitoticity from this it follows that autoreducibility and mitoticity are not equivalent for all reducibilities between 2 tt and t although the notions coincide for m and 1 tt reducibility

reductions on np and p selective sets abstract p selective sets are used to distinguish polynomial time bounded reducibilities on np in particular we consider different kinds of positive reductions these preserve membership in np and are not a priori closed under complements we show that the class of all sets which are both p selective and have positive reductions to their complements is p this is used to show that if dext next then there exists a set in np p that is not positive reducible to its complement various similar results are obtained we also show that p is the class of all sets which are both p selective and positive truth table self reducible from this result it follows that various naturally defined apparently intractible problems are not p selective unless p np

residual diagnostics for growth mixture models examining the impact of a preventive intervention on multiple trajectories of aggressive behavior growth mixture modeling has become a prominent tool for studying the heterogeneity of developmental trajectories within a population in this article we develop graphical diagnostics to detect misspecification in growth mixture models regarding the number of growth classes growth trajectory means and covariance structures for each model misspecification we propose a different type of empirical bayes residual to quantify the departure our procedure begins by imputing multiple independent sets of growth classes for the sample then from these so called pseudoclass draws we form diagnostic plots to examine the averaged empirical distributions of residuals in each such class our proposals draw on the property that each single set of pseudoclass adjusted residuals is asymptotically normal with known mean and co variance when the underlying model is correct these methods are justified in simulation studies involving two classes of linear growth curves that also differ by their covariance structures

splittings robustness and structure of complete sets we investigate the structure of exp complete and hard sets under various kinds of reductions in particular we are interested in the way in which information that makes the set complete is stored in the set we study for various types of reductions the question of whether the set difference a s for a hard set a and a sparse set s is still hard we also address the question of which complete sets a can be split into sets a1 and a2 such that a equiv p r a 1 equiv p r a 2 for reduction type r i e which complete sets are mitotic we obtain both positive and negative answers to these questions depending on the reduction type and the structure of the sparse set

influence diagnostics and outlier tests for semiparametric mixed models summary semiparametric mixed models are useful in biometric and econometric applications especially for longitudinal data maximum penalized likelihood estimators mples have been shown to work well by zhang and co workers for both linear coefficients and nonparametric functions this paper considers the role of influence diagnostics in the mple by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component we focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the mple algorithm we also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers the influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

a connection between local influence analysis and residual diagnostics local influence analysis of perturbations of the response vector is shown to be the same as the usual regression diagnostics in the fixed effects model this result provides a further justification for local influence analysis

on testing trained vector quantizer codebooks this paper discusses a criterion for testing a vector quantizer vq codebook that is obtained by training when a vq codebook is designed by a clustering algorithm using a training set time average distortion which is called the training set distortion tsd is usually calculated in each iteration of the algorithm since the input probability function is unknown in general and cumbersome to deal with the algorithm stops when the tsd ceases to significantly decrease in order to test the resultant codebook validating set distortion vsd is calculated on a separate validating set vs codebooks that yield small difference between the tsd and the vsd are regarded as good ones however the difference vsd tsd is not necessarily a desirable criterion for testing a trained codebook unless certain conditions are satisfied a condition that is previously assumed to be important is that the vs has to be quite large to well approximate the source distribution this condition implies greater computational burden of testing a codebook in this paper we first discuss the condition under which the difference vsd tsd is a meaningful codebook testing criterion then convergence properties of the vsd a time average quantity are investigated finally we show that for large codebooks a vs size as small as the size of the codebook is sufficient to evaluate the vsd this paper consequently presents a simple method to test trained codebooks for vq s experimental results on synthetic data and real images supporting the analysis are also provided and discussed

local influence of predictors in multiple linear regression local influence diagnostics can be used to assess the influence of predictor values in multiple linear regression for n observations and k regressors an eigenanalysis of an nk nk matrix is required to assess the influence on the estimated coefficients we provide the analytic expressions for the eigenvectors and show that they are easily computed describe influence on the parameter estimates of a principal components regression and are related to leverage outliers and added variables plots the results indicate that multicollinearity and overfitting contribute to a fitted model s sensitivity leading to strategies for model assessment and selection

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

parameter estimation and inference in the linear mixed model the paper reviews the linear mixed model with a focus on parameter estimation and inference parameter estimation for the different components of the model are reviewed with an emphasis on variance parameter estimation inferential procedures for the fixed effects random effects or a combination of both fixed and random effects are also discussed

nonlinear space variant postprocessing of block coded images an important application of spatial filtering techniques is in the postprocessing of images degraded by coding linear space invariant filters are inadequate to reduce the noise produced by block coders the noise in block coded images is correlated with the local characteristics of the signal and such filters are unable to exploit this correlation to reduce the noise we propose a new nonlinear space variant filtering algorithm which smooths jagged edges without blurring them and smooths out abrupt intensity changes in monotone areas edge sharpness is preserved because near edges the filtering of the signal is negligible consequently in band noise is not reduced but the well known masking effect reduces the visibility of this in band noise the algorithm is only slightly more complex to implement than simple linear filtering we present examples of processed images and snr figures to demonstrate that a significant improvement in subjective and objective quality is achieved

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

robust estimation of variance components outliers may occur with respect to any of the random components in the mixed linear model a procedure for limiting the influence of these outliers on the estimates of the model parameters is described given the variances or estimates of them the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects as appropriate and winsorized the robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of huber s proposal 2 a numerical example illustrates the use of the methodology both as a diagnostic and as an estimation tool

bayesian and frequentist predictive inference for the patterns of care studies abstract the patterns of care studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy in this article we propose and evaluate models which if acceptable permit bayesian and frequentist model based predictive inference for the desired finite population parameters using both hierarchical bayesian and frequentist mixed linear models we describe methodology for making the desired inferences emphasizing the use of transformed random variables finally we compare the frequentist bayes and empirical bayes approaches using data from one of the surveys all three methods produce essentially the same value for the finite population mean the standard empirical bayes and frequentist measures of variability are very much smaller than those derived from the bayesian approach the latter reflecting uncertainty about the values of the scale parameters in the model

assessing influence on predictions from generalized linear models influence diagnostics for predictions from a normal linear model examine the effect of deleting a single case on either the point prediction or the predictive density function instead of deleting cases we apply the local influence method of cook 1986 to assess the effect of small perturbations of continuous data on a specified point prediction from a generalized linear model based on local perturbations of the vector of responses case weights explanatory variables or the components of one case the diagnostics can detect different kinds of influence some of the diagnostics are illustrated with an example and compared to standard diagnostic methods

analyzing genotype environment data by mixed models with multiplicative terms where yij mean yield of ith genotype in jth environment general mean gi effect of ith genotype ej effect of jth environment ge ij interaction of ith genotype and jth environment eij random error associated with means yij assumed to be distributed as n o ac2 this model is appropriate for the analysis of means from equally replicated data with homoscedastic errors in an analysis of g x e data it may be useful to fit a more specific model describing the interaction the most common of such models is the regression model first suggested by yates and cochran 1938 which was further elaborated by finlay and wilkinson 1963 and eberhart and russell 1966 it may be written as

spatial analysis of field experiments an extension to two dimensions the one dimensional spatial analysis procedure proposed by gleeson and cullis 1987 biometrics 43 277 288 is extended to two dimensions using the subclass of separable lattice processes to model the errors residual maximum likelihood estimation of the models is described and diagnostics for testing model adequacy are derived results from the analysis of 24 sets of uniformity data indicate the frequent need for a two dimensional analysis even when the plot shape is highly rectangular these results also indicate the potential gain from using a two dimensional spatial analysis rather than a row column analysis an example is presented of the analysis of a field experiment on tobacco

local influence on the ratio and horvitz thompson estimators through the second order approach abstract since cook introduced the notion of local influence in 1986 a great number of papers have appeared in statistics handling this topic in a wide variety of areas however until we know there is no paper focussed on local influence in survey sampling this paper assesses the local influence through the curvature of the perturbation formed surface of the ratio estimator in a simple random sampling without replacement and the horvitz thompson estimator in an inclusion proportional to size sampling design both estimators use auxiliary information x and can be obtained through a model assisted reasoning where the ratio model with variance proportional to x plays an important role two perturbation schemes are considered a model perturbation and an auxiliary variable perturbation we illustrate the effectiveness of the method in order to identify influential points with two real examples

local influence for generalized linear models with missing covariates in the analysis of missing data sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions in this article we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data we examine two types of perturbation schemes the single case and global perturbation schemes for perturbing various assumptions in this setting we show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation we also develop several local influence measures to identify influential points and test model misspecification simulation studies are conducted to evaluate our methods and real datasets are analyzed to illustrate the use of our local influence measures

a new approach to reduce the blocking effect of transform coding image coding a combined transform coding ctc scheme to reduce the blocking effect of conventional block transform coding and hence to improve the subjective performance is presented the scheme is described and its information theoretic properties are discussed computer simulation results for a chest x ray image are presented the ctc scheme the jpeg baseline scheme and the conventional discrete walsh hadamard transform dwht are compared to demonstrate the performance improvement for the ctc scheme the advantages of the ctc scheme include no ringing effect as there is no error propagation across the boundary no additional computation and distortion always held within a certain level

low rank decomposition based restoration of compressed images via adaptive noise estimation images coded at low bit rates in real world applications usually suffer from significant compression noise which significantly degrades the visual quality traditional denoising methods are not suitable for the content dependent compression noise which usually assume that noise is independent and with identical distribution in this paper we propose a unified framework of content adaptive estimation and reduction for compression noise via low rank decomposition of similar image patches we first formulate the framework of compression noise reduction based upon low rank decomposition compression noises are removed by soft thresholding the singular values in singular value decomposition of every group of similar image patches for each group of similar patches the thresholds are adaptively determined according to compression noise levels and singular values we analyze the relationship of image statistical characteristics in spatial and transform domains and estimate compression noise level for every group of similar patches from statistics in both domains jointly with quantization steps finally quantization constraint is applied to estimated images to avoid over smoothing extensive experimental results show that the proposed method not only improves the quality of compressed images obviously for post processing but are also helpful for computer vision tasks as a pre processing method

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

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

concealment of damaged block transform coded images using projections onto convex sets an algorithm for lost signal restoration in block based still image and video sequence coding is presented problems arising from imperfect transmission of block coded images result in lost blocks the resulting image is flawed by the absence of square pixel regions that are notably perceived by human vision even in real time video sequences error concealment is aimed at masking the effect of missing blocks by use of temporal or spatial interpolation to create a subjectively acceptable approximation to the true error free image this paper presents a spatial interpolation algorithm that addresses concealment of lost image blocks using only intra frame information it attempts to utilize spatially correlated edge information from a large local neighborhood of surrounding pixels to restore missing blocks the algorithm is a gerchberg 1974 type spatial domain spectral domain constraint satisfying iterative process and may be viewed as an alternating projections onto convex sets method

gilmour s approach to mixed and stochastic restricted ridge predictions in linear mixed models abstract this article is concerned with the predictions in linear mixed models under stochastic linear restrictions mixed and stochastic restricted ridge predictors are introduced by using gilmour s approach we also investigate assumptions that the variance parameters are not known under stochastic linear restrictions and attain estimators of variance parameters superiorities the linear combinations of the predictors are done in the sense of mean square error matrix criterion finally a hypothetical data set is considered to illustrate the findings

genotype by environment variance heterogeneity in a two stage analysis the analysis of a series of crop variety trials often proceeds using a mixed model in which the data are the combined means from individual trials the residual variation for this model consists of genotype by environment g e interactions and within trial error variation the latter is regarded as known from the analyses of individual trials and any associated heterogeneity can be accounted for in the overall mixed model by the use of weights the g e interactions may also have nonconstant variance and since the variances themselves are often of interest we propose that heterogeneity arising from these sources be accommodated by modelling the g e variances as a log linear function of explanatory variables we present a residual maximum likelihood estimation method and develop a diagnostic technique for detecting dependence the approach is demonstrated using a large unbalanced set of crop variety testing data the methodology is easily generalized to residual variance modelling in any mixed model application

leverage in least squares additive plus multiplicative fits for two way tables abstract an additive plus multiplicative model can describe both main effects and row x column interactions in two way tables of data when each cell contains exactly one observation a least squares fit for this nonlinear model calculates the main effects using means of rows and columns and then fits a multiplicative term to the additive residuals using the singular value decomposition a natural extension of the hat matrix for a linear model yields a definition of leverage that provides insights about the impact of erroneous data values on the fit theoretical and numerical investigations reveal the complex nature of leverage for this nonlinear model

theory of projection onto the narrow quantization constraint set and its application since the postprocessing of coded images using a priori information depends on the constraints imposed on the coded images it is important to utilize constraints that are best suited to postprocessing techniques among the constraint sets the quantization constraint set qcs is commonly used in the iterative algorithms that are especially based on the theory of projections onto convex sets pocs the converged image in the iteration is usually a boundary point of the qcs but we can easily conjecture that the possible location of the original image is inside the qcs in order to obtain an image inside the qcs we proposed a new convex constraint set a subset of the qcs called narrow qcs nqcs as a substitute for the qcs in order to demonstrate that the nqcs works better than the qcs on natural images we present mathematical analysis with examples and simulations by reformulating the iterative algorithm of the constrained minimization problem or of the pocs using the probability theory since the initial image of the iteration is the centroid of the qcs we reach a conclusion that the first iteration is enough to recover the coded image which implies no need of any theories that guarantee the convergences