conformal deformation of a riemannian metric to a scalar flat metric with constant mean curvature on the boundary one of the most celebrated theorems in mathematics is the riemann mapping theorem it says that an open simply connected proper subset of the plane is conformally diffeomorphic to the disk in higher dimensions very few regions are conformally diffeomorphic to the ball however we can still ask whether a domain is conformally diffeomorphic to a manifold that resembles the ball in two ways namely it has zero scalar curvature and its boundary has constant mean curvature in this paper we generalize the riemann mapping theorem to higher dimensions in that sense

a new linear adaptive controller design analysis and performance the certainty equivalence and polynomial approach widely used for designing adaptive controllers leads to simple adaptive control designs that guarantee stability asymptotic error convergence and robustness but not necessarily good transient performance backstepping and tuning functions techniques on the other hand are used to design adaptive controllers that guarantee stability and good transient performance at the expense of a highly nonlinear controller in this paper we use elements from both design approaches to develop a new certainty equivalence based adaptive controller by combining backstepping based control law with a normalized adaptive law the new adaptive controller guarantees stability and performance as well as parametric robustness for the nonadaptive controller that are comparable with the tuning functions scheme without the use of higher order nonlinearities

robust fitting of the binomial model we consider the problem of robust inference for the binomial m pi model the discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results for example the maximum likelihood estimator mle is quite robust it cannot be improved on for m 1 but can be for m 1 we discuss four other classes of estimators m estimators minimum disparity estimators optimal mgp estimators and a new class of estimators which we call e estimators we show that e estimators have a non standard asymptotic theory which challenges the accepted relationship between robustness concepts and thereby provided new perspectives on these concepts

robustness of nonlinear control systems with respect to unmodeled dynamics in theory it can be established that nonlinear control laws for linear or nonlinear plants can be used to meet strict performance requirements the success of these control designs in practical situations will very much depend on whether they can still meet the expected performance characteristics in the presence of inevitable modeling errors in this paper we develop necessary and sufficient conditions for a general class of nonlinear control laws in the presence of high frequency unmodeled dynamics under which global signal boundedness or asymptotic stability is guaranteed we show that a wide class of nonlinear control laws does not satisfy these conditions and therefore does not guarantee global stability in the presence of high frequency unmodeled dynamics

the affine polya szego principle equality cases and stability a brothers ziemer type theorem for the affine polya szego principle and a quantitative affine polya szego principle are established

affine poisson non poisson trace principles for h 1 α 12 rn 1 2 abstract this note discovers not only an affine non sharp poisson trace inequality but also its sharp non poisson version for a sobolev function with the fractional antiderivative

some new estimation methods for weighted regression where there are possible outliers the problem considered is the robust estimation of the variance parameter in a heteroscedastic linear model we treat the situation in which the variance is a function of the explanatory variables to estimate robustly the variance in this case it is necessary to guard against the influence of outliers in the design as well as outliers in the response by analogy with the homoscedastic regression case we propose two estimators that do this their performances are evaluated on a number of data sets we had considerable success with estimators that bound the self influence that is the influence an observation has on its own fitted value we conjecture that in other situations e g homoscedastic regression bounding the selfinfluence will lead to estimators with good robustness properties

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

a note on a albert and j a anderson s conditions for the existence of maximum likelihood estimates in logistic regression models summary this note expands the paper by albert anderson 1984 on the existence and uniqueness of maximum likelihood estimates in logistic regression models their three possible mutually exclusive data pattems i overlap ii complete separation and iii quasiseparation are considered the maximum likelihood estimate exists only in i modifications of the statement and proofs of albert anderson s results are given for ii and iii the identifiability for a more general model arising in the study of iii is discussed together with the maximization of the corresponding likelihood a linear program is presented which determines whether data is of type i ii or iii and in the case of iii identifies albert anderson s minimal set qm

assessing robustness of generalised estimating equations and quadratic inference functions in the presence of data contamination or outliers some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour this paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference we show that quadratic inference functions lead to bounded influence functions and the corresponding m estimator has a redescending property but the generalised estimating equation approach does not we also illustrate that unlike generalised estimating equations quadratic inference functions can still provide consistent estimators even if part of the data is contaminated we conclude that the quadratic inference function is a preferable method to the generalised estimating equation as far as robustness is concerned this conclusion is supported by simulations and real data examples

binary regression models for contaminated data on etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires on propose un modele simple qui permet qu un petit nombre de reponses binaires soit mal enregistre

median regression models for longitudinal data with dropouts summary recently median regression models have received increasing attention when continuous responses follow a distribution that is quite different from a normal distribution usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily in this article we discuss using median regression models to deal with longitudinal data with dropouts weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data where the weights are determined by modeling the dropout process consistency and the asymptotic distribution of the resultant estimators are established the proposed method is used to analyze a longitudinal data set arising from a controlled trial of hiv disease volberding et al 1990 the new england journal of medicine 322 941 949 simulation studies are conducted to assess the performance of the proposed method under various situations an extension to estimation of the association parameters is outlined

deletion diagnostics for generalised estimating equations summary deletion diagnostics are proposed for generalised estimating equations the diagnostics consider leverage and residuals to measure the influence of a subset of observations on the estimated regression parameters and on the estimated values of the linear predictor computational formulae are provided which correspond to the influence of a single observation and of an entire cluster of correlated observations additionally diagnostics are given which approximate the effect of deletion of an arbitrary subset of observations under a model with general covariance structure and arbitrary link function extending proposition 3 of christensen pearson johnson 1992 the proposed measures are applied to medical data

generalized additive models some applications abstract generalized additive models have the form x fj x j where might be the regression function in a multiple regression or the logistic transformation of the posterior probability pr y 1 x in a logistic regression in fact these models generalize the whole family of generalized linear models x x where x g x is some transformation of the regression function we use the local scoring algorithm to estimate the functions fj xj nonparametrically using a scatterplot smoother as a building block we demonstrate the models in two different analyses a nonparametric analysis of covariance and a logistic regression the procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis a variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions these include confidence curves degrees of freedom estimates and approximat

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

a generalized linear model for analysing receiver operating characteristic curves we present a continuation ratio model for analysing ordinal categorical data and we apply the model to the problem of estimating receiver operating characteristic roc curves we apply the methods to post prandial capillary blood glucose measurements as a criterion for a potential screening test for diabetes mellitus one can obtain point estimates of sensitivity and specificity and their associated standard errors at any value along the observed range of post prandial capillary blood glucose measurements also in comparison to the models for rocs described by tosteson and begg roc curves based on the continuation ratio model have the desired features that allow rocs to be concave but not necessarily symmetric

least median of weighted squares in logistic regression with large strata summary one aim of robust regression is to find estimators with high finite sample breakdown points although various robust estimators have been proposed in logistic regression models their breakdown points are not yet known here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point provided the estimator has to fulfill a weak condition in logistic regression models with large strata however a modification of rousseeuw s least median of squares estimator is shown to have a finite sample breakdown point of approximately 2

asymmetric affine lp sobolev inequalities abstract a new sharp affine l p sobolev inequality for functions on r n is established this inequality strengthens and implies the previously known affine l p sobolev inequality which in turn is stronger than the classical l p sobolev inequality

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

influence functions for iteratively defined statistics summary hampel s influence function and its finite sample counterparts are the basis for a number of diagnostic statistics these diagnostics can be expensive to compute in the natural way when the estimation calculations are iterative as they frequently are when maximum likelihood or robust methods are used we show how the influence function can be calculated in these situations by implicit differentiation of the fixed point equation satisfied by the limit of the iterative procesb we consider in particular the cases of newton s method and iteratively reweighted least squares where interesting analytic results are available as an application we consider the generalization of pregibon s 1981 logistic regression diagnostics to cover generalized linear models with noncanonical link functions such as probit regression

minimum distance estimation for the logistic regression model summary it is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations several robust alternatives have been proposed however if we consider the model from the case control viewpoint it is clear that current techniques can exhibit poor behaviour in many common situations a new robust class of estimation procedures is introduced the estimators are constructed via a minimum distance approach after identifying the model with a semiparametric biased sampling model the approach is developed under the case control sampling scheme yet is shown to be applicable under prospective sampling as well a weighted cramer von mises distance is used as an illustrative example of the methodology

infinitesimal robustness for diffusions we develop infinitesimally robust statistical procedures for the general diffusion processes we first prove the existence and uniqueness of the times series influence function of conditionally unbiased m estimators for ergodic and stationary diffusions under weak conditions on the martingale estimating function used we then characterize the robustness of m estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators to compute these estimators we propose a general algorithm which exploits approximation methods for diffusions in the computation of the robust estimating function monte carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real data application

consistency of deviance based m estimators summary in a general estimation problem the deviance function generates statistics that are similar to squared standardized residuals a deviance based m estimator dbme is defined as an adaptively weighted maximum likelihood estimator where the weights depend upon the deviances in both a single parameter and a regression setting we give some general conditions under which a dmbe is consistent for a suitable weighting scheme these conditions are satisfied in many continuous cramer rao regular families and in related linear or nonlinear regression cases the conditions fail and the estimator is inconsistent in most discrete families

weighted likelihood equations with bootstrap root search abstract we discuss a method of weighting likelihood equations with the aim of obtaining fully efficient and robust estimators we discuss the case of continuous probability models using unimodal weighting functions these weighting functions downweight observations that are inconsistent with the assumed model at the true model therefore the proposed estimating equations behave like the ordinary likelihood equations we investigate the number of solutions of the estimating equations via a bootstrap root search the estimators obtained are consistent and asymptotically normal and have desirable robustness properties an extensive simulation study and real data examples illustrate the operating characteristics of the proposed methodology

on the _ minkowski problem a volume normalized formulation of the lp minkowski problem is presented this formulation has the advantage that a solution is possible for all p 1 including the degenerate case where the index p is equal to the dimension of the ambient space a new approach to the lp minkowski problem is presented which solves the volume normalized formulation for even data and all p 1

residuals in generalized linear models abstract generalized linear models are regression type models for data not normally distributed appropriately fitted by maximum likelihood rather than least squares typical examples are models for binomial or poisson data with a linear regression model for a given ordinarily nonlinear function of the expected values of the observations use of such models has become very common in recent years and there is a clear need to study the issue of appropriate residuals to be used for diagnostic purposes several definitions of residuals are possible for generalized linear models the statistical package glim baker and nelder 1978 routinely prints out residuals where v is the function relating the variance to the mean of y and is the maximum likelihood estimate of the ith mean as fitted to the regression model these residuals are the signed square roots of the contributions to the pearson goodness of fit statistic another choice of residual is the signed square root of the contribution to the devia

a sharp trace inequality for functions of bounded variation in the ball the best constant in a mean value trace inequality for functions of bounded variation on admissible domains n is shown to agree with an isoperimetric constant associated with the existence and form of extremals is also discussed this result is exploited to compute the best constant in the relevant trace inequality when is a ball the existence and the form of extremals in this special case turn out to depend on the dimension n in particular the best constant is not achieved when is a disc in 2

robust inference for generalized linear models by starting from a natural class of robust estimators for generalized linear models based on the notion of quasi likelihood we define robust deviances that can be used for stepwise model selection as in the classical framework we derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination the binomial and poisson models are treated in detail two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures

asymmetric blaschke santalo functional inequalities abstract in this work we establish functional asymmetric versions of the celebrated blaschke santalo inequality as consequences of these inequalities we recover their geometric counter parts with equality cases as well as another inequality with strong probabilistic flavor that was firstly obtained by lutwak yang and zhang we present a brief study on an l p functional analogue to the center of mass that is necessary for our arguments and that might be of independent interest

on the use of nonparametric regression for model checking summary the use of nonparametric regression is explored to check the fit of a parametric regression model the principal aim is to check the validity of the regression curve rather than necessarily to detect outliers a pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model the types of data considered include discrete response variables where standard diagnostic techniques are often not appropriate and first order autoregressive series several numerical examples are given nonparametric regression can be used in an informal graphical way to assess the relationship between a response and an explanatory variable in this paper we aim to develop more formal methods of assessing the assumptions of a parametric model in particular when regression diagnostics of the type developed for normal linear models are not readily available the principal aim is to check the validity of the systematic part of the model by comparing a nonparametric estimate of the regression curve with a parametric one such a comparison may also identify outliers although the distinction between outliers and model inadequacy is not always easy two techniques are used to assess the fit of a parametric model in 2 confidence bands are constructed around the fitted regression curve by simulation a comparison of these with the nonparametric curve gives an indication of the nature of any departures from the model in 3 a pseudo likelihood ratio test is developed this provides a quantitative global assessment of fit in applying these ideas special emphasis is given to discrete data and notably logistic regression because of the difficulty in applying standard residual based model checking techniques to this type of response variable a poisson regression example is discussed in 4 however the underlying ideas have wider applications autoregressive time series of order 1 are discussed in 6 sections 5 and 7 discuss general issues we first discuss the context of binary regression with a single covariate and the difficulties caused by the discreteness of the response variable the observed data are assumed to be of the form xi yi ni where xi is a covariate value and yi has a binomial

robust logistic discrimination summary logistic discrimination is a well established method for allocating observations to one of two or more populations in this paper we show how the logistic model can be adapted to make it robust against outlying observations from the populations the new model is successfully tested using simulated data against ordinary logistic discrimination and also against logistic discrimination where parameters are fitted using resistant methods the model is then used on data collected from the teeth of rats logistic discrimination is a partially parametric method for discrimination applicable in many situations and under several sampling schemes notable references to the method are day kerridge 1967 anderson 1972 1979 1982 and anderson blair 1982 the appeal of the logistic method for discrimination is that only the ratio of likelihoods has to be modelled and not the full distributional form of the underlying variables press wilson 1978 and byth mclachlan 1980 show that in many circumstances logistic discrimination is preferable to the usual linear discrimination based on either normal populations with equal covariance matrices or fisher s linear discriminant for the two group case suppose x is a vector of observations h1 and h2 are the two groups and a a parameter vector then the log likelihood ratio is modelled as

robust inference with binary data in this paper robustness properties of the maximum likelihood estimator mle and several robust estimators for the logistic regression model when the responses are binary are analysed it is found that the mle and the classical rao s score test can be misleading in the presence of model misspecification which in the context of logistic regression means either misclassification s errors in the responses or extreme data points in the design space a general framework for robust estimation and testing is presented and a robust estimator as well as a robust testing procedure are presented it is shown that they are less influenced by model misspecifications than their classical counterparts they are finally applied to the analysis of binary data from a study on breastfeeding

the affine sobolev zhang inequality on bv rn abstract the affine sobolev zhang inequality is extended to b v r n the space of functions of bounded variation on r n and the equality cases are characterized as a consequence the petty projection inequality for sets of finite perimeter which implies the isoperimetric inequality for sets of finite perimeter is established

optimally bounded score functions for generalized linear models with applications to logistic regression summary we study optimally bounded score functions for estimating regression parameters in a generalized linear model our work extends results obtained by krasker welsch 1982 for the linear model and provides a simple proof of krasker welsch s first order condition for strong optimality the application of these results to logistic regression is studied in some detail with an example given comparing the bounded influence estimator with maximum likelihood where h q and c are known functions and 0 is a vector of regression parameters models of this type include logistic and probit regression poisson regression linear regression with known variance and certain models for lifetime data our motivation for seeking robust estimators is the same as that in the linear model maximum likelihood estimation is sometimes sensitive to outlying data for logistic regression pregibon 1981 1982 has documented the nonrobustness of the maximum likelihood estimator and expounded the benefits of diagnostics as well as robust or resistant fitting procedures see also johnson 1985 much of the work on robust estimation concerns finding estimators which sacrifice little efficiency at the assumed model while providing protection against outliers and model violations we follow this course finding bounded influence estimators minimizing certain functionals of the asymptotic covariance matrix related work includes that of hampel 1978 krasker 1980 and krasker welsch 1982 when fitting models to data two important issues are identification of outliers and influential cases and accommodation of these observations frequently when influential cases are present the fitted model is not representative of the bulk of the data to rectify this one can simply delete influential cases and refit via standard methods but this

on the bounded influence regression estimator of krasker and welsch abstract recently krasker and welsch 1982 considered a class of bounded influence regression estimators they showed that within this class the so called krasker welsch estimator is the only solution to a first order necessary condition for strong optimality that is for minimizing in the sense of positive definiteness the asymptotic covariance matrix however whether any strongly optimal estimator in fact exists remained an open question in this article an example is given where no strongly optimal estimator exists moreover the practical significance of the lack of a strongly optimal estimator is discussed

prospective analysis of logistic case control studies abstract in a classical case control study prentice and pyke proposed to ignore the study design and instead base estimation and inference on a random sampling i e prospective formulation we generalize this prospective formulation of case control studies to include multiplicative models stratification missing data measurement error robustness and other examples the resulting estimators which ignore the case control study aspect and instead are based on a random sampling formulation are typically consistent for nonintercept parameters and are asymptotically normally distributed we derive the resulting asymptotic covariance matrix of the parameter estimates the covariance matrix obtained by ignoring the case control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems a simple sufficient condition guaranteeing the latter is obtained

confidence bands for logistic regression with restricted predictor variables confidence bands are constructed for the logistic response function when there is an interval restriction on each of the predictor variables the construction involves application of a general fitting procedure using scheffe s s method described by casella and strawderman 1980 journal of the american statistical association 75 862 868 specific details are given for the case of one predictor variable along with details for a fixed width alternative to the s method bands in the one predictor case monte carlo results suggest that both bands are conservative for small sample sizes such as n 25 by n 200 the s method s coverage probabilities are seen to attain their nominal levels while the fixed width bands remain conservative the procedures are exemplified with data from a genetic toxicology experiment

an analysis of density dependent viability selection abstract generalized linear modeling techniques and resistant fitting methods were used to analyze the results of two experiments to test for density dependent viability selection on chromosomal variants in drosophila pseudoobscura fruit flies in the framework of the generalized linear model a series of nested hypotheses were fitted by the maximum likelihood method the hypotheses describe how the viabilities of two genotypes relative to a third varied with density and other factors an additional analysis of the absolute viabilities of the three genotypes was also performed by the maximum likelihood method estimates were computed by the em algorithm resistant methods of fitting were then performed for the best fitting relative viability models the analyses confirm that the relative viability of one genotype increased linearly with density with slope and intercept viability differences between genotypes can thus be explained by variation in density

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

the lp busemann petty centroid inequality abstract the ratio between the volume of the p centroid body of a convex body k in r n and the volume of k attains its minimum value if and only if k is an origin symmetric ellipsoid this result the lp busemann petty centroid inequality was recently proved by lutwak yang and zhang in this paper we show that all the intrinsic volumes of the p centroid body of k are convex functions of a time like parameter when k is moved by shifting all the chords parallel to a fixed direction the lp busemann petty centroid inequality is a consequence of this general fact

data analytic methods for matched case control studies the recent introduction of complex multivariate statistical models in matched case control studies is a mixed blessing their use can lead to a better understanding of the way in which many variables contribute to the risk of disease on the other hand these powerful methods can obscure salient features in the data that might have been detected by other less sophisticated methods this shortcoming is due to a lack of support methodology for the routine use of these models satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model goodness of fit must be examined if inferences are to be trusted this paper is concerned with the analysis of matched case control studies with logistic models analogies of these models to linear regression models are emphasized in particular basic concepts such as analysis of variance multiple correlation coefficient one degree of freedom tests and residual analysis are discussed the fairly new field of regression diagnostics is also introduced all procedures are illustrated on a study of bladder cancer in males

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

robust analysis of generalized linear mixed models the method of maximum likelihood ml is widely used for analyzing generalized linear mixed models glmm s a full maximum likelihood analysis requires numerical integration techniques for calculation of the log likelihood and to avoid the computational problems involving irreducibly high dimensional integrals several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log likelihood function although these likelihood algorithms are useful for fitting the glmm s efficiently under strict model assumptions they can be highly influenced by the presence of unusual data points in this article the author develops a technique for finding robust maximum likelihood rml estimates of the model parameters in glmm s which appears to be useful in downweighting the influential data points when estimating the parameters the asymptotic properties of the robust estimators are investigated under some regularity conditions small simulations are

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

projection estimators for generalized linear models we introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression these projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter we found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction e of outlier contamination for small e this bias is approximately twice the maximum bias of the initial estimator independently of the number of regressors since these projection estimators are not asymptotically normal we define one step weighted m estimators starting at the projection estimators these estimators have the same asymptotic normal distribution as the m estimator and a degree of robustness close to the one of the projection estimator we perform a monte carlo simulation for the case of binomial and poisson regression with canonical links this study shows that the proposed estimators compare favorab

conditionally unbiased bounded influence estimation in general regression models with applications to generalized linear models abstract in this article robust estimation in generalized linear models for the dependence of a response y on an explanatory variable x is studied a subclass of the class of m estimators is defined by imposing the restriction that the score function must be conditionally unbiased given x within this class of conditionally fisher consistent estimators optimal bounded influence estimators of regression parameters are identified and their asymptotic properties are studied the estimators studied in this article and the efficient bounded influence estimators studied by stefanski carroll and ruppert 1986 depend on an auxiliary centering constant and nuisance matrix the centering constant can be given explicitly for the conditionally fisher consistent estimators and thus they are easier to compute than the estimators studied by stefanski et al 1986 in addition estimation of the nuisance matrix has no effect on the asymptotic distribution of the conditionally fisher consistent estimators the sam

an overview of the variables selection methods for the minimum sum of absolute errors regression the minimum sum of absolute errors regression is a robust alternative to the least squares regression whenever the errors follow a distribution for which the sample median is a more efficient estimator of location parameter than the sample mean the errors follow a long tailed distribution there are outliers in the values of the response variable in the data or the absolute error loss function is more appropriate than the quadratic loss function often an initial model may contain a large number of variables however in many situations it is neither necessary nor important to include all the variables in the model the methods for variable selection for the minimum sum of absolute errors regression are not as well documented and known as for the least squares regression our objective is to present an overview of the procedures to fit models with fewer variables and some criteria for selecting a model

best constant in sobolev trace inequalities on the half space using a mass transportation method we study optimal sobolev trace inequalities on the half space and prove a conjecture made by escobar in 1988 about the minimizers

sharp convex lorentz sobolev inequalities new sharp lorentz sobolev inequalities are obtained by convexifying level sets in lorentz integrals via the lp minkowski problem new lp isocapacitary and isoperimetric inequalities are proved for lipschitz star bodies it is shown that the sharp convex lorentz sobolev inequalities are analytic analogues of isocapacitary and isoperimetric inequalities

positive solutions of nonlinear problems involving the square root of the laplacian abstract we consider nonlinear elliptic problems involving a nonlocal operator the square root of the laplacian in a bounded domain with zero dirichlet boundary conditions for positive solutions to problems with power nonlinearities we establish existence and regularity results as well as a priori estimates of gidas spruck type in addition among other results we prove a symmetry theorem of gidas ni nirenberg type

design of softer robust nonlinear control laws abstract we show that the lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily hard control laws having undesirable high gain properties we present a new lyapunov function and use it to design softer control laws which exhibit the high gain properties to a much lesser extent we show that the soft designs eliminate the chattering exhibited by the hard designs and achieve the same or better performance with less control effort

least absolute deviations fits for generalized linear models reference stap article 1992 004view record in web of science record created on 2006 04 04 modified on 2016 08 08

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results

a robust confidence interval for location robust estimation procedures have been the subject of a large number of comparative studies less attention has been paid to confidence intervals and tests based on these procedures and to cases in which the underlying distribution is nonsymmetric this article investigates the properties of just one interval m estimator of location the estimator is quite easy to compute and the associated point estimator of location has proven to be quite efficient in comparative studies the results indicate that in most cases including some skewed distributions the confidence coefficient of the estimator holds quite close to its specified value

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

robust regression for clustered data with application to binary responses summary generalized estimating equations gee can be highly influenced by the presence of unusual data points a generalization of the gee procedure which yields parameter estimates and fitted values that are resistant to influential data is introduced resistant generalized estimating equations regee include weights in the estimating equations to downweight influential observations or clusters influential observations are downweighted according to their leverage or residual in an example of correlated binary regression applied to 137 urinary incontinent elderly patients from 38 medical practices

resistant fits for some commonly used logistic models with medical application logistic regression type models are used in many applications some examples include the classical dose response experiment prospective and retrospective studies of disease incidence with and without matching and the analysis of ordinal data in most instances the model is fitted by the method of maximum likelihood which like least squares is sensitive to atypical observations an alternative to maximum likelihood is proposed and illustrated by examples

on the covariance between parameter estimates in models of twin data we study the covariance between estimates of additive genetic variance and either dominance genetic variance or common environmental variance in likelihood based twin analyses the central tools used in these investigations are the asymptotic covariances of variance component estimates which we present for several commonly used twin models we first illustrate the use of the asymptotic covariance terms for determining the optimal ratio of monozygotic to dizygotic group sample sizes for a twin study we then focus attention on the asymptotic correlations between estimates of additive genetic variance and either dominance genetic variance or common environmental variance and their use in understanding when parameters are efficiently estimable from twin data the results of this investigation are confirmed by simulation studies and highlight inherent limitations of the twin model in the sense that having only twin data limits the ability to detect individual variance components finally remarks on possible alternative statistical methods are given and results are presented to illustrate the improvements in efficiency that are possible with additional family data in particular the results provide insight into the limitations of inference from twin data

general l_p affine isoperimetric inequalities sharp l p affine isoperimetric inequalities are established for the entire class of l p projection bodies and the entire class of l p centroid bodies these new inequalities strengthen the l p petty projection and the l p busemann petty centroid inequality

on robustness in the logistic regression model summary we investigate robustness in the logistic regression model copas has studied two forms of robust estimator a robust resistant estimate of pregibon and an estimate based on a misclassification model he concluded that robust resistant estimates are much more biased in small samples than the usual logistic estimate is and recommends a bias corrected version of the misclassification estimate we show that there are other versions of robust resistant estimates which have bias often approximately the same as and sometimes even less than the logistic estimate these estimates belong to the mallows class in addition the corrected misclassification estimate is inconsistent at the logistic model we develop a simple consistent modification the modified estimate is a member of the mallows class but unlike most robust estimates it has an interpretable tuning constant the results are illustrated on data sets featuring different kinds of outliers

lp affine isoperimetric inequalities the lp analogues of the petty projection inequality and the busemannpetty centroid inequality are established an affine isoperimetric inequality compares two functionals associated with convex or more general bodies where the ratio of the functionals is invariant under non degenerate linear transformations these isoperimetric inequalities are more powerful than their better known euclidean relatives

the sharp affine l 2 sobolev trace inequality and variants we establish a sharp affine l p sobolev trace inequality by using the l p busemann petty centroid inequality for p 2 our affine version is stronger than the famous sharp l 2 sobolev trace inequality proved independently by escobar and beckner our approach allows also to characterize all extremizers in this case for this new inequality no euclidean geometric structure is needed

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12