in vivo estimation of the glenohumeral joint rotation center from scapular bony landmarks by linear regression in this paper a method is described for in vivo prediction of the glenohumeral joint rotation center gh r necessary for the construction of a humerus local coordinate system in shoulder kinematic studies the three dimensional positions of five scapula bony landmarks as well as a large number of data points on the surface of the glenoid and humeral head were collected at 36 sets of cadaver scapulae and adjacent humeri the position of gh r in each scapula was estimated by mathematically fitting spheres to the glenoid and humeral head gh r prediction from scapula geometry parameters by linear regression resulted in a rmse between measured and predicted gh r of 2 32 mm for the x coordinate 2 69 mm for the y coordinate and 3 04 mm for the z coordinate application in vivo revealed a random humerus orientation error due to measurement inaccuracies of 1 35 0 29 and 1 26 degrees standard deviation per rotation angle the estimated total humerus orientation error including the offset error due to the regression model inaccuracy was 2 86 0 84 and 2 69 degrees standard deviation as these errors were about 15 and 20 of respectively the intra and inter subject variability of the humerus orientations measured it is concluded that the method described in this paper allows for an adequate construction of a humerus local coordinate system

schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

tests of equal forecast accuracy and encompassing for nested models we examine the asymptotic and finite sample properties of tests for equal forecast accuracy and encompassing applied to 1 step ahead forecasts from nested linear models we first derive the asymptotic distributions of two standard tests and one new test of encompassing and provide tables of asymptotically valid critical values monte carlo methods are then used to evaluate the size and power of tests of equal forecast accuracy and encompassing the simulations indicate that post sample tests can be reasonably well sized of the post sample tests considered the encompassing test proposed in this paper is the most powerful we conclude with an empirical application regarding the predictive content of unemployment for inflation

asymmetricalgebraicriccatiequation ahomeomorphicparametrizationofthesetof solutions abstract in this paper asymmetric algebraic riccati equations are analyzed in particular we derive a new parametrization of the set of solutions generalizing on the symmetric case the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related feedback matrices moreover the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo hamiltonian matrix associated with the equation we finally show that also the newly introduced parametrization is given by a homeomorphic map

one two sided residue interpolation for matrix valuedh2 functions with symmetries abstract the two sided lagrange sylvester interpolation problem introduced by ball gohberg and rodman is solved in the framework ofh2functions when some symmetry constraints are added

the effect of muscle loading on the kinematics of in vitro glenohumeral abduction this in vitro study evaluated the effects of four different muscle loading ratios on active glenohumeral joint abduction eight cadaveric shoulders were tested using a shoulder simulator designed to reproduce unconstrained abduction of the humerus via computer controlled pneumatic actuation forces were applied to cables that were sutured to tendons or fixed to bone to simulate loading of the supraspinatus subscapularis infraspinatus teres minor and anterior middle and posterior deltoid muscles four sets of muscle loading ratios were employed based on 1 equal loads 2 average physiological cross sectional areas pcsas 3 constant values of the product of electromyographic emg data and pcsas and 4 variable ratios of the emg and pcsa data which changed as a function of abduction angle the investigator generated passive motions with no muscle loads simulated repeatability was quantified by five successive trials of the passive and simulated active motions there was improved repeatability in the simulated active motions versus passive motions significant for abduction angles less than 40 degrees p 0 02 no difference was found in the repeatability of the four different muscle loading ratios for simulated active motions p0 067 for all angles the improved repeatability of active over passive motion suggests simulated active motion should be employed for in vitro simulations of shoulder motion

numerical stability properties of a qr based fast least squares algorithm the numerical stability of a recent qr based fast least squares algorithm is established from a backward stability perspective a stability domain approach applicable to any least squares algorithm constructed from the set of reachable states in exact arithmetic is presented the error propagation question is shown to be subordinate to a backward consistency constraint which requires that the set of numerically reachable variables be contained within the stability domain associated to the algorithm this leads to a conceptually lucid approach to the numerical stability question which frees the analysis of stationary assumptions on the filtered sequences and obviates the tedious linearization methods of previous approaches moreover initialization phenomena and considerations related to poorly exciting inputs admit clear interpretations from this perspective the algorithm under study is proved in contrast to many fast algorithms to be minimal

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

structured invariant spaces of vector valued rational functions hermitian matrices and a generalization of the lohvidov laws abstract finite dimensional indefinite inner product spaces of vector valued rational functions which are 1 invariant under the generalized backward shift and 2 subject to a structural identity and subspaces and superspaces thereof are studied the theory of these spaces is then applied to deduce a generalization of a pair of rules due to lohvidov for evaluating the inertia of certain subblocks of hermitian toeplitz and hermitian hankel matrices the connecting link rests on the identification of a hermitian matrix as the gram matrix of a space of vector valued functions of the type considered in the first part of the paper corresponding generalizations of another pair of theorems by lohvidov on the rank of certain subblocks of non hermitian teoplitz and non hermitian hankel matrices are also stated but the proofs will be presented elsewhere

caratheodory fejer interpolation in the ball abstract we use the theory of reproducing kernel hilbert spaces to solve a caratheodory fejer interpolation problem in the class of schur multipliers of the reproducing kernel hilbert space of functions analytic in the unit ball of c n with reproducing kernel 1 1 1 n z k w k

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural

on bitangential interpolation in the time varying setting for hilbert schmidt operators the continuous time case abstract the hilbert space of lower triangular hilbert schmidt operators on the real line is a natural analogue of the hardy space of a half plane where the complex numbers are now replaced by matrix valued functions one can associate with a bounded operator its values at a matrix valued function see ballet al oper theory adv appl 56 1992 52 89 and this allows see ballet al integral equations operator theory20 1994 1 43 to define and solve the analogue of the two sided nudelman interpolation problem for bounded operators which form an analogue ofh c in this paper we consider the two sided interpolation problem with a hilbert schmidt norm constraint rather than the more common operator norm constraint on the interpolant

on a new class of structured reproducing kernel spaces abstract a class of reproducing kernel spaces with reproducing kernels of the form k j j with p a a is characterized in terms of invariance under a pair of generalized shift operators and a structural identity this incorporates a characterization of de branges for the line case and a later analogue due to ball for the circle case as well as many other possibilities by specializing the choice of these results also permit the extension of some earlier characterizations by the authors of finite dimensional spaces with reproducing kernels of the form given above to the infinite dimensional case the non hermitian case is also considered

bitangential interpolation problems for symmetric rational matrix functions abstract we develop the zero pole structure of rational matrix functions s that satisfy an identity of the form s t v s v for some square matrix v for which v vt where 1 as an application we describe the set of symmetric or antisymmetric solutions of a set of bitangential interpolation conditions solutions of bitangential interpolation conditions satisfying other types of symmetries are also discussed

the schur algorithm and reproducing kernel hilbert spaces in the ball abstract using reproducing kernel hilbert spaces methods we develop a schur type algorithm for a subclass of the functions analytic and contractive in the ball we also consider the nevanlinna pick interpolation problem in that class

pairs of functions with indefinite pick matrices results of factorization type are proved that characterize pairs of functions whose pick matrices have not more than a prescribed number of negative eigenvalues these results are in turn used to describe functions having caratheodory matrices with bounded number of negative eigenvalues

operators affiliated to the free shift on the free hardy space abstract the smirnov class for the classical hardy space is the set of ratios of bounded analytic functions in the open complex unit disk with outer denominators this definition extends naturally to the commutative and non commutative multi variable settings of the drury arveson space and the full fock space over c d identifying the fock space with the free multi variable hardy space of non commutative or free holomorphic functions in a non commutative open unit ball in several matrix variables we prove that any closed densely defined operator affiliated to the right free multiplier algebra of the full fock space acts as right multiplication by a non commutative function in the right free smirnov class and analogously replacing right with left

using out of sample mean squared prediction errors to test the martingale difference hypothesis abstract we consider using out of sample mean squared prediction errors mspes to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable under the null of no predictability the population mspe of the null no change model equals that of the linear alternative we show analytically and via simulations that despite this equality the alternative model s sample mspe is expected to be greater than the null s for rolling regression estimators of the alternative model s parameters we propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample mspe of the alternative model our simulations indicate that our proposed procedure works well

gleason s problem and homogeneous interpolation in hardy and dirichlet type spaces of the ball we solve gleason s problem in the reproducing kernel hilbert spaces with reproducing kernels 1 1 1nzjwj r for real r 0 and their counterparts for r 0 and study the homogeneous interpolation problem in these spaces

backward shift operator and finite dimensional de branges rovnyak spaces in the ball recently bolotnikov and rodman characterized finite dimensional backward shift invariant subspaces of the arveson space in this note we study finite dimensional backward shift invariant hilbert spaces contractively included in the arveson space to that purpose we redefine in an appropriate way the backward shift operators in terms of power series expansions

j unitary preserving automorphisms of rational matrix functions state space theory interpolation and factorization abstract let glm r be the multiplicative group of c m m valued rational functions of one complex variable z with determinant not vanishing identically we analyze general inner automorphisms of glm r that preserve the set of matrix functions whose values are unitary with respect to an indefinite scalar product for real or unimodular values of z the analysis is based on state space representations in particular homogeneous interpolation problems are studied for the rational matrix functions associated with such a general inner automorphism we also develop results on minimal factorizations within the group associated with j unitary preserving generalized inner automorphism

boundary interpolation in the ball we solve a boundary interpolation problem in the reproducing kernel hilbert space of functions analytic in the unit ball of cn with reproducing kernel 1 1 1nzkwk we introduce the notion of brune factor or blaschke potapov factor of the third kind in this setting

geometry parameters for musculoskeletal modelling of the shoulder system a dynamical finite element model of the shoulder mechanism consisting of thorax clavicula scapula and humerus is outlined the parameters needed for the model are obtained in a cadaver experiment consisting of both shoulders of seven cadavers in this paper in particular the derivation of geometry parameters from the measurement data is described the results for one cadaver are presented as a typical example morphological structures are modelled as geometrical forms parameters describing this form are estimated from 3 d position coordinates of a large number of datapoints on the morphological structure using a least squares criterion muscle and ligament attachments are represented as a plane or as a curved line muscle paths are determined by a geometrical form of the bony contour around which the muscle is wrapped muscle architecture is determined by the distribution of muscle bundles over the attachment area mapping the distribution of the origin to the insertion joint rotation centers are derived from articular surfaces hence muscle moment arms can be calculated the result of this study is a set of parameters for each cadaver describing very precisely the geometry of the shoulder mechanism this set allows positioning of muscle force vectors a posteriori and recalculation of position coordinates and moment arms for any position of the shoulder

uniformly more powerful one sided tests for hypotheses about linear inequalities let x have a multivariate p dimensional normal distribution p 2 with unknown mean and known nonsingular covariance consider testing h 0 b i 0 for some i 1 k versus h 1 b i 0 for all i 1 k where b 1 b k k 2 are known vectors that define the hypotheses for any 0 1 2 we construct a size test that is uniformly more powerful than the size a likelihood ratio test lrt the proposed test is an intersection union test other authors have presented uniformly more powerful tests under restrictions on the covariance matrix and on the hypothesis being tested our new test is uniformly more powerful than the lrt for all known nonsingular covariance matrices and all hypotheses so our results show that in a very general class of problems the lrt can be uniformly dominated

asymptotics for out of sample tests of granger causality abstract this paper presents analytical monte carlo and empirical evidence concerning out of sample tests of granger causality the environment is one in which the relative predictive ability of two nested parametric regression models is of interest results are provided for three statistics a regression based statistic suggested by granger and newbold 1977 forecasting economic time series academic press inc london a t type statistic comparable to those suggested by diebold and mariano 1995 comparing predictive accuracy journal of business and economic statistics 13 253 263 and west 1996 asymptotic inference about predictive ability econometrica 64 1067 1084 and an f type statistic akin to theil s u since the asymptotic distributions under the null are nonstandard tables of asymptotically valid critical values are provided monte carlo evidence supports the theoretical results an empirical example evaluates the predictive content of the chicago fed national activity index for growth in industrial production and core pce based inflation

on applications of schauderʼs fixed point theorem for the solution of the non symmetric algebraic riccati equation abstract in this article we give sufficient conditions for the existence of contractive solutions for the non symmetric algebraic riccati equation the conditions are given in terms of the matrix of the coefficients only we also provide sufficient conditions for unique contractive solution which is a unique minimal norm solution the results are generalized to contractive solutions with respect to generalized unit matrix balls

two sided residue interpolation in matrix h2 spaces with symmetries conformal conjugate involutions we consider two sided and one sided residue interpolation problem in classes of matrix valued hardy functions with various symmetries these symmetries are defined in terms of conformal conjugate involutions of the unit disk problems with additional norm restrictions are studied as well applications are made to two point interpolation

tangential interpolation problems for a class of automorphic matrix functions tangential interpolation problems are studied for matrix valued functions of class r analytic in the upper half plane with non negative imaginary part which are invariant under a linear fractional transformation of finite order

two sided tangential interpolation with real rational units in h the problem of computing units in rh that satisfy ball gohberg rodman two sided tangential interpolation conditions over the open right half complex plane is considered we first show that every unit in rh can be written up to left multiplication by an orthogonal matrix as a finite product of positive real functions in rh with invertible value at this factorization is used to recast interpolation conditions on units as coupled positive real interpolation problems for the factors an algebraic necessary and sufficient condition for the existence of solutions and a parameterization of all solutions when one exists are given we introduce a multivariable parity interlacing property for left interpolation data and present an algorithm to compute units the algorithm involves a line search and is guaranteed to terminate in a finite number of operations when the data set has parity interlacing property as an application strong stabilization of lti plants is discussed a procedure to construct a stable stabilizing controller is given the results are illustrated with a simple mimo example a necessary and sufficient condition characterizing all real rational units that satisfy tangential interpolation conditions is given an algorithm to compute units for left interpolation is presented

caratheodory fejer interpolation in the ball with mixed derivatives we use reproducing kernel hilbert space methods to solve a caratheodory fejer type interpolation problem with mixed derivatives corresponding to a so called lower inclusive set in the class of schur multipliers

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

a unified approach to structured covariances fast generalized sliding window rls recursions for arbitrary basis this paper extends the existing fast rls recursions originally intended to exponentially windowed problems for general models to a generalized sliding window formulation gswrls from a matrix algebra perspective we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast gswrls calculates these rank factors in a fast manner the recursions hold regardless of the first order data structure induced and show that fast fixed order and order recursive rls algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models showing that efficient representations of their inverse covariances are not limited to factor circulants but rather constructed from any arbitrary operator these bezoutians usually expressed via reproducing kernel relations can be represented exactly in matrix form along with a precise correspondence to variables of a gswrls as a fallout we obtain a vector relation stating the so called minimality property for extended models and windows as opposed to analogous generating function arguments normally seen in original approaches these results pave the way to a more general framework of polynomial vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials this has further impact on several signal processing applications including superfast realization of equalizers in communications scenarios

a predictability test for a small number of nested models we introduce quasi likelihood ratio tests for one sided multivariate hypotheses to evaluate the null that a parsimonious model performs equally well as a small number of models which nest the benchmark the limiting distributions of the test statistics are non standard for critical values we consider i bootstrapping and ii simulations assuming normality of the mean square prediction error difference the proposed tests have good size and power properties compared with existing equal and superior predictive ability tests for multiple model comparison we apply our tests to study the predictive ability of a phillips curve type for the us core inflation

existence and uniqueness of contractive solutions of some riccati equations abstract in this paper we establish criteria for the existence and uniqueness of contractive solutions k of the riccati equation kbk ka dk c 0 under the assumption that the spectra of a and d are disjoint

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

a characterization of all the static stabilizing controllers for lti systems abstract in this article we give a complete characterization geared towards a parametrization of all the static feedbacks of a given lti system triplet in terms of the coefficients of some reduced order riccati equation with simultaneously stabilizing solutions and structural constraints on the coefficients

the structure of inner multipliers on spaces with complete nevanlinna pick kernels let k be the reproducing kernel for a hilbert space h k of analytic functions on bd the open unit ball in cd d 1 k is called a complete np kernel if k0 1 and if 1 1 k z is positive definite on bd bd let d be a separable hilbert space and consider h k d h k d and think of it as a space of d valued h k functions a theorem of mccullough and trent j funct anal 178 2000 226 249 partially extends the beurling lax halmos theorem for the invariant subspaces of the hardy space h2 d they show that if k is a complete np kernel and if d is a separable hilbert space then for any scalar multiplier invariant subspace m of h k d there exists an auxiliary hilbert space e and a multiplication operator h k e h k d such that is a partial isometry and m h k e such multiplication operators are called inner multiplication operators and they satisfy the orthogonal projection onto m in this paper we shall show that for many interesting complete np kernels the analogy with the beurling lax halmos theorem can be strengthened we show that for almost every z bd the nontangential limit z of the multiplier bd b e d associated with an inner multiplication operator is a partial isometry and that rank z is equal to a constant almost everywhere the result applies to certain weighted dirichlet spaces and to the space h2d which is determined by the kernel k z 11 z d z bd in particular our result implies that the curvature invariant of arveson proc natl acad sci usa96 1999 11 096 11 099 of a pure contractive hilbert module of finite rank is an integer this answers a question of w arveson proc natl acad sci usa96 1999 11096 11099

parametrization of all minimal square spectral factors abstract two different parametrizations of minimal square spectral factors are given these parametrizations extend recent results by picci and pinzoni since they characterize spectral factors without specification on the zero or pole structure

on the tangential interpolation problem for functions the aim of this paper is to solve a matrix valued version of the nevanlinna pick interpolation problem for hi functions we reduce this prob lem to a nevanlinna pick interpolation problem for schur functions and obtain a linear fractional transformation which describes the set of all solutions

the glenohumeral joint rotation centre in vivo within the framework of the current call for standardization in upper extremity research three methods to determine the glenohumeral joint rotation centre in vivo were tested therefore subjects performed humeral movements while a 3d electromagnetic tracking device registered the motion of the humerus with respect to the scapula for the first method to estimate the glenohumeral joint rotation centre five scapular bony landmarks served as input to regression equations the second method fitted a sphere through the humeral position data and the third method calculated the rotation centre determining an optimal helical axis the experiment consisted of two parts at first one subject was measured 10 times subsequently one observer measured 10 subjects twice and another observer measured these subjects once the first part of the experiment demonstrated that all methods are capable to reproduce the rotation centre within 4mm but the location of the centre differed significantly between methods p 0 001 the second part showed that inter and intra observer reliability was sufficiently for the sphere fitting method and for the helical axes method the two observations of one observer differed significantly p 0 008 using the regression method the authors prefer the helical axes method it is a reliable and valid method which can be applied in movement registration of healthy subjects and patients with a shoulder endoprosthesis it can be applied in hinge joints to determine a rotation axis instead of a rotation centre which is desirable in standardized upper extremity research and calculation time is short

past input reconstruction in fast least squares algorithms this paper solves the following problem given the computed variables in a fast least squares prediction algorithm determine all past input sequences that would have given rise to the variables in question this problem is motivated by the backward consistency approach to numerical stability in this algorithm class the set of reachable variables in exact arithmetic is known to furnish a stability domain our problem is equivalent to a first and second order interpolation problem introduced by mullis and roberts 1976 and studied by others our solution differs in two respects first relations to classical interpolation theory are brought out which allows us to parametrize all solutions by products of our formulation are correct necessary and sufficient conditions for the problem to be solvable in contrast to previous works whose claimed sufficient conditions are shown to fall short second our solution obtains any valid past input as the impulse response of an appropriately constrained orthogonal filter whose rotation parameters derive in a direct manner from the computed variables in a fast least squares prediction algorithm formulas showing explicitly the form of all valid past inputs should facilitate the study of what past input perturbation is necessary to account for accumulated arithmetic errors in this algorithm class this in turn is expected to have an impact in studying accuracy aspects in fast least squares algorithms

complete nevanlinna pick kernels abstract we give a new treatment of quiggin s and mccullough s characterization of complete nevanlinna pick kernels we show that a kernel has the matrix valued nevanlinna pick property if and only if it has the vector valued nevanlinna pick property we give a representation of all complete nevanlinna pick kernels and show that they are all restrictions of a universal complete nevanlinna pick kernel

a gleason kahane żelazko theorem for the dirichlet space abstract we show that every linear functional on the dirichlet space that is non zero on nowhere vanishing functions is necessarily a multiple of a point evaluation continuity of the functional is not assumed as an application we obtain a characterization of weighted composition operators on the dirichlet space as being exactly those linear maps that send nowhere vanishing functions to nowhere vanishing functions we also investigate possible extensions to weighted dirichlet spaces with superharmonic weights as part of our investigation we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane

on the existence and construction of solutions to the partial lossless inverse scattering problem with applications to estimation theory the partial lossless inverse scattering plis problem which plays a fundamental role in the solution of a alpha stationary estimation problems is considered some open problems connected with this theory are treated necessary and sufficient conditions for a hermitian matrix to be positive say a covariance matrix are derived in terms of its alpha stationary wave representation a generalization of the recursive construction of plis solutions is proposed it is shown that each invariant subspace of the backward shift operator has a corresponding solution of the plis problem provided the operator that generalized the classical pick matrix is positive definite it is also shown that under fairly general conditions all solutions of the h sup infinity type are essentially obtained in this way and a characterization of the residual wave quantities generated by the scatterer is given stochastic models and forward and backward order recursive innovation filters are derived

two sided interpolation for matrix functions with entries in the hardy space abstract the two sided lagrange sylvester interpolation problem is solved in the framework of h2 functions the extra hilbert space structure allows us to give self contained and independent arguments

approximately normal tests for equal predictive accuracy in nested models abstract forecast evaluation often compares a parsimonious null model to a larger model that nests the null model under the null that the parsimonious model generates the data the larger model introduces noise into its forecasts by estimating parameters whose population values are zero we observe that the mean squared prediction error mspe from the parsimonious model is therefore expected to be smaller than that of the larger model we describe how to adjust mspes to account for this noise we propose applying standard methods west k d 1996 asymptotic inference about predictive ability econometrica 64 1067 1084 to test whether the adjusted mean squared error difference is zero we refer to nonstandard limiting distributions derived in clark and mccracken 2001 tests of equal forecast accuracy and encompassing for nested models journal of econometrics 105 85 110 2005a evaluating direct multistep forecasts econometric reviews 24 369 404 to argue that use of standard normal critical values will yield actual sizes close to but a little less than nominal size simulation evidence supports our recommended procedure

factorizations induced by complete nevanlinna pick factors abstract we prove a factorization theorem for reproducing kernel hilbert spaces whose kernel has a normalized complete nevanlinna pick factor this result relates the functions in the original space to pointwise multipliers determined by the nevanlinna pick kernel and has a number of interesting applications for example for a large class of spaces including dirichlet and drury arveson spaces we construct for every function f in the space a pluriharmonic majorant of f 2 with the property that whenever the majorant is bounded the corresponding function f is a pointwise multiplier

some impossibility theorems in econometrics with applications to structural and dynamic models general characterizations of valid confidence sets and tests in problems which involve locally almost unidentified lau parameters are provided and applied to several econo metric models two types of inference problems are studied i inference about parame ters which are not identifiable on certain subsets of the parameter space and ii inference about parameter transformations with discontinuities when a lau parameter or parametric function has an unbounded range it is shown under general regularity conditions that any valid confidence set with level 1 a for this parameter must be unbounded with probability close to 1 a in the neighborhood of nonidentification subsets and will have a nonzero probability of being unbounded under any distribution compatible with the model no valid confidence set which is almost surely bounded does exist these properties hold even if identifying restrictions are imposed similar results also obtain for parameters with bounded ranges consequently a confidence set which does not satisfy this characterization has zero coverage probability level this will be the case in particular for wald type confidence intervals based on asymptotic standard errors furthermore wald type statistics for testing given values of a lau parameter cannot be pivotal functions i e they have distributions which depend on unknown nuisance param eters and even cannot be usefully bounded over the space of the nuisance parameters these results are applied to several econometric problems inference in simultaneous equations instrumental variables iv regressions linear regressions with autoregressive errors inference about long run multipliers and cointegrating vectors for example it is shown that standard asymptotically justified confidence intervals based on iv estimators such as two stage least squares and the associated standard errors have zero coverage probability and the corresponding t statistics have distributions which cannot be bounded by any finite set of distribution functions a result of interest for interpreting iv regressions with weak instruments furthermore expansion methods e g edgeworth expansions and bootstrap techniques cannot solve these difficulties finally in a number of cases where wald type methods are fundamentally flawed e g iv regressions with poor instruments it is observed that likelihood based methods e g likelihood ratio tests and confidence sets combined with projection techniques can easily yield valid tests and confidence sets

the relationship between two different mechanical cost functions and muscle oxygen consumption abstract inverse dynamic models often use cost functions to solve the load sharing problem although it is often assumed that energy is minimised most cost functions are based on mechanically related measures like muscle force or stress the aim of this study was to analyse the relationships of two cost functions with experimentally determined data on muscle energy consumption four subjects performed isometric contractions generating combinations of elbow flexion extension and pro supination moments muscle oxygen consumption v o 2 of the m biceps breve m biceps longum m brachioradialis and m triceps laterale was measured with near infrared spectroscopy both cost functions were implemented into an existing inverse dynamic shoulder and elbow model and the individual cost values per muscle were calculated normalised and subsequently compared to experimental v o 2 values the minimum stress cost function led to a good correspondence between v o 2 and cost for the m triceps laterale but for the flexor muscles cost was significantly lower a newly proposed energy related cost function showed however a far better correspondence the inclusion of a linear term and muscle mass in the new criterion led model results to correspond better to experimental results the energy related cost function appeared to be a better measure for muscle energy consumption than the stress cost function and led to more realistic predictions of muscle activation

on a bitangential interpolation problem for contractive valued functions on the unit ball we solve the bitangential interpolation problem with a finite number of interpolation nodes for a multivariable analogue of the schur class consisting of matrix valued analytic functions on the ball the interpolation conditions are formulated via a generalized functional calculus with operator argument thereby generalizing in a compact way the simple first order interpolation conditions considered for this class of functions in earlier work the description of all solutions is given via a redheffer transform whose entries are given explicitly in terms of the interpolation data

multichannel stable systems that extend the partial impulse response matrices this paper addresses the problem of identifying the class of all multichannel stable system transfer functions that extend the given partial impulse response matrix sequence this is achieved by making use of the left and right schur recursion algorithms for bounded matrix functions and in this context the classical pade approximations that are also stable are shown to be a special case of this general formulation further the theory developed here is utilized to generate multichannel non minimum phase optimal rational approximations to multichannel nonrational systems from their partial impulse response matrix sequence

invariant subspaces and nevanlinna pick kernels abstract a theorem of beurling lax halmos represents a subspace m of h2 c d the hardy space of analytic functions with values in the hilbert space e and square summable power series invariant for multiplication by z as h2 f where f is a subspace of e and is an inner function with values in l f e when the hardy space is replaced by the hilbert space h k determined by a nevanlinna pick kernel k such as the dirichlet kernel or the row contraction kernel on the ball in c d the blh theorem survives with f an auxiliary hilbert space and a l f e valued function which is inner in the sense that the operator m of multiplication by is a partial isometry under mild additional hypotheses when e c mz the operator of multiplication by z is cellularly indecomposable and has the codimension one property however if m is invariant for mz m mz m need not be a cyclic subspace for mz restricted to m

a consistent test for nonlinear out of sample predictive accuracy abstract in this paper we draw on both the consistent specification testing and the predictive ability testing literatures and propose an integrated conditional moment type predictive accuracy test that is similar in spirit to that developed by bierens j econometr 20 1982 105 econometrica 58 1990 1443 and bierens and ploberger econometrica 65 1997 1129 the test is consistent against generic nonlinear alternatives and is designed for comparing nested models one important feature of our approach is that the same loss function is used for in sample estimation and out of sample prediction in this way we rule out the possibility that the null model can outperform the nesting generic alternative model it turns out that the limiting distribution of the icm type test statistic that we propose is a functional of a gaussian process with a covariance kernel that reflects both the time series structure of the data as well as the contribution of parameter estimation error as a consequence critical values that are data dependent and cannot be directly tabulated one approach in this case is to obtain critical value upper bounds using the approach of bierens and ploberger econometrica 65 1997 1129 here we establish the validity of a conditional p value method for constructing critical values the method is similar in spirit to that proposed by hansen econometrica 64 1996 413 and inoue econometric theory 17 2001 156 although we additionally account for parameter estimation error in a series of monte carlo experiments the finite sample properties of three variants of the predictive accuracy test are examined our findings suggest that all three variants of the test have good finite sample properties when quadratic loss is specified even for samples as small as 600 observations however non quadratic loss functions such as linex loss require larger sample sizes of 1000 observations or more in order to ensure reasonable finite sample performance

on parametrization of all the exact pole assignment state feedbacks for lti systems in this technical note we provide a parametrization of all the exact pole assignment state feedbacks for lti systems when the set of poles to be assigned contains sufficient number of real eigenvalues we also refute a recent conjecture concerning the explicit form of all the state feedbacks assigning a given set of poles to the closed loop

how to find all roots of complex polynomials by newton s method we investigate newton s method to find roots of polynomials of fixed degree d appropriately normalized we construct a finite set of points such that for every root of every such polynomial at least one of these points will converge to this root under newton s map the cardinality of such a set can be as small as 1 11 d log2d if all the roots of the polynomial are real it can be 1 30 d

the power of tests of predictive ability in the presence of structural breaks this paper presents analytical monte carlo and empirical evidence on the effects of structural breaks on tests for equal forecast accuracy and encompassing we show that out of sample predictive content can be hard to find because out of sample tests are highly dependent on the timing of the predictive ability moreover predictive content is harder to find with some tests than others in power f type tests of equal forecast accuracy and encompassing often dominate t type alternatives based on these results and evidence from an empirical application we conclude that structural breaks under the alternative may explain why researchers often find evidence of in sample but not out of sample predictive content

a transformation method to estimate muscle attachments based on three bony landmarks abstract in order to create musculoskeletal models that can be scalable to different subject specificities the calculation of the exact locations of muscle attachment is required for this purpose a scaling method is presented that estimates muscle attachment locations in homologous segments using three bony landmarks per segment a data set of 17 muscles attachment lines from the shoulders of seven cadavers was used to assess the estimation quality of the scaling method by knowing from the cadaver data the measured location of the muscles attachment lines it is possible to assess the quality of the estimated ones the scaling results showed an overall mean rmse for the scapula and humerus muscles of 7 6 and 11 1 mm respectively these results were then analyzed with an upper extremity model in order to compute the influence of the rmse in glenohumeral elevation muscle moment arms in the scapular plane the results presented were considered to be satisfactory among other error contributors the inter and intra subject variability should be further investigated along with the sensitivity of a biomechanical model to these error variations

measuring muscle and joint geometry parameters of a shoulder for modeling purposes abstract an extensive set of muscle and joint geometry parameters was measured of the right shoulder of an embalmed male for all muscles the optimal muscle fiber length was determined by laser diffraction measurements of sarcomere length in addition tendon length and physiological cross sectional area were determined the parameter set was needed to enhance the reliability of a computer model of the shoulder van der helm 1994a van der helm 1994b journal of biomechanics 27 527 550 551 569 with the model an abduction of the arm was simulated in seven positions at 30 intervals in each of the simulated arm positions actual sarcomere lengths were calculated from the lengths of 104 muscle elements distributed over 16 shoulder muscles for most muscle elements the simulated abduction appeared to take place within the sarcomere length range in which the muscle elements can exert force the muscle elements can then act on the ascending limb as well as on the plateau and on the descending limb of the relative force length curves of sarcomeres the produced data set is not only important for the refinement of shoulder modeling but also for functional analyses of shoulder movements in general