new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

shrinkage estimators applied to prediction of french winter wheat yield summary the paper shows that it is possible to pool departmental information to predict regional wheat yield in an msep mean squared error of prediction context shrinkage estimation in linear agrometeorological models improves regional prediction cross validation is not precise enough to enable comparison between models the authors calculate the msep using the hypothesis of a multinormal distribution in simple cases the distribution parameters are estimated with data input and simulations are used for complex cases stein like estimators are shown to be a superior alternative to the conventional estimators usually applied for prediction

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

penalized estimating equations les modeles avec penalisation comme l estimateur ridge l estimateur de stein l estimateur en pont et le lasso ont ete proposes pour prendre en compte la collineariteen regression le lasso a ete applique au modele lineaire a la regression logistique au modele des hasards proportionnels de cox et aux reseaux de neurones cet article etudie le modele avec penalisation en pont pour une penalite j j applique aux equations d estimation et applique ce modele avec penalisation aux equations d estimation generalisees gee dans des etudes longitudinales le defaut de vraisemblance jointe dans les gee est surmonte par les equations d estimation penalisees pour lesquelles aucune vraisemblance jointe n est requise on donne les resultats asymptotiques pour l estimateur sons penalite on montre par des simulations et une application que les cee avec penalisation ameliorent potentiellement les resultats de l estimateur gee et presentent les memes proprietes que les modeles lineaires penalises

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

non commutative crepant resolution of minimal nilpotent orbit closures of type a and mukai flops abstract in this article we construct a non commutative crepant resolution nccr of a minimal nilpotent orbit closure b 1 of type a and study relations between an nccr and crepant resolutions y and y of b 1 more precisely we show that the nccr is isomorphic to the path algebra of the double beilinson quiver with certain relations and we reconstruct the crepant resolutions y and y of b 1 as moduli spaces of representations of the quiver we also study the kawamata namikawa s derived equivalence between crepant resolutions y and y of b 1 in terms of an nccr we also show that the p twist on the derived category of y corresponds to a certain operation of the nccr which we call multi mutation and that a multi mutation is a composition of iyama wemyss s mutations

random calibration with many measurements an application of stein estimation in the problem considered a vector of many imprecise measurements e g spectroscopic is used to linearly predict a quantity whose precise measurement is difficult or expensive the regression vector is estimated from a calibration experiment having both types of measurements for a random sample most previous approaches to this problem adjust for approximate multicollinearity which often results from the correlations among the imprecise measurements by inverting an approximation e g factor analytic to their covariance matrix in the approach here it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix it is then estimated by applying a stein contraction of the least squares estimator to the principal components regression estimator examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation

nonparametric independence screening in sparse ultra high dimensional varying coefficient models the varying coefficient model is an important class of nonparametric statistical model which allows us to examine how the effects of covariates vary with exposure variables when the number of covariates is large the issue of variable selection arises in this article we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra high dimensional varying coefficient models the proposed nonparametric independence screening nis selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable the sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order and the dimensionality reduction of nis is quantified to enhance the practical utility and finite sample performance two data driven iterative nis inis methods are proposed for selecting thresholding parameters and variables conditional permutation and greedy metho

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

contour integration solution for a thermoelastic problem of a spherical cavity abstract we study a 1d problem of a spherical cavity whose surface is traction free and kept at a temperature that depends on the time laplace transform techniques are utilized we use contour integration and the complex inversion formula to get the inverse transforms as definite integrals numerical computations are illustrated graphically

predicting multivariate responses in multiple linear regression we look at the problem of predicting several response variables from the same set of explanatory variables the question is how to take advantage of correlations between the response variables to improve predictive accuracy compared with the usual procedure of doing individual regressions of each response variable on the common set of predictor variables a new procedure is introduced called the curds and whey method its use can substantially reduce prediction errors when there are correlations between responses while maintaining accuracy even if the responses are uncorrelated in extensive simulations the new procedure is compared with several previously proposed methods for predicting multiple responses including partial least squares and exhibits superior accuracy one version can be easily implemented in the context of standard statistical packages

cohen macaulayness of semi invariants for tori in this paper we give a new method in terms of one parameter subgroups to study semi invariants for algebraic tori in some cases we obtain extensions to results in 7 in other cases we obtain different proofs

additive risk models for survival data with high dimensional covariates as a useful alternative to cox s proportional hazard model the additive risk model assumes that the hazard function is the sum of the baseline hazard function and the regression function of covariates this article is concerned with estimation and prediction for the additive risk models with right censored survival data especially when the dimension of the covariates is comparable to or larger than the sample size principal component regression is proposed to give unique and numerically stable estimators asymptotic properties of the proposed estimators component selection based on the weighted bootstrap and model evaluation techniques are discussed this approach is illustrated with analysis of the primary biliary cirrhosis clinical data and the diffuse large b cell lymphoma genomic data it is shown that this methodology is numerically stable and effective in dimension reduction while still being able to provide satisfactory prediction and classification results

continuum regression is not always continuous in regression with near collinear explanatory variables the least squares predictor has large variance ordinary least squares regression olsr often leads to unrealistic regression coefficients several regularized regression methods have been proposed as alternatives well known are principal components regression pcr ridge regression rr and continuum regression cr the latter two involve a continuous metaparameter offering additional flexibility for a univariate response variable cr incorporates olsr plsr and pcr as special cases for special values of the metaparameter cr is also closely related to rr however cr can in fact yield regressors that vary discontinuously with the metaparameter thus the relation between cr and rr is not always one to one we develop a new class of regression methods lsrr essentially the same as cr but without discontinuities and prove that any optimization principle will yield a regressor proportional to a rr provided only that the principle implies maximizing some function of the regressor s sample correlation coefficient and its sample variance for a multivariate response vector we demonstrate that a number of well established regression methods are related in that they are special cases of basically one general procedure we try a more general method based on this procedure with two meta parameters in a simulation study we compare this method to ridge regression multivariate plsr and repeated univariate plsr for most types of data studied all methods do approximately equally well there are cases where rr and lsrr yield larger errors than the other methods and we conclude that one factor methods are not adequate for situations where more than one latent variable are needed to describe the data among those based on latent variables none of the methods tried is superior to the others in any obvious way

singular derived categories of factorial terminalizations and maximal modification algebras abstract let x be a gorenstein normal 3 fold satisfying elf with local rings which are at worst isolated hypersurface e g terminal singularities by using the singular derived category d sg x and its idempotent completion d sg x we give necessary and sufficient categorical conditions for x to be q factorial and complete locally q factorial respectively we then relate this information to maximal modification algebras mmas introduced in 20 by showing that if an algebra is derived equivalent to x as above then x is q factorial if and only if is an mma thus all rings derived equivalent to q factorial terminalizations in dimension three are mmas as an application we extend some of the algebraic results in 6 and 14 using geometric arguments

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

application of fractional order theory of thermoelasticity to a 2d problem for a half space a 2d half space problem for the new fractional order theory of thermoelasticity laplace and exponential fourier transform techniques are used the inverse transforms are obtained using a numerical technique predictions of the theory are discussed and compared with older theory in this work we apply the fractional order theory of thermoelasticity to a 2d problem for a half space the surface of the half space is taken to be traction free and is subject to heating there are no body forces or heat sources affecting the medium laplace and exponential fourier transform techniques are used to solve the problem the inverse laplace transforms are obtained using a numerical technique the predictions of the theory are discussed and compared with those for the generalized theory of thermoelasticity we also study the effect of the fractional derivative parameter on the behavior of the solution numerical results are computed and represented graphically for the temperature displacement and stress distributions

cohen macaulayness of modules of covariants let g be a connected reductive algebraic group over an algebraically closed field k of characteristic zero and let w be a finite dimensional representation of g then g acts on the polynomial ring r s w and the hochster roberts theorem asserts that r a is cohen macaulay a natural question would be whether the same is true for modules of covariants i e let u be another finite dimensional g representation then u r is a free rmodule and a natural generalization of the hochster roberts theorem would be that u r g is a cohen macaulay ra module unfortunately it is easy to see that this cannot be true in general see 10 ex 3 1 for a simple counter example for an arbitrary irreducible character z stanley defines r as the sum of all irreducible subrepresentations of r with character 7 assume that u is irreducible and let be the character of u then it is easy to see that

variable inclusion and shrinkage algorithms the lasso is a popular and computationally efficient procedure for automatically performing both variable selection and coefficient shrinkage on linear regression models one limitation of the lasso is that the same tuning parameter is used for both variable selection and shrinkage as a result it typically ends up selecting a model with too many variables to prevent overshrinkage of the regression coefficients we suggest an improved class of methods called variable inclusion and shrinkage algorithms visa our approach is capable of selecting sparse models while avoiding overshrinkage problems and uses a path algorithm and so also is computationally efficient we show through extensive simulations that visa significantly outperforms the lasso and also provides improvements over more recent procedures such as the dantzig selector relaxed lasso and adaptive lasso in addition we provide theoretical justification for visa in terms of nonasymptotic bounds on the estimation error that suggest it shoul

semi invariants of quivers and saturation for littlewood richardson coefficients q is defined in the space of all weights by one homogeneous linear equation and by a finite set of homogeneous linear inequalities in particular the set q is saturated i e if n q then also q these results when applied to a special quiver q tn n n and to a special dimension vector show that the gln module v appears in v v if and only if the partitions and satisfy an explicit set of inequalities this gives new proofs of the results of klyachko 7 3 and knutson and tao 8 the proof is based on another general result about semi invariants of quivers theorem 1 in the paper 10 schofield defined a semi invariant cw for each indecomposable representation w of q we show that the semi invariants of this type span each weight space in si q this seems to be a fundamental fact connecting semi invariants and modules in a direct way given this fact the results on sets of weights follow at once from the results in another paper of schofield 11

local linear regression on manifolds and its geometric interpretation high dimensional data analysis has been an active area and the main focus areas have been variable selection and dimension reduction in practice it occurs often that the variables are located on an unknown lower dimensional nonlinear manifold under this manifold assumption one purpose of this article is regression and gradient estimation on the manifold and another is developing a new tool for manifold learning as regards the first aim we suggest directly reducing the dimensionality to the intrinsic dimension d of the manifold and performing the popular local linear regression llr on a tangent plane estimate an immediate consequence is a dramatic reduction in the computational time when the ambient space dimension p d we provide rigorous theoretical justification of the convergence of the proposed regression and gradient estimators by carefully analyzing the curvature boundary and nonuniform sampling effects we propose a bandwidth selector that can handle heteroscedastic errors with re

a formal inverse to the cayley hamilton theorem abstract we prove that a q algebra r with formal trace can be realized as n n matrices if and only if it satisfies the cayley hamilton identity of degree n

representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities we give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products with parameter t 0 and the derived category of coherent sheaves on a crepant resolution of the spectrum of the centre of these algebras

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

biased regression the case for cautious application biased regression br methods have received only lukewarm approval largely because of the practical difficulty in using data driven methods to find a biased estimator that is better than ordinary least squares ols nevertheless we believe there are situations where br methods are worthy contenders for example we focus on multivariate calibration using chemical spectra where the goal is to predict all component concentrations we illustrate a cautious application of several br methods on both real and simulated data in which we keep the ols solution unless there is strong evidence that the br solution is better

sparse estimators and the oracle property or the return of hodges estimator abstract we point out some pitfalls related to the concept of an oracle property as used in fan and li 2001 variable selection via nonconcave penalized likelihood and its oracle properties journal of the american statistical association 96 1348 1360 2002 variable selection for cox s proportional hazards model and frailty model annals of statistics 30 74 99 2004 new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis journal of the american statistical association 99 710 723 which are reminiscent of the well known pitfalls related to hodges estimator the oracle property is often a consequence of sparsity of an estimator we show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function in particular the maximal risk diverges to infinity whenever the loss function is unbounded for ease of presentation the result is set in the framework of a linear regression model but generalizes far beyond that setting in a monte carlo study we also assess the extent of the problem in finite samples for the smoothly clipped absolute deviation scad estimator introduced in fan and li 2001 variable selection via nonconcave penalized likelihood and its oracle properties journal of the american statistical association 96 1348 1360 we find that this estimator can perform rather poorly in finite samples and that its worst case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

principal components regression with data chosen components and related methods multiple regression with correlated explanatory variables is relevant to a broad range of problems in the physical chemical and engineering sciences chemometricians in particular have made heavy use of principal components regression and related procedures for predicting a response variable from a large number of highly correlated variables in this article we develop a general theory for selecting principal components that yield estimates of regression coefficients with low mean squared error our numerical results suggest that the theory also can be used to improve partial least squares regression estimators and regression estimators based on rotated principal components although our work has been motivated by the statistical genetics problem of mapping quantitative trait loci the results are applicable to any problem in which estimation of regression coefficients for correlated explanatory variables is of interest

a note on automatic variable selection using smooth threshold estimating equations this paper develops smooth threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero the resulting estimator enjoys the oracle property in the sense of fan li 2001 even in estimators for which the covariance assumption of wang leng 2007 is violated such as the buckley james estimator furthermore the estimator can be obtained without solving a convex optimization problem a bic type criterion for tuning parameter selection is also proposed it is shown that the criterion achieves consistent model selection a numerical study confirms the performance of the method

partial desingularisations of quotients of nonsingular varieties and their betti numbers when a reductive group g acts linearly on a nonsingular complex projective variety x one can define a projective quotient variety x g using mumford s geometric invariant theory if the condition that every semistable point be properly stable is satisfied this quotient is the ordinary topological quotient of an open subset xss of the variety by the group in k a formula is obtained for the rational cohomology of x g under this condition the formula involves the rational cohomology of x and various linear sections of x together with the rational cohomology of the classifying spaces of g and certain reductive subgroups of g in many interesting examples the condition required in k is not satisfied thus the question arises as to what information we can obtain in general the quotient x g can now have serious singularities in contrast to the good case considered in k where the only singularities are those caused by finite isotropy groups it will be shown in this paper that there is a systematic way of blowing up x along a sequence of nonsingular subvarieties to obtain a variety x with a linear action of g such that every semistable point of x is stable the only assumption that we have to make is that there exists at least one stable point of x then x g is almost a resolution of singularities of x1 g in the sense that the most serious singularities have been resolved moreover there is a formula for the rational cohomology of x g again involving the rational cohomology of x and certain linear sections of x together with the rational cohomology of the classifying spaces of g and some reductive subgroups of g see theorem 8 14 for convenience we shall assume throughout that g is connected however the construction of x works in general and it is straightforward to modify the cohomological formulas to apply to the general case the construction of x g can also be modified to apply in some cases when x has no stable points the layout of the paper is as follows section 1 is a review of the basic facts of geometric invariant theory which will be needed and section 2 describes the relationship of geometric invariant theory with symplectic geometry and the moment map in section 3 semistability and stability in a blow up of x along a nonsingular c invariant subvariety are related to semistability and stability in x

non commutative desingularization of determinantal varieties i we show that determinantal varieties defined by maximal minors of a generic matrix have a non commutative desingularization in that we construct a maximal cohen macaulay module over such a variety whose endomorphism ring is cohen macaulay and has finite global dimension in the case of the determinant of a square matrix this gives a non commutative crepant resolution

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

the frobenius morphism in invariant theory abstract let r be the homogeneous coordinate ring of the grassmannian g gr 2 n defined over an algebraically closed field of characteristic p 0 in this paper we give a completely characteristic free description of the decomposition of r considered as a graded r p module into indecomposables frobenius summands as a corollary we obtain a similar decomposition for the frobenius pushforward of the structure sheaf of g and we obtain in particular that this pushforward is almost never a tilting bundle on the other hand we show that r provides a noncommutative resolution for r p when p n 2 generalizing a result known to be true for toric varieties in both the invariant theory and the geometric setting we observe that if the characteristic is not too small the frobenius summands do not depend on the characteristic in a suitable sense in the geometric setting this is an explicit version of a general result by bezrukavnikov and mirkovic on frobenius decompositions for partial flag varieties we are hopeful that it is an instance of a more general p uniformity principle

remarks on non commutative crepant resolutions of complete intersections abstract we study obstructions to existence of non commutative crepant resolutions in the sense of van den bergh over local complete intersections

restricted least squares estimation of the spectra and concentration of two unknown constituents available in mixtures the problem considered is the identification of two unknown chemical compounds and the estimation of their proportions in a set of unknown mixtures of the two compounds given data that are vectors of measurements on their mixtures it is assumed that the expected value of a mixture vector is an unknown convex linear combination of two unknown component vectors and least squares estimation is used to obtain a set of possible solutions of the mixing proportions and the component vectors obtaining a unique solution requires additional constraints or information the solution set is interpreted geometrically and examples involving amino acids and light absorbance data are given

regularity of trace rings of generic matrices is called the ring of m generic n x n matrices g n the f subalgebra of m em generated by g and tr g is the ring of m generic n x n matrices and is denoted by t n these trace rings appear naturally in the study of finite dimensional representations of free algebras and in the invariant theory of n x n matrices 7 unlike rings of generic matrices t n shares some properties with commutative polynomial rings e g they are maximal orders and even unique factorization rings in the sense of chatters and jordan however their homological properties are far from being understood the main aim of this paper is to prove the following result

a flexible semiparametric forecasting model for time series in this paper we propose a semiparametric procedure called the model averaging marginal regression mamar that is flexible for forecasting of time series this procedure considers approximating a multivariate regression function by an affine combination of one dimensional marginal regression functions the weight parameters involved in the approximation are estimated by least squares on the basis of the first stage nonparametric kernel estimates of the marginal regressions under some mild conditions we have established asymptotic normality for the estimated weights and the regression function in two cases case i considers that the number of the covariates is fixed while case ii allows the number of the covariates depending on the sample size and diverging as the observations are assumed to be stationary and near epoch dependent the approach developed is applicable to both the estimation and forecasting issues in time series analysis furthermore the method and result are augmented by a simulation study and illustrated by an application in forecasting the high frequency volatility of the ftse100 index

fractional order theory of thermoelasticity in this work a new theory of thermoelasticity is derived using the methodology of fractional calculus the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases a uniqueness theorem for this model is proved a variational principle and a reciprocity theorem are derived

local cohomology of modules of covariants abstract let g be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let w u be two finite dimensional representations of g in this paper we compute the local cohomology of u sw g provided a certain relatively weak technical condition is true

multivariate calibration when the error covariance matrix is structured this article concerns multivariate calibration in linear models the error covariance matrix is assumed to have linear factor structure a new approach to calibration incorporating distributional properties of the observations of the calibration set is proposed the proposed predictor is based on estimating the parameters in the best linear predictor in the assumed model the predictor is tested on two data sets meat data and fish data

covariance regularized regression and classification for high dimensional problems in recent years many methods have been developed for regression in high dimensional settings we propose covariance regularized regression a family of methods that use a shrunken estimate of the inverse covariance matrix of the features in order to achieve superior prediction an estimate of the inverse covariance matrix is obtained by maximizing its log likelihood under a multivariate normal model subject to a constraint on its elements this estimate is then used to estimate coefficients for the regression of the response onto the features we show that ridge regression the lasso and the elastic net are special cases of covariance regularized regression and we demonstrate that certain previously unexplored forms of covariance regularized regression can outperform existing methods in a range of situations the covariance regularized regression framework is extended to generalized linear models and linear discriminant analysis and is used to analyze gene expression data sets with multiple class and survival outcomes

a group bridge approach for variable selection in multiple regression problems when covariates can be naturally grouped it is important to carry out feature selection at the group and within group individual variable levels simultaneously the existing methods including the lasso and group lasso are designed for either variable selection or group selection but not for both we propose a group bridge approach that is capable of simultaneous selection at both the group and within group individual variable levels the proposed approach is a penalized regularization method that uses a specially designed group bridge penalty it has the oracle group selection property in that it can correctly select important groups with probability converging to one in contrast the group lasso and group least angle regression methods in general do not possess such an oracle property in group selection simulation studies indicate that the group bridge has superior performance in group and individual variable selection relative to several existing methods

robust variable selection with exponential squared loss robust variable selection procedures through penalized regression have been gaining increased attention in the literature they can be used to perform variable selection and are expected to yield robust estimates however to the best of our knowledge the robustness of those penalized regression procedures has not been well characterized in this article we propose a class of penalized robust regression estimators based on exponential squared loss the motivation for this new procedure is that it enables us to characterize its robustness in a way that has not been done for the existing procedures while its performance is near optimal and superior to some recently developed methods specifically under defined regularity conditions our estimators are consistent and possess the oracle property importantly we show that our estimators can achieve the highest asymptotic breakdown point of 1 2 and that their influence functions are bounded with respect to the outliers in either the response or the covari

sparsity and error analysis of empirical feature based regularization schemes we consider a learning algorithm generated by a regularization scheme with a concave regularizer for the purpose of achieving sparsity and good learning rates in a least squares regression setting the regularization is induced for linear combinations of empirical features constructed in the literatures of kernel principal component analysis and kernel projection machines based on kernels and samples in addition to the separability of the involved optimization problem caused by the empirical features we carry out sparsity and error analysis giving bounds in the norm of the reproducing kernel hilbert space based on a priori conditions which do not require assumptions on sparsity in terms of any basis or system in particular we show that as the concave exponent q of the concave regularizer increases to 1 the learning ability of the algorithm improves some numerical simulations for both artificial and real mhc peptide binding data involving the lq regularizer and the scad penalty are presented to demonstrate the sparsity and error analysis

the peculiar shrinkage properties of partial least squares regression partial least squares regression has been widely adopted within some areas as a useful alternative to ordinary least squares regression in the manner of other shrinkage methods such as principal components regression and ridge regression in this paper we examine the nature of this shrinkage and demonstrate that partial least squares regression exhibits some undesirable properties

continuum regression cross validated sequentially constructed prediction embracing ordinary least squares partial least squares and principal components regression read before the royal statistical society at a meeting organized by the research section on wednesday october 25th 1989 professor d v hinkley in the chair summary the paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression in the context of a general sequential procedure for doing this it is shown that with a particular objective criterion for the construction the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum with partial least squares lying in between there are two adjustable parameters controlling the procedure alpha in the continuum 0 11 and omega the number of regressors finally accepted these control parameters are chosen by crossvalidation the method is illustrated by a range of examples of its application

non commutative resolutions of quotient singularities for reductive groups in this paper we generalize standard results about non commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups we show in particular that quotient singularities for reductive groups always have non commutative resolutions in an appropriate sense moreover we exhibit a large class of such singularities which have twisted non commutative crepant resolutions we discuss a number of examples both new and old that can be treated using our methods notably we prove that twisted non commutative crepant resolutions exist in previously unknown cases for determinantal varieties of symmetric and skew symmetric matrices in contrast to almost all prior results in this area our techniques are algebraic and do not depend on knowing a commutative resolution of the singularity

categorical resolution of singularities abstract building on the concept of a smooth dg algebra we define the notion of a smooth derived category we then propose the definition of a categorical resolution of singularities our main example is the derived category d x of quasi coherent sheaves on a scheme x we prove that d x has a canonical categorical resolution if the base field is perfect and x is a separated scheme of finite type with a dualizing complex

non commutative resolutions of toric varieties abstract let r be the coordinate ring of an affine toric variety we prove using direct elementary methods that the endomorphism ring end r a where a is the finite direct sum of all isomorphism classes of conic r modules has finite global dimension equal to the dimension of r this gives a precise version and an elementary proof of a theorem of spenko and van den bergh implying that end r a has finite global dimension furthermore we show that end r a is a non commutative crepant resolution if and only if the toric variety is simplicial for toric varieties over a perfect field k of prime characteristic we show that the ring of differential operators d k r has finite global dimension

simultaneous factor selection and collapsing levels in anova when performing an analysis of variance the investigator often has two main goals to determine which of the factors have a significant effect on the response and to detect differences among the levels of the significant factors level comparisons are done via a post hoc analysis based on pairwise differences this article proposes a novel constrained regression approach to simultaneously accomplish both goals via shrinkage within a single automated procedure the form of this shrinkage has the ability to collapse levels within a factor by setting their effects to be equal while also achieving factor selection by zeroing out entire factors using this approach also leads to the identification of a structure within each factor as levels can be automatically collapsed to form groups in contrast to the traditional pairwise comparison methods these groups are necessarily nonoverlapping so that the results are interpretable in terms of distinct subsets of levels the proposed procedure is shown to have the oracle property in that asymptotically it performs as well as if the exact structure were known beforehand a simulation and real data examples show the strong performance of the method

some notes on the nonnegative garrote some notes on the use of the nonnegative garrote ng are given in this article the main result is that compared with other penalized least squares methods the ng has a natural selection of penalty function according to an estimator of prediction risk furthermore two natural estimators of the tuning parameter which only involve very simple computations are proposed corresponding to the akaike information criterion aic and bayesian information criterion bic respectively this indicates that to select tuning parameters it may be unnecessary to optimize a model selection criterion repeatedly several reasonable ng estimators with natural tuning parameters are proposed for multicollinearity problems and other problems simulation results and a real data analysis are reported for testing the results obtained previously

informative sensor and feature selection via hierarchical nonnegative garrote placing sensors in every station of a process or every element of a system to monistor its state or performance is usually too expensive or physically impossible therefore a systematic method is needed to select important sensing variables the method should not only be capable of identifying important sensors signals among multistream signals from a distributed sensing system but should also be able to extract a small set of interpretable features from the high dimensional vector of a selected signal for this purpose we develop a new hierarchical regularization approach called hierarchical nonnegative garrote nng at the first level of hierarchy a group nng is used to select important signals and at the second level the individual features within each signal are selected using a modified version of nng that possesses good properties for the estimated coefficients performance of the proposed method is evaluated and compared with other existing methods through monte carlo simulation a case stud

the sparse laplacian shrinkage estimator for high dimensional regression we propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors this method is based on a combination of the minimax concave penalty and laplacian quadratic associated with a graph as the penalty function we call it the sparse laplacian shrinkage sls method the sls uses the minimax concave penalty for encouraging sparsity and laplacian quadratic penalty for promoting smoothness among coefficients associated with the correlated predictors the sls has a generalized grouping property with respect to the graph represented by the laplacian quadratic we show that the sls possesses an oracle property in the sense that it is selection consistent and equal to the oracle laplacian shrinkage estimator with high probability this result holds in sparse high dimensional settings with p n under reasonable conditions we derive a coordinate descent algorithm for computing the sls estimates simulation studies are conducted to evaluate the performance of the sls method and a real data example is used to illustrate its application

how much does stein estimation help in multiple linear regression the use of stein estimation in multiple linear regression is considered tables and graphs are presented that compare the prediction mean squared errors of positive part james stein preliminary test reduced and full model least squares estimates the appropriateness of using stein contraction on possibly extraneous variables is emphasized and a procedure is presented for evaluating the likely savings in using stein estimation on the problem at hand an example is given

noncommutative resolution f blowups and d modules abstract we explain the isomorphism between the g hilbert scheme and the f blowup from the noncommutative viewpoint after van den bergh in doing this we immediately and naturally arrive at the notion of d modules we also find as a byproduct a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic

prediction by supervised principal components in regression problems where the number of predictors greatly exceeds the number of observations conventional regression techniques may produce unsatisfactory results we describe a technique called supervised principal components that can be applied to this type of problem supervised principal components is similar to conventional principal components analysis except that it uses a subset of the predictors selected based on their association with the outcome supervised principal components can be applied to regression and generalized regression problems such as survival analysis it compares favorably to other techniques for this type of problem and can also account for the effects of other covariates and help identify which predictor variables are most important we also provide asymptotic consistency results to help support our empirical findings these methods could become important tools for dna microarray data where they may be used to more accurately diagnose and treat cancer

simplicity of rings of differential operators in prime characteristic let w be a finite dimensional representation of a linearly reductive group g over a field k motivated by their work on classical rings of invariants levasseur and stafford asked whether the ring of invariants under g of the symmetric algebra of w has a simple ring of differential operators in this paper we show that this is true in prime characteristic indeed if r is a graded subring of a polynomial ring over a perfect field of characteristic p 0 and if the inclusion r hookrightarrow s splits then d k r is a simple ring in the last section of the paper we discuss how one might try to deduce the characteristic zero case from this result as yet however this is a subtle problem and the answer to the question of levasseur and stafford remains open in characteristic zero http www luc ac be research algebra 1991 mathematics subject classification 16s32 16g60 13a35

maximal modifications and auslander reiten duality for non isolated singularities we first generalize classical auslander reiten duality for isolated singularities to cover singularities with a one dimensional singular locus we then define the notion of ct modules for non isolated singularities and we show that these are intimately related to noncommutative crepant resolutions nccrs when r has isolated singularities ct modules recover the classical notion of cluster tilting modules but in general the two concepts differ then wanting to generalize the notion of nccrs to cover partial resolutions of operatorname spec r in the main body of this paper we introduce a theory of modifying and maximal modifying modules under mild assumptions all the corresponding endomorphism algebras of the maximal modifying modules for three dimensional gorenstein rings are shown to be derived equivalent we then develop a theory of mutation for modifying modules which is similar but different to mutations arising in cluster tilting theory our mutation works in arbitrary dimension and in dimension three the behavior of our mutation strongly depends on whether a certain factor algebra is artinian

regularization parameter selections via generalized information criterion we apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators this approach relies heavily on the choice of regularization parameter which controls the model complexity in this paper we propose employing the generalized information criterion encompassing the commonly used akaike information criterion aic and bayesian information criterion bic for selecting the regularization parameter our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches we show that the bic type selector enables identification of the true model consistently and the resulting estimator possesses the oracle property in the terminology of fan and li 2001 in contrast however the aic type selector tends to overfit with positive probability we further show that the aic type selector is asymptotically loss efficient while the bic type selector is not

penalized partial likelihood regression for right censored data with bootstrap selection of the penalty parameter le modele de cox a risque proportionnel est souvent utilise pour estimer l association entre des covariables et un delai de survenue d un evenement qui peut etre censure les estimateurs bases sur la vraisemblance partielle sont utilises pour l estimation et la prediction du risque relatif de l evenement cependant ces estimateurs sont instables et ont une grande variance en cas de colinearite entre les covariables ou quand le nombre d evenements n est pas nettement plus grand que le nombre de covariables une vraisemblance partielle penalisee est proposee pour donner des estimateurs du risque relatif plus precis nous montrons qu asymptotiquement il existe toujours un parametre de penalite pour la vraisemblance partielle penalisee qui reduit le carre moyen de l erreur d estimation du logarithme du risque relatif nous proposons une methode de reechantillonnage pour choisir le parametre de penalite des simulations et un exemple montrent que des estimateurs bases sur la vraisemblance partielle penalisee et la methode du bootstrap peuvent dans certaines circonstances avoir un biais plus petit que celui des estimateurs bases sur la vraisemblance partielle ainsi qu un carre moyeu plus petit de l erreur d estimation et de prediction du logarithme du risque relatif nous illustrons ces methodes avec des donnees d une etude sur le myelome multiple du eastern cooperative oncology group ecog