exponentiation of the spinor representation of the lorentz group an exact finite expression for the exponentiation of the spin 12 spinor representation of the lorentz group is obtained from this expression an exact finite expression for the exponentiation of the vector representation of the lorentz group is derived the two expressions are compared with the literature in the special cases of either spatial rotations or boosts only

qualitative robustness for stochastic processes in this paper we generalize hampel s concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non i i d observations defining appropriate metrics between samples we also present a different approach to qualitative robustness which formalizes the notion of resistance we give two definitions based on this approach strong and weak resistance we show that for estimating a finite dimensional real parameter pi robustness is equivalent to weak resistance and in the i i d case is also equivalent to strong resistance finally we prove the strong resistance of a class of estimators which includes common gm estimates for linear models and autoregressive processes

closed forms for the exponential mapping on matrix lie groups based on putzer s method we present closed forms for the exponential of some infinitesimal generators of lie groups which play an important role in physics and engineering applications these explicit forms are based on the putzer s method we also compare this methodology and results with related work by other authors

principes d invariance faible pour la mesure empirique d une suite de variables aleatoires melangeante we give weak invariance principles for the empirical measure of a stationary strongly mixing sequence xi k k geqq 0 x n f frac 1 sqrt n sum limits k 1 n f xi k ef xi k for the case where f b s the unit ball of the sobolev space h s x of a riemannian compact manifold and f is a lip function frac 1 2 0 such that mathbb p text mathop text sup limits text x in k text nh n d text text 1 2 hat g n x g x y n x geqq cn a leqq cn a if h n n b finally we give estimates of the kind e mathop sup limits x in k text hat g n x g x 2 leqq cn a text if h n n b here h n is the window of the kernel estimate hat g n

nonparametric density estimation prediction and regression for markov sequences abstract let xi be a stationary markov sequence having a transition probability density function f y x giving the pdf of x i 1 xi x in this study nonparametric density and regression techniques are employed to infer f y x and m x e x i 1 xi x it is seen that under certain regularity and markovian assumptions the asymptotic convergence rate of the nonparametric estimator mn x to the predictor m x is the same as it would have been had the xi s been independently and identically distributed and this rate is optimal in a certain sense consistency can be maintained after differentiability and even the markovian assumptions are abandoned computational and modeling ramifications are explored i claim that my methodology offers an interesting alternative to the popular arma approach

hammerstein system identification with the nearest neighbor algorithm the nonlinear characteristic in a hammerstein system i e a system in which a nonlinear memoryless subsystem and a linear dynamic are connected in a cascade is recovered with the nonparametric nearest neighbor regression estimate the a priori information is nonparametric both the nonlinear characteristic and the impulse response are completely unknown and can be of any form local and global properties of the estimate are examined whatever the probability density of the input signal the estimate converges at every continuity point of the characteristic as well as in the global sense we derive the asymptotic bias and variance of the proposed estimate as a result the optimal rate of convergence is established that additionally is independent of the shape of the input density results of numerical simulations are also presented

the uniqueness of plethystic factorisation we prove that a plethysm product of two schur functions can be factorised uniquely and classify homogeneous and indecomposable plethysm products

on the irreducibility of irreducible characters of simple lie algebras we establish an irreducibility property for the characters of finite di mensional irreducible representations of simple lie algebras or simple algebraic groups over the complex numbers i e that the characters of irreducible represen tations are irreducible after dividing out by generalized weyl denominator type factors for sl r the irreducibility result is the following let a1 a2 ar 1 0 be the highest weight of an irreducible rational representation vof sl r as sume that the integers a1 r 1 a2 r 2 ar 1 1 are relatively prime then the character of vis strongly irreducible in the following sense for any natural number d the function g d g sl r c is irreducible in the ring of regular functions of sl r c

proprietes de convergence presque complete du predicteur a noyau let z n be a mixing process which is valued in mathbb e subset mathbb r q g be a real measurable function defined on mathbb e s and k be two positive integers we suppose the existence of a function r satisfying r e g z n s z n k 1 z n n n k and estimate the function r from a sequence z i i 1 n by r n with r n u frac sum limits i k n s g z i s k u z i k 1 cdots z i h n 1 sum limits i k n s k u z i k 1 cdots z i h n 1 forall u in mathbb e k where k is a kernel of kq and h n h n 0 we give various conditions on both the sequences h n and the sequence n which is associated with z n for the two following properties uniform complete convergence to r for the functional estimator r n and complete convergence to 0 for the real random variable r n z n k 1 z n r zn k 1 z n this last result concerns the predictor r n z n k 1 z n of g z n s from z i i 1 n when the process z n is stationary and markovian of order k

relativistic chasles theorem and the conjugacy classes of the inhomogeneous lorentz group this work is devoted to the relativistic generalization of chasles theorem namely to the proof that every proper orthochronous isometry of minkowski spacetime which sends some point to its chronological future is generated through the frame displacement of an observer which moves with constant acceleration and constant angular velocity the acceleration and angular velocity can be chosen either aligned or perpendicular and in the latter case the angular velocity can be chosen equal or smaller than the acceleration we start reviewing the classical euler s and chasles theorems both in the lie algebra and group versions we recall the relativistic generalization of euler s theorem and observe that every infinitesimal transformation can be recovered from information of algebraic and geometric type the former being identified with the conjugacy class and the latter with some additional geometric ingredients the screw axis in the usual non relativistic version then the proper orthochronous inhomog

unique decomposition of tensor products of irreducible representations of simple algebraic groups we show that a tensor product of irreducible finite dimensional representations of a simple lie algebra over a field of characteristic zero determines the individual constituents uniquely this is analogous to the uniqueness of prime factorisation of natural numbers

robust nonparametric regression with simultaneous scale curve estimation on considere l estimation non parametrique simultanee par des lissages de type m l approche est etroitement liee a l estimation m simultanee de position et d echelle

necessary and sufficient conditions for the pointwise convergence of nearest neighbor regression function estimates where v 1 v is a given probability vector and xt x yl x x x y x is a permutation of x1 i71 x y according to increasing values of ilxi x i x e r a when ixi xll h x j x l but i 1 and some constant c 0

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

asymptotic distribution of robust estimators for nonparametric models from mixing processes stable url http links jstor org sici sici 0090 5364 28199006 2918 3a2 3c891 3aadoref 3e2 0 co 3b2 xthe annals of statistics is currently published by institute of mathematical statistics your use of the jstor archive indicates your acceptance of jstor s terms and conditions of use available athttp www jstor org about terms html jstor s terms and conditions of use provides in part that unless you have obtainedprior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content inthe jstor archive only for your personal non commercial use please contact the publisher regarding any further use of this work publisher contact information may be obtained athttp www jstor org journals ims html each copy of any part of a jstor transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission the jstor archive is a trusted digital repository providing for long term preservation and access to leading academicjournals and scholarly literature from around the world the archive is supported by libraries scholarly societies publishers and foundations it is an initiative of jstor a not for profit organization with a mission to help the scholarly community takeadvantage of advances in technology for more information regarding jstor please contact support jstor org http www jstor orgmon mar 10 00 58 58 2008