generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

generalized n dimensional biomechanical field analysis using statistical parametric mapping a variety of biomechanical data are sampled from smooth n dimensional spatiotemporal fields these data are usually analyzed discretely by extracting summary metrics from particular points or regions in the continuum it has been shown that in certain situations such schemes can compromise the spatiotemporal integrity of the original fields an alternative methodology called statistical parametric mapping spm designed specifically for continuous field analysis constructs statistical images that lie in the original biomechanically meaningful sampling space the current paper demonstrates how spm can be used to analyze both experimental and simulated biomechanical field data of arbitrary spatiotemporal dimensionality firstly 0 1 2 and 3 dimensional spatiotemporal datasets derived from a pedobarographic experiment were analyzed using a common linear model to emphasize that spm procedures are practically identical irrespective of the data s physical dimensionality secondly two probabilistic finite element simulation studies were conducted examining heel pad stress and femoral strain fields respectively to demonstrate how spm can be used to probe the significance of field wide simulation results in the presence of uncontrollable or induced modeling uncertainty results were biomechanically intuitive and suggest that spm may be suitable for a wide variety of mechanical field applications spm s main theoretical advantage is that it avoids problems associated with a priori assumptions regarding the spatiotemporal foci of field signals spm s main practical advantage is that a unified framework encapsulated by a single linear equation affords comprehensive statistical analyses of smooth scalar fields in arbitrarily bounded n dimensional spaces

globally efficient non parametric inference of average treatment effects by empirical balancing calibration weighting the estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks existing globally efficient estimators require non parametric estimation of a propensity score function an outcome regression function or both but their performance can be poor in practical sample sizes without explicitly estimating either functions we consider a wide class calibration weights constructed to attain an exact three way balance of the moments of observed covariates among the treated the control and the combined group the wide class includes exponential tilting empirical likelihood and generalized regression as important special cases and extends survey calibration estimators to different statistical problems and with important distinctions global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators the results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function we also propose a consistent estimator for the efficient asymptotic variance which does not involve additional functional estimation of either the propensity score or the outcome regression functions the proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function

bootstrap confidence bands for regression curves and their derivatives confidence bands for regression curves and their first p derivatives are obtained via local pth order polynomial estimation the method allows for multiparameter local likelihood estimation as well as other unbiased estimating equations as an alternative to the confidence bands obtained by asymptotic distribution theory we also study smoothed bootstrap confidence bands simulations illustrate the finite sample properties of the methodology

freezing and collapse of flexible polymers on regular lattices in three dimensions we analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face centered cubic lattices by means of sophisticated chain growth methods in contrast to the bond fluctuation polymer model in certain parameter ranges where these two conformational transitions were found to merge in the thermodynamic limit we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths the reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here

finite size corrections and scaling dimensions of solvable lattice models an analytic method a general analytic method for calculating finite size corrections central charges and scaling dimensions of solvable lattice models is presented the approach is to solve the special functional equations or inversion identities satisfied by the commuting row transfer matrices of these lattice models at criticality for purposes of illustration the method is applied to calculate the central charge c 4 5 and leading magnetic scaling dimension x 2 15 of hard hexagons these numbers are rational due to special values of rogers dilogarithms

nonparametric estimation of mean functionals with data missing at random abstract this article considers a distribution free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology without parametric modeling of the missing mechanism or the joint distribution kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern a generalization of the method of cheng and wei is verified under the assumption of missing at random asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study the nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study the comparison shows that the proposed nonparametric estimators attain reliable performances in general

semiparametric inference in generalized mixed effects models summary the paper presents a study of the generalized partially linear model including random effects in its linear part we propose an estimator that combines likelihood approaches for mixed effects models with kernel methods following the methodology of hardie and co workers we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model the critical values are estimated by using a bootstrap procedure the asymptotic theory for the methods is provided as are the results of a simulation study these verify the feasibility and the excellent behaviour of the methods for samples of even moderate size the usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in galicia spain

efficient estimation of population level summaries in general semiparametric regression models this article considers a wide class of semiparametric regression models in which interest focuses on population level quantities that combine both the parametric and the nonparametric parts of the model special cases in this approach include generalized partially linear models generalized partially linear single index models structural measurement error models and many others for estimating the parametric part of the model efficiently profile likelihood kernel estimation methods are well established in the literature here our focus is on estimating general population level quantities that combine the parametric and nonparametric parts of the model e g population mean probabilities etc we place this problem in a general context provide a general kernel based methodology and derive the asymptotic distributions of estimates of these population level quantities showing that in many cases the estimates are semiparametric efficient for estimating the population mean with no missing data we s

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

nonparametric benefit risk assessment using marker process in the presence of a terminal event abstractbenefit risk assessment is a crucial step in medical decision process in many biomedical studies both longitudinal marker measurements and time to a terminal event serve as important endpoints for benefit risk assessment the effect of an intervention or a treatment on the longitudinal marker process however can be in conflict with its effect on the time to the terminal event thus questions arise on how to evaluate treatment effects based on the two endpoints for the purpose of deciding on which treatment is most likely to benefit the patients in this article we present a unified framework for benefit risk assessment using the observed longitudinal markers and time to event data we propose a cumulative weighted marker process to synthesize information from the two endpoints and use its mean function at a prespecified time point as a benefit risk summary measure we consider nonparametric estimation of the summary measure under two scenarios i the longitudinal marker is measured inter

estimation of semiparametric models when the criterion function is not smooth we provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated our results extend existing theories such as those of pakes and pollard 1989 andrews 1994a and newey 1994 we also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters we apply our results to two examples a hit rate and a partially linear median regression with some endogenous regressors

critical and multicritical o n models soluble o n models on the square lattice are found via the yang baxter equations in a parameter space of three coupling constants a number of distinct soluble cases are found for each value of n some of these constitute critical or multicritical points in the phase diagram for all solutions the free energy per spin can be determined using the bethe ansatz by studying the finite size corrections at the critical points the critical exponents and the central charge can be found in some cases analytically and failing that numerically by extrapolation of exact results for finite size systems

discretely holomorphic parafermions and integrable loop models we define parafermionic observables in various lattice loop models including examples where no kramers wannier duality holds for a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are discretely holomorphic they satisfy a lattice version of the cauchy riemann equations as long as the boltzmann weights satisfy certain linear constraints in the cases considered the weights then also satisfy the critical yang baxter equations with the spectral parameter being related linearly to the angle of the elementary rhombus

two dimensional o n model in a staggered field nienhuis truncated o n model gives rise to a model of self avoiding loops on the hexagonal lattice each loop having a fugacity of n we study such loops subjected to a particular kind of staggered field w which for n has the geometrical effect of breaking the three phase coexistence linked to the three colourability of the lattice faces we show that at t 0 for w 1 the model flows to the ferromagnetic potts model with q n2 states with an associated fragmentation of the target space of the coulomb gas for t 0 there is a competition between t and w which gives rise to multicritical versions of the dense and dilute loop universality classes via an exact mapping and numerical results we establish that the latter two critical branches coincide with those found earlier in the o n model on the triangular lattice using transfer matrix studies we have found the renormalization group flows in the full phase diagram in the t w plane with fixed n superposing three copies of such hexagonal lattice loop models with staggered fields produces a variety of one or three species fully packed loop models on the triangular lattice with certain geometrical constraints possessing integer central charges 0 c 6 in particular we show that benjamini and schramm s rgb loops have fractal dimension df 3 2

optimal bandwidth choice for density weighted averages abstract this paper characterizes the optimal bandwidth value for estimating density weighted averages statistics that arise in semiparametric estimation methods for index models and models of selected samples based on nonparametric kernel estimators the optimal bandwidth is derived by minimizing the leading terms of mean squared error of the density weighted average the optimal bandwidth formulation is developed by comparison to the optimal pointwise bandwidth of a naturally associated nonparametric estimation problem highlighting the role of sample size and the structure of nonparametric estimation bias the methods are illustrated by estimators of average density density weighted average derivatives and conditional covariances and bandwidth values are calculated for normal designs a simple plug in estimator for the optimal bandwidth is proposed finally the optimal bandwidth for estimating ratios of density weighted averages is derived showing that the earlier optimal formulae can be implemented directly using naturally defined residual values

semi flexible interacting self avoiding trails on the square lattice abstract self avoiding walks self interacting via nearest neighbours isaw and self avoiding trails interacting via multiply visited sites isat are two models of the polymer collapse transition of a polymer in a dilute solution on the square lattice it has been established numerically that the collapse transition of each model lies in a different universality class it has been shown that by adding stiffness to the isaw model a second low temperature phase eventuates and a more complicated phase diagram ensues with three types of transition that meet at a multi critical point for large enough stiffness the collapse transition becomes first order interestingly a phase diagram of a similar structure has been seen to occur in an extended isat model on the triangular lattice without stiffness it is therefore of interest to see the effect of adding stiffness to the isat model we have studied by computer simulation a generalised model of self interacting self avoiding trails on the square lattice with a stiffness parameter added intriguingly we find that stiffness does not change the order of the collapse transition for isat on the square lattice for a very wide range of stiffness weights while at the lengths considered there are clear bimodal distributions for very large stiffness our numerical evidence strongly suggests that these are simply finite size effects associated with a crossover to a first order phase transition at infinite stiffness

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

a new exactly solvable case of an o n model on a hexagonal lattice a new solvable case of o n model on a hexagonal lattice is presented it is shown that the model has a phase transition at n 2 this phase transition can be interpreted as phase transition between percolating and non percolating phases

a practical bayesian framework for backpropagation networks a quantitative and practical bayesian framework is described for learning of mappings in feedforward networks the framework makes possible 1 objective comparisons between solutions using alternative network architectures 2 objective stopping rules for network pruning or growing procedures 3 objective choice of magnitude and type of weight decay terms or additive regularizers for penalizing large weights etc 4 a measure of the effective number of well determined parameters in a model 5 quantified estimates of the error bars on network parameters and on network output and 6 objective comparisons with alternative learning and interpolation models such as splines and radial basis functions the bayesian evidence automatically embodies occam s razor penalizing overflexible and overcomplex models the bayesian approach helps detect poor underlying assumptions in learning models for learning models well matched to a problem a good correlation between generalization ability and the bayesian evidence is obtained

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

efficiency loss caused by linearity condition in dimension reduction linearity sometimes jointly with constant variance is routinely assumed in the context of sufficient dimension reduction it is well understood that when these conditions do not hold blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace surprisingly we discover that even if these conditions do hold using them will bring efficiency loss this paradoxical phenomenon is illustrated through sliced inverse regression and principal hessian directions the efficiency loss also applies to other dimension reduction procedures we explain this empirical discovery by theoretical investigation

order parameters of the dilute a models the free energy and local height probabilities of the dilute a models with borken 2 symmetry are calculated analytically using inversion and corner transfer matrix methods these models possess four critical branches the first two branches provide new realizations of the unitary minimal series and the other two branches give a direct product of this series with an ising model we identify the integrable perturbations which move the dilute a models away from the critical limit generalized order parameters are defined and their critical exponents extracted the associated conformal weights are found to occur on the diagonal of the relevant kac table in an appropriate regime the dilute a3 model lies in the universality class of the ising model in a magnetic field in this case we obtain the magnetic exponent 15 directly without the use of scaling relations

on estimation efficiency of the central mean subspace summary we investigate the estimation efficiency of the central mean subspace in the framework of sufficient dimension reduction we derive the semiparametric efficient score and study its practical applicability despite the difficulty caused by the potential high dimension issue in the variance component we show that locally efficient estimators can be constructed in practice we conduct simulation studies and a real data analysis to demonstrate the finite sample performance and gain in efficiency of the proposed estimators in comparison with several existing methods

critical properties of the izergin korepin and solvable o n models and their related quantum spin chains the central charge of the izergin korepin model the corresponding quantum spin chain and the o n model is calculated analytically via the bethe ansatz the calculation extends a technique recently developed for the zamolodchikov fateev model in addition critical exponents and the central charge for these models are obtained from numerical solutions of bethe ansatz equations for finite systems as a physical application the authors find the exponents v 12 23 and gamma 53 46 for the theta transition of polymers in two dimensions

twicing kernels and a small bias property of semiparametric estimators the purpose of this note is to show how semiparametric estimators with a small bias property can be constructed the small bias property sbp of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based we show that semiparametric estimators based on twicing kernels have the sbp we also show that semiparametric estimators where nonparametric kernel estimation does not affect the asymptotic variance have the sbp in addition we discuss an interpretation of series and sieve estimators as idempotent transformations of the empirical distribution that helps explain the known result that they lead to the sbp in monte carlo experiments we find that estimators with the sbp have mean square error that is smaller and less sensitive to bandwidth than those that do not have the sbp

boundary critical behavior of d 2 self avoiding walks on correlated and uncorrelated vacancies in this paper we present exact results for the critical exponents of interacting self avoiding walks with ends at a linear boundary effective interactions are mediated by vacancies correlated and uncorrelated on the dual lattice by choosing different boundary conditions several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the mathcal o n 1 model in particular the problem of boundary exponents at the point is fully solved and implications for point universality are discussed the surface crossover exponent at the special transition of noninteracting self avoiding walks is also interpreted in terms of percolation dimensions

a scaling theory of the collapse transition in geometric cluster models of polymers and vesicles much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk polygon and animal models the crossover exponent phi has been of special interest and sometimes is assumed to obey the relation 2 alpha 1 phi with the alpha the canonical thermodynamic exponent that characterizes the divergence of the specific heat the reasons for the validity of this relation are not widely known the authors present a scaling theory of collapse transitions in such models the free energy and canonical partition functions have finite length scaling forms whilst the grand partition function has a tricritical scaling form the link between the grand and canonical ensembles leads to the above scaling relation they then comment on the validity of current estimates of the crossover exponent for interacting self avoiding walks in two dimensions and propose a test involving the scaling relation which may be used to check these values

the o n model on the triangular lattice to find critical points of o n models on the triangular lattice we apply two methods first we investigate the yang baxter equations on the triangular lattice we find only solvable points directly related to those for the square lattice second we construct intersections with the potts model this yields eight branches of critical points parametrized by n we establish the equivalence of these branches with the known critical points of the o n model on the square lattice transfer matrix calculations are performed to obtain the conformal anomaly and the thermal exponent of these branches these results include a numerical analysis of a q 3 potts tricritical point we find analytic relations between potts and o n models as well as among o n models with different values of n and among potts models with different values of q

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

non parametric heteroscedastic transformation regression models for skewed data with an application to health care costs summary we develop a new non parametric heteroscedastic transformation regression model for predicting the expected value of the outcome of a patient with given patient s covariates when the distribution of the outcome is highly skewed with a heteroscedastic variance in our model we allow both the transformation function and the error distribution function to be unknown we show that under some regularity conditions the estimators for regression parameters the expected value of the original outcome and the transformation function converge to their true values at the rate n 1 2 in our simulation studies we demonstrate that our proposed non parametric method is robust with little loss of efficiency finally we apply our model to a study on health care costs

scaling limit of the ising model in a field the dilute mathrm a 3 model is a solvable interaction round a face model with three local states and adjacency conditions encoded by the dynkin diagram of the lie algebra mathrm a 3 it can be regarded as a solvable spin 1 ising model at the critical temperature in a magnetic field one therefore expects the scaling limit to be governed by zamolodchikov s integrable perturbation of the c 1 2 conformal field theory indeed a recent thermodynamic bethe ansatz approach succeeded in unveiling the corresponding mathrm e 8 structure under certain assumptions on the nature of the bethe ansatz solutions in order to check these conjectures we perform a detailed numerical investigation of the solutions of the bethe ansatz equations for the critical and off critical models scaling functions for the ground state corrections and for the lowest spectral gaps are obtained which give very precise numerical results for the lowest mass ratios in the massive scaling limit while these agree perfectly with the mathrm e 8 mass ratios we observe one state that seems to violate the assumptions underlying the thermodynamic bethe ansatz calculation we also analyze the critical spectrum of the dilute mathrm a 3 model which exhibits excitations with a finite gap on top of the massless spectrum of the ising conformal field theory

collapse of a polymer in two dimensions abstract we numerically investigate the influence of self attraction on the critical behaviour of a polymer in two dimensions by means of an analysis of finite size results of transfer matrix calculations the transfer matrix is constructed on the basis of the o n loop model in the limit n 0 it yields finite size results for the magnetic correlation length of systems with a cylindrical geometry a comparison with the predictions of finite size scaling enables us to obtain information about the phase diagram as a function of the chemical potential of the loop segments and the strength of the attractive potential results for the magnetic scaling dimension can be interpreted in terms of known universality classes in particular when the attractive potential is increased we observe the crossover between the polymer critical behaviour of the self avoiding walk type to behaviour described earlier for the theta point

identification of a polymer growth process with an equilibrium multicritical collapse phase transition the meeting point of swollen collapsed and crystalline polymers we have investigated a polymer growth process on the triangular lattice where the configurations produced are self avoiding trails we show that the scaling behavior of this process is similar to the analogous process on the square lattice however while the square lattice process maps to the collapse transition of the canonical interacting self avoiding trail isat model on that lattice the process on the triangular lattice model does not map to the canonical equilibrium model on the other hand we show that the collapse transition of the canonical isat model on the triangular lattice behaves in a way reminiscent of the point of the interacting self avoiding walk isaw model which is the standard model of polymer collapse this implies an unusual lattice dependency of the isat collapse transition in two dimensions by studying an extended isat model we demonstrate that the growth process maps to a multicritical point in a larger parameter space in this extended parameter space the collapse phase transition may be either point like second order or first order and these two are separated by a multicritical point it is this multicritical point to which the growth process maps furthermore we provide evidence that in addition to the high temperature gaslike swollen polymer phase coil and the low temperature liquid drop like collapse phase globule there is also a maximally dense crystal like phase crystal at low temperatures dependent on the parameter values the multicritical point is the meeting point of these three phases our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the isaw and isat models in two dimensions as well as the behavior of the trail growth process

critical behaviour and conformal anomaly of the o n model on the square lattice finite size scaling and transfer matrix techniques are used to determine the conformal anomaly and critical exponents of o n models on the square lattice these calculations were performed on five branches of critical points parametrised by n the results for two of the branches agree with the known universal properties of the o n model as derived for the honeycomb lattice finite size convergence is poor for most of the third branch so that in this case the classification in terms of known models is uncertain the authors data show that the fourth branch can be interpreted in terms of a combination of a low temperature o n and a critical ising model finally the numerical results for the o n model on the remaining branch agree accurately with the known results for the low temperature o n 1 model they prove this equivalence by means of an exact mapping

collapse transition of self avoiding trails on the square lattice abstract the collapse transition of an isolated polymer has been modelled by many different approaches including lattice models based on self avoiding walks and self avoiding trails in two dimensions previous simulations of kinetic growth trails which map to a particular temperature of interacting self avoiding trails showed markedly different behaviour for what was argued to be the collapse transition than that which has been verified for models based of self avoiding walks on the other hand it has been argued that kinetic growth trails represent a special simulation that does not give the correct picture of the standard equilibrium model in this work we simulate the standard equilibrium interacting self avoiding trail model on the square lattice up to lengths over 2 000 000 steps and show that the results of the kinetic growth simulations are in fact entirely in accord with standard simulations of the temperature dependent model in this way we verify that the collapse transition of interacting self avoiding walks and trails are indeed in different universality classes in two dimensions

development of a neural network based control algorithm for powered ankle prosthesis abstract lower limb amputation is partial or complete removal of the limb due to disease accident or trauma surface electromyograms semg of a large number of muscles and force sensors have been used to develop control algorithms for lower limb powered prostheses but there are no commercial semg controlled prostheses available to date unlike ankle disarticulation transtibial amputation yields less intact lower leg muscle mass therefore minimizing the use of semg muscle sources utilized will make powered prosthesis controller economic and limiting the use of specifically the lower leg muscles will make it flexible presently we have used healthy population data to 1 test the feasibility of the neural network nn approach for developing a powered ankle prosthesis control algorithm that successfully predicts sagittal ankle angle and moment during walking using exclusively semg and 2 rank all muscle combination variations according to their success to determine the economic and flexible nn s semg amplitudes of five lower extremity muscles were used as inputs the tibialis anterior ta medial gastrocnemius mg rectus femoris rf biceps femoris bf and gluteus maximus gm a time delay feed forward multilayer architecture nn algorithm was developed muscle combination variations were ranked using pearson s correlation coefficient r 0 95 indicates successful correlations and root mean square error between actual vs estimated ankle position and moment the trained nn ta mg was successful rposition 0 952 rmoment 0 997 whereas ta mg bf rposition 0 981 rmoment 0 996 and mg bf gm rposition 0 955 rmoment 0 995 were distinguished as the economic and flexible variations respectively the algorithms developed should be trained and tested for data acquired from amputees in new studies

efficient semiparametric estimator for heteroscedastic partially linear models summary we study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function an interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated to avoid this we propose a family of consistent estimators and investigate their asymptotic properties we show that the optimal semiparametric efficiency bound can be reached by a semiparametric kernel estimator in this family building upon our theoretical findings and heuristic arguments about the equivalence between kernel and spline smoothing we conjecture that a weighted partial spline estimator could also be semiparametric efficient properties of the proposed estimators are presented through theoretical illustration and numerical simulations

quasi likelihood estimation in semiparametric models abstract suppose the expected value of a response variable y may be written h x t where x and t are covariates each of which may be vector valued is an unknown parameter vector is an unknown smooth function and h is a known function in this article we outline a method for estimating the parameter of this type of semiparametric model using a quasi likelihood function algorithms for computing the estimates are given and the asymptotic distribution theory for the estimators is developed the generalization of this approach to the case in which y is a multivariate response is also considered the methodology is illustrated on two data sets and the results of a small monte carlo study are presented

a corner transfer matrix renormalization group investigation of the vertex interacting self avoiding walk model ar ecently introduced extension of the corner transfer matrix renormalization group method useful for the study of self avoiding walk type models is presented in detail and applied to a class of interacting self avoiding walks due to bl ote and nienhuis this model displays two different types of collapse transition depending on model parameters one is the standard point transition the other is found to give rise to a first order collapse transition despite being known to be in other respects critical

profile likelihood and conditionally parametric models in this paper we outline a general approach to estimating the parametric component of a semiparametric model for the case of a scalar parametric component the method is based on the idea of first estimating a one dimensional subproblem of the original problem that is least favorable in the sense of stein the likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem the scalar parameter is then estimated by maximizing this generalized profile likelihood this method of estimation is applied to a particular class of semiparametric models where it is shown that the resulting estimator is asymptotically efficient

an analytic treatment of finite size corrections in the spin 1 antiferromagnetic xxz chain it is known that the standard method for calculating finite size corrections in bethe ansatz solvable systems is not applicable to the takhtajan babujian model and its anisotropic xxz generalisation the authors develop a new analytic method explicitly avoiding root densities and associated problems nonlinear integral equations are derived whose solutions yield the correct central charges c 1 and c 3 2 for the spin 1 2 and spin 1 xxz chains respectively in the spin 1 case the authors obtain as a by product the finite size deviation of the bethe ansatz roots from the 2 string formation

the yang baxter equation for mathcal pt invariant 19 vertex models we study the solutions of the yang baxter equation associated with 19 vertex models invariant by the parity time symmetry from the perspective of algebraic geometry we determine the form of the algebraic curves constraining the respective boltzmann weights and find that they possess a universal structure this allows us to classify the integrable manifolds into four different families reproducing three known models besides uncovering a novel 19 vertex model in a unified way the introduction of the spectral parameter on the weights is made via the parameterization of the fundamental algebraic curve which is a conic the diagonalization of the transfer matrix of the new vertex model and its thermodynamic limit properties are discussed we point out a connection between the form of the main curve and the nature of the excitations of the corresponding spin 1 chains

a semiparametric correction for attenuation abstract a correction method is proposed for models including the generalized linear model when the covariate is measured with error the method requires a separate validation data set that consists of the surrogate w and the true covariate x or an unbiased estimate x of x we do not require the classical additive measurement error model in which the surrogate is unbiased for the true covariates we first obtain an estimate of e x w by using nonparametric kernel regression of x or x on w based on the validation data then we perform a standard analysis with the unknown x replaced by the estimate of e x w the asymptotic distribution of the resulting regression parameter estimator is obtained generalizations to include components of x measured without error are also discussed

efficient estimation and computation of parameters and nonparametric functions in generalized semi non parametric regression models abstract the efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature bickel et al 1993 in this paper we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi non parametric regression models which cover commonly used semiparametric models such as partially linear models partially linear single index models and two sample semiparametric models we propose a maximum likelihood principle combined with the local linear technique for estimating the parameters and nonparametric functions the proposed estimators of the parameters and a linear functional of the nonparametric functions are consistent and asymptotically normal and are further shown to be semiparametrically efficient an efficient computational algorithm to achieve the maximization is proposed extensive simulation experiments show the superiority of the proposed methods three real data examples are analyzed and presented as an illustration

an asymptotic theory for model selection inference in general semiparametric problems summary hjort claeskens 2003 developed an asymptotic theory for model selection model averaging and subsequent inference using likelihood methods in parametric models along with associated confidence statements in this article we consider a semiparametric version of this problem wherein the likelihood depends on parameters and an unknown function and model selection averaging is to be applied to the parametric parts of the model we show that all the results of hjort claeskens hold in the semiparametric context if the fisher information matrix for parametric models is replaced by the semiparametric information bound for semiparametric models and if maximum likelihood estimators for parametric models are replaced by semiparametric efficient profile estimators our methods of proof employ le cam s contiguity lemmas leading to transparent results the results also describe the behaviour of semiparametric model estimators when the parametric component is misspecified and also have implications for pointwise consistent model selectors somekeywords akaike information criterion bayes information criterion efficient semiparametric estimation frequentist model averaging model averaging model selection profile likelihood semiparametric model

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation