algebraic reflexivity of sets of bounded operators on vector valued lipschitz functions abstract in this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued lipschitz functions we also derive a representation for the generalized bi circular projections on these spaces

examples of generalized bi circular idempotents on spaces of continuously differentiable functions abstract in this note we investigate the form of a class of idempotents called generalized bi circular idempotents on spaces of continuously differentiable functions defined on the interval 0 1 and with values in the complex numbers

local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

generalized tricircular projections on minimal norm ideals in b h abstract a nonzero projection p on a complex banach space x is said to be a generalized tricircular projection if there exist distinct modulus one complex numbers and not equal to 1 and nonzero projections q and r on x such that p q r i and p q r is an isometry we determine the structure of generalized tricircular projections on minimal norm ideals in b h different from the hilbert schmidt class

projections in the convex hull of three surjective isometries on c ω abstract let be a compact connected hausdorff space we define generalized n circular projection on c as a natural analogue of generalized bi circular projection and show that such a projection p can always be represented as p i t t 2 t n 1 n where i is the identity operator and t is a surjective isometry on c such that t n i we next show that if convex combination of three distinct surjective isometries on c is a projection then it is a generalized 3 circular projection

efficient estimates in semiparametric additive regression models with unknown error distribution several authors have shown how to efficiently estimate beta in the semiparametric additive model y x beta g t text error g t smooth but unknown when the error distribution is normal however the general theory suggests that efficient estimation should be possible for general error distributions with finite fisher information even when the error distribution is unknown in this note we construct a sequence of estimators which achieves this goal under technical assumptions

homomorphisms between algebras of lipschitz functions with the values in function algebras abstract we give a characterization of algebra homomorphisms and isomorphisms between banach algebras of lipschitz functions with the values in unital commutative c algebras we prove that such homomorphisms are composition operators of the form and preserve some properties

algebraic reflexivity of some subsets of the isometry group let x be a compact first countable space in this paper we show that the set of isometries of c x that are involutions is algebraically reflexive as a consequence of a recent work of botelho and jamison this leads to the conclusion that the set of generalized bi circular projections on c x is also algebraically reflexive we also consider these questions for the space c x e where e is a uniformly convex banach space

algebraic reflexivity of the isometry group of some spaces of lipschitz functions abstract we show that the isometry groups of lip x d and lip x d with 0 1 for a compact metric space x d are algebraically reflexive we also prove that the sets of isometric reflections and generalized bi circular projections on such spaces are algebraically reflexive in order to achieve this we characterize generalized bi circular projections on these spaces

efficient scores variance decompositions and monte carlo swindles abstract monte carlo swindles or variance reduction techniques exploit the experimenter s knowledge of the stochastic structure governing the simulated data to construct more precise estimates of unknown parameters alternatively one can reduce the number of replications and thus the cost needed to gain a desired level of precision this article reviews the common case of swindles based on variance decompositions for estimating efficiencies and variances of location and regression estimators we then propose a new swindle based on fisher s efficient score function that can be applied profitably to a much wider range of situations than can the gaussian over independent swindles used in many studies of robust estimators we compare these methods by performing simulations for the efficiencies of location estimates and by placing them in a simple geometric framework as an illustration the score function swindle is used to estimate the variances of pitman estimates of location for samples from selected

subgroups of containing let psu n be the image of the unitary group u n under the representation x axa 1 on the space mn c of n by n complex matrices we classify all connected lie subgroups of gl n2 c containing psu n we use this result to obtain a description of all abstract overgroups of psu n in gl n2 c we apply this classification to solve the problem of describing all invertible linear transformations of mn c which preserve the set of normal matrices our results can be applied to solve many other problems of similar nature

the c algebras of finitely aligned higher rank graphs we generalise the theory of cuntz krieger families and graph algebras to the class of finitely aligned k graphs this class contains in particular all row finite k graphs the cuntz krieger relations for non row finite k graphs look significantly different from the usual ones and this substantially complicates the analysis of the graph algebra we prove a gauge invariant uniqueness theorem and a cuntz krieger uniqueness theorem for the c algebras of finitely aligned k graphs

local isometries of function spaces abstract we show that for a large class of function spaces any isometry that coincides locally with a surjective isometry must be automatically surjective this class includes finite codimensional subspaces of c left x right and spaces c left x e right of e valued continuous functions for finite dimensional or uniformly convex and algebraically reflexive e

semiparametric inference in a partial linear model in a partial linear model the dependence of a response variate y on covariates w x is given by y w x e where e is independent of w x with densities g and f respectively in this paper an asymptotically efficient estimator of is constructed solely under mild smoothness assumptions on the unknown f and g thereby removing the assumption of finite residual variance on which all least squares type estimators available in the literature are based

generalized chi square goodness of fit tests for location scale models when the number of classes tends to infinity in this paper we consider generalized chi square goodness of fit tests based on increasingly finer partitions as the sample size increases for models with location scale nuisance parameters the asymptotic distributions are derived both under the null hypothesis and under local alternatives obtained by taking contamination families of densities between the null hypothesis and fixed altemative hypotheses if the number of random cells increases to infinity the rao robson nikulin test statistic is shown to be superior to the watson roy and dzhaparidze nikulin statistics conditions are derived under which it is optimal to let the number of classes tend to infinity

generalized bicircular projections on jb triples abstract let a be a jb triple and let p a a be a linear projection it is proved that p id p is an isometry for some modulus one complex number 1 if and only if either 1 or p is hermitian it is also proved that every rank one bicontractive projection on a is hermitian the particular case when a is a c algebra is discussed through several examples

affine buildings tiling systems and higher rank cuntz krieger algebras to an r dimensional subshift of finite type satisfying certain special properties we associate a c algebra a this algebra is a higher rank version of a cuntz krieger algebra in particular it is simple purely infinite and nuclear we study an example if is a group acting freely on the vertices of an a2 building with finitely many orbits and if is the boundary of that building then c o is the algebra associated to a certain two dimensional subshift

a cross validatory choice of smoothing parameter in adaptive location estimation abstract this article proposes a new data driven method for selecting the smoothing parameter involved in constructing kernel based adaptive location estimators the method consists of minimizing a cross validatory criterion with respect to the bandwidth occurring in the kernel type estimators of the efficient score function it is shown that the location estimator with a data driven bandwidth selector is indeed an adaptive estimator a simulation study reveals that the method is also practicable showing that our estimator performs well in comparison with some other well known location estimators it also shows that our method has comparable finite sample performance with the bootstrap method of selecting the smoothing parameter and yet has great computational advantages

optimal rank based tests for homogeneity of scatter we propose a class of locally and asymptotically optimal tests based on multivariate ranks and signs for the homogeneity of scatter matrices in m elliptical populations contrary to the existing parametric procedures these tests remain valid without any moment assumptions and thus are perfectly robust against heavy tailed distributions validity robustness nevertheless they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under all efficiency robustness in particular their normal score version outperforms traditional gaussian likelihood ratio tests and their pseudo gaussian robustifications under a very broad range of non gaussian densities including for instance all multivariate student and power exponential distributions

second order approximation in the partially linear regression model we examine the second order properties of various quantities of interest in the partially linear regression model we obtain a stochastic expansion with remainder op n 2 4 where u 1 2 for the standardized semiparametric least squares estimator a standard error estimator and a studentized statistic we use the second order expansions to correct the standard error estimates for second order effects and to define a method of bandwidth choice a monte carlo experiment provides favorable evidence on our method of bandwidth choice

on 2 local isometries on continuous vector valued function spaces article history received 24 july 2008 available online 24 december 2008 submitted by j d m wright a not necessarily linear mapping from a banach space x to a banach space y is said to be a 2 local isometry if for any pair x y of elements of x t here is as urjective linear isometry t x y such that tx x and ty y we show that under certain conditions on locally compact hausdorff spaces q k and a banach space e e very 2 local isometry on c0 q e to c0 k e is linear and surjective we also show that every 2 local isometry on p is linear and surjective for 1 p p 2 but this fails for the hilbert space 2

estimating with partial statistics the parameters of ergodic finite markov sources parameter estimation based on data emitted from a finite ergodic markov source is discussed this can be considered an extension of the memoryless case first an asymptotically optimal estimator is suggested for the case where the parametric model is completely known for an unknown parametric model e g unknown noise distribution with training sequences available a necessary condition is given for the existence of a universally optimum estimate a universal estimate is then suggested that is asymptotically nearly optimal the results hold under fairly mild regularity conditions

hermitian projections on some banach spaces and related topics abstract in the setting of various complex banach spaces we consider the questions of when a square of a hermitian operator is also hermitian and when a hermitian operator has a hermitian square root we also describe the structure of hermitian projections and hermitian square roots of the identity operator

generalized bicircular projections via the operator equation αx2ay2 βxay a 0 abstract the operator equation x 2 ay 2 xay a 0 is used to determine the structure of a projection p such that for some complex unit 1 the mapping p i p is a uav a ua v or a ua t v for some fixed operators u v some applications of these results are also given

local isometries on spaces of continuous functions let x and y be banach spaces and s a subset of the space of linear continuous operators from x to y we say that an operator t belongs locally to s if for every x x there is s s possibly depending on x such that tx sx pointwise should be better than locally but we have followed tradition if each operator that belongs locally to s belongs in fact to s we say that s is algebraically reflexive when y x and s iso x is the group of isometries of x we say that t is a local isometry of x in this paper isometry means linear surjective isometry similarly a local automorphism of a banach algebra is an operator which agrees at every point with some automorphism also we will consider approximate local isometries and automorphisms these are operators having with the following property given x x and e 0 there is an isometry respectively an automorphism s of x such that tx sx e the study of local isometries and automorphisms of banach algebras spurred a considerable interest in recent years see the bibliography of the dissertation 16 in this paper we deal with local isometries and automorphisms of the algebras c0 l as usual we write c0 l or c k 0 l for the banach algebra of all continuous k valued functions on the locally compact space l vanishing at infinity where k is either c or r if l is compact the subscript will be omitted by the banach stone theorem if t is local isometry of c0 l then for each f there are a homeomorphism of l and a continuous unitary u l k such that tf u f

projections as convex combinations of surjective isometries on c ω we study properties of operators that are in the convex hull of a finite set of surjective isometries on the banach space of complex valued continuous maps defined on a compact and connected topological space we characterize those projections that are in the convex combination of two surjective isometries and we show that they are generalized bi circular projections

primitive ideal space of higher rank graph c algebras and decomposability abstract in this paper we describe primitive ideal space of the c algebra c associated to any locally convex row finite k graph to do this we will apply the farthing s desourcifying method on a recent result of carlsen kang shotwell and sims we also characterize certain maximal ideals of c furthermore we study the decomposability of c we apply the description of primitive ideals to show that if i is a direct summand of c then it is gauge invariant and isomorphic to a certain k graph c algebra so we may characterize decomposable higher rank c algebras by giving necessary and sufficient conditions for the underlying k graphs moreover we determine all such c algebras which can be decomposed into a direct sum of finitely many indecomposable c algebras

generalized bi circular projections on certain hardy spaces abstract we characterize generalized bi circular projections on the hardy space of the torus and show that they can be represented as the average of the identity and an isometric reflection we also show that the average of two distinct isometries on the hardy space of the disk is a projection if and only if it is a generalized bi circular projection

2 local automorphisms of operator algebras abstract a not necessarily continuous linear or multiplicative function from an algebra a into itself is called a 2 local automorphism if agrees with an automorphism of a at each pair of points in a in this paper we study when a 2 local automorphism of a c algebra or a standard operator algebra on a locally convex space is an automorphism

some aspects of the theory of norms abstract let v be a finite dimensional vector space motivated by theory or applications one might want to consider different kinds of norms on v in this paper we discuss some results and problems involving different classes of norms on a vector space studied by this author in the past few years the paper consists of five sections section 1 concerns the conditions on two vectors x y v satisfying x y for all in a certain class of norms section 2 concerns the isometry groups of g invariant norms i e norms that satisfy g x x for all x v and for all g g where g is a group of unitary orthogonal operators on v section 3 concerns g invariant norms that satisfy some special properties section 4 concerns the best approximation s x 0 t of y where y t v with respect to different kinds of norms additional open problems topics and references are mentioned in section 5

a counterexample to wood s conjecture abstract we prove that if the one point compactification of a locally compact noncompact hausdorff space l is the topological space called pseudoarc then c 0 l c is almost transitive we also obtain two necessary conditions on a metrizable locally compact hausdorff space l for c 0 l being almost transitive

adaptive estimation in time series regression models this work develops adaptive estimators for a linear regression model with serially correlated errors we show that these results continue to hold when the order of the arma process characterizing the errors is unknown the finite sample results are promising indicating that substantial efficiency gains may be possible for samples as small as 50 observations we use these estimators to investigate the behavior of the forward foreign exchange market

isometries of norm ideals of compact operators abstract let j be a symmetric norm ideal of compact operators on hilbert space h and assume that the finite rank operators are dense in j and that j is not the ideal of hilbert schmidt operators a linear transformation on j is an isometry of j onto itself if and only if there are unitary operators u and v on h such that either x uxv or x uxtv where xt denotes the transpose of x with respect to a fixed orthonormal basis of h

the number of classes in chi squared goodness of fit tests abstract the power of pearson chi squared and likelihood ratio goodness of fit tests based on different partitions is studied by considering families of densities between the null density and fixed alternative densities for sample sizes n local asymptotic theory with respect to the number of classes k is developed for such families simple sufficient and almost necessary conditions are derived under which it is asymptotically optimal to let k tend to infinity with n a numerical study shows that the results of the asymptotic local theory for contamination families agree well with the actual power performance of the tests for heavy tailed alternatives the tests have the best power when k is relatively large unbalanced partitions with some small classes in the tails perform surprisingly well in particular when the alternatives have fairly heavy tails

on maximum likelihood estimation in infinite dimensional parameter spaces an approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions in this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter we provide conditions under which the rate of convergence can be established this rate is essentially governed by the size of the space of score functions as measured by an entropy index we also show that for a large class of smooth functionals the plug in maximum likelihood estimate is asymptotically efficient that is it achieves the minimal fisher information bound the theory is illustrated by several nonparametric or semiparametric examples

algebraic reflexivity of isometry groups of algebras of lipschitz maps abstract we study groups of surjective linear isometries on banach algebras of lipschitz maps with values in some unital c algebras in this paper these spaces are endowed with the sum norm for the case where the c algebras are commutative whose groups of all surjective isometries are algebraically reflexive we prove that the group of all surjective isometries on the corresponding banach algebra of lipschitz maps are algebraically reflexive we also prove that the group of unital surjective isometries between matrix valued lipschitz algebras are reflexive

projections and averages of isometries on lipschitz spaces abstract we characterize projections on spaces of lipschitz functions expressed as the average of two and three linear surjective isometries generalized bi circular projections are the only projections on these spaces given as the convex combination of two surjective isometries

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

overgroups of some classical linear groups with applications to linear preserver problems abstract the study of linear operators on a matrix space that leave invariant certain functions subsets or relations is commonly referred to as the study of linear preserver problems and has attracted the attention of many mathematicians in the last few decades dynkin in his classic paper studied maximal subgroups of the classical groups and showed how his results may be used to study preserver problems the purpose of this paper is to further exploit this very powerful approach the subgroups g of the general linear group that we deal with are not necessarily maximal for the applications that we have in mind we obtained a description of all possible overgroups of g the results are then applied to various linear preserver problems shorter alternative proofs for various existing results are given and some open questions are answered

the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources abstract we catalogue the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph the primitive ideals in the cuntz krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group the cuntz krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic

isometries between function spaces surjective isometries between some classical function spaces are investigated we give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding hausdorff compact spaces in particular the answer is positive for the c x ac 0 1 lip0 x and lip0 x spaces provided with various natural norms

semiparametrically efficient inference based on signed ranks in symmetric independent component models we consider semiparametric location scatter models for which the p variate observation is obtained as x lambda z mu where mu is a p vector lambda is a full rank p p matrix and the unobserved random p vector z has marginals that are centered and mutually independent but are otherwise unspecified as in blind source separation and independent component analysis ica the parameter of interest throughout the paper is lambda on the basis of n i i d copies of x we develop under a symmetry assumption on z signed rank one sample testing and estimation procedures for lambda we exploit the uniform local and asymptotic normality ulan of the model to define signed rank procedures that are semiparametrically efficient under correctly specified densities yet as usual in rank based inference the proposed procedures remain valid correct asymptotic size under the null for hypothesis testing and root n consistency for point estimation under a very broad range of densities we derive the asymptotic properties of the proposed procedures and investigate their finite sample behavior through simulations

efficiency improvements in inference on stationary and nonstationary fractional time series we consider a time series model involving a fractional stochastic component whose integration order can lie in the stationary invertible or nonstationary regions and be unknown and an additive deterministic component consisting of a generalized polynomial the model can thus incorporate competing descriptions of trending behavior the stationary input to the stochastic component has parametric autocorrelation but innovation with distribution of unknown form the model is thus semiparametric and we develop estimates of the parametric component which are asymptotically normal and achieve an m estimation efficiency bound equal to that found in work using an adaptive lam lan approach a major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies this is relevant also when the innovation density is parameterized and we provide a result for that case also our semiparametric estimates employ nonparametric series estimation which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models our work thus also contributes to methods and theory for nonfractional time series models such as autoregressive moving averages a monte carlo study of finite sample performance of the semiparametric estimates is included

asymptotic minimax estimation in semiparametric models we give several conditions on the estimator of efficient score function for estimating the parametric component of semiparametric models a semiparametric version of the one step mle using an estimator of efficient score function which fulfills the conditions is shown to converge to the normal distribution with minimum variance locally uniformly over a fairly large neighborhood around the assumed semiparametric model consequently it is shown to be asymptotically minimax with bounded subconvex loss functions a few examples are also considered

bicircular projections on some matrix and operator spaces a projection on a complex banach space is bicircular if its linear combinations with the complementary projection having coefficients of modulus one are isometries such projections are always bicontractive in this paper we prove structure theorems for bicircular projections acting on the spaces of the full operator algebra symmetric operators and antisymmetric operators

g invariant norms and bicircular projections abstract it is shown that for many finite dimensional normed vector spaces v over c a linear projection p v v will have nice structure if p i p is an isometry for some complex unit not equal to one from these results one can readily determine the structure of bicircular projections i e those linear projections p such that p i p is an isometry for every complex unit the key ingredient in the proofs is the knowledge of the isometry group of the given norm the proof techniques also apply to real vector spaces in such cases characterizations are given to linear projections p such that p i p 2p i is an isometry

bicircular projections on some banach spaces in this paper we show that the bicircular projections are precisely the hermitian projections and prove some immediate consequences of this result

on methods of sieves and penalization we develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates mle s in parametric semiparametric and nonparametric models we find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices the degree of smoothness of the functional and the local size of the underlying parameter space we show that when the local size of the parameter space is not very large the substitution standard nonsieve substitution sieve and substitution penalized mle s are asymptotically efficient in the fisher sense under certain stochastic equicontinuity conditions of the loglikelihood moreover when the convergence rate of the estimate is slow the degree of smoothness of the functional needs to compensate for the slowness of the rate in order to achieve efficiency when the size of the parameter space is very large the standard and penalized maximum likelihood procedures may be inefficient whereas the method of sieves may be able to overcome this difficulty this phenomenon is particularly manifested when the functional of interest is very smooth especially in the semiparametric case

reflexivity of the automorphism and isometry groups of the suspension of b h the aim of this paper is to show that the automorphism and isometry groups of the suspension of b h h being a separable infinite dimensional hilbert space are algebraically reflexive this means that every local automorphism respectively every local surjective isometry ofc0 r b h is an automorphism respectively a surjective isometry

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

generalized bi circular projections abstract recall that a projection p on a complex banach space x is a generalized bi circular projection if p i p is a surjective isometry for some such that 1 and 1 it is easy to see that every hermitian projection is generalized bi circular a generalized bi circular projection is said to be nontrivial if it is not hermitian botelho and jamison showed that a projection p on c 0 1 is a nontrivial generalized bi circular projection if and only if p i p is a surjective isometry in this article we prove that if p is a projection such that p i p is a surjective isometry for some then either p is hermitian or is an n th unit root of unity we also show that for any n th unit root of unity there are a complex banach space x and a nontrivial generalized bi circular projection p on x such that p i p is an isometry

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

projections as averages of isometries on minimal norm ideals abstract in this paper we consider projections on minimal norm ideals of b h that are represented as the average of two surjective isometries we describe projections of the form p t a 1 tb 1 a 2 tb 2 2 where a 1 a 2 b 1 and b 2 are unitary operators satisfying a commutativity condition we also characterize classes of projections of the form p t at t t b 2 and p t at t t t b 2 with a and b unitary operators satisfying a spectral condition

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models