local linear regression smoothers and their minimax efficiencies in this paper we introduce a smooth version of local linear regression estimators and address their advantages the mse and mise of the estimators are computed explicitly it turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency they are not only efficient in rates but also nearly efficient in constant factors in the nonparametric regression context the asymptotic minimax lower bound is developed via the heuristic of the hardest onedimensional subproblem of donoho and liu connections of the minimax risk with the modulus of continuity are made the lower bound is also applicable for estimating conditional mean regression and conditional quantiles for both fixed and random design regression problems

bandwidth selection in local polynomial regression using eigenvalues summary local polynomial regression is commonly used for estimating regression functions in practice however with rough functions or sparse data a poor choice of bandwidth can lead to unstable estimates of the function or its derivatives we derive a new expression for the leading term of the bias by using the eigenvalues of the weighted design matrix where the bias depends on the arrangement of the x values in the bandwidth window we then use this result to determine a local data driven bandwidth selection method and to provide a diagnostic for poor bandwidths that are chosen by using other methods we show that our data driven bandwidth is asymptotically equivalent to the optimal local bandwidth and that it performs well for relatively small samples when compared with other methods in addition we provide simulation results for first derivative estimation we illustrate its performance with data from mars global surveyor

reducing variance in univariate smoothing a variance reduction technique in nonparametric smoothing is proposed at each point of estimation form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged the nearby points are chosen to maximize the variance reduction we study in detail the case of univariate local linear regression while the new estimator retains many advantages of the local linear estimator it has appealing asymptotic relative efficiencies bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation a simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes this technique is very general and has a wide range of applications

spatial smoothing of geographically aggregated data with application to the construction of incidence maps abstract we address the commonly encountered situation in spatial statistics where data such as counts of incidences of a certain disease are available only in geographically aggregated form we develop fairly general models and propose a modified version of the locally weighted least squares method to recover the unknown smooth spatial function that is assumed to generate the observations in the special case of count data the target function is the intensity function conditional on the total number of observations our method avoids the arbitrariness of selecting a point within each geographic area at which the measurement for the whole area is supposed to be located we derive basic asymptotic properties and apply our methods to acquired immune deficiency syndrome aids incidence data in san francisco for 1980 1992 where counts are available aggregated over zip code areas

mass recentred kernel smoothers the local linear smoother usually gives better performance than the nadaraya watson smoother an exception is the case of data sparsity here we discuss a modification of the nadaraya watson smoother by muller song 1993 based on a horizontal shift of the kernel weights towards the local centre of mass of the design points this gives performance similar to the local linear when that works well and better performance when it does not the new smoother also preserves monotonicity shifting towards the centre of mass is also used to develop a modified kernel density estimate which cancels the well known peak spreading effect

nonparametric regression penalizing deviations from additivity due to the curse of dimensionality estimation in a multidimensional nonparametric regression model is in general not feasible hence additional restrictions are introduced and the additive model takes a prominent place the restrictions imposed can lead to serious bias here a new estimator is proposed which allows penalizing the nonadditive part of a regression function this offers a smooth choice between the full and the additive model as a byproduct this penalty leads to a regularization in sparse regions if the additive model does not hold a small penalty introduces an additional bias compared to the full model which is compensated by the reduced bias due to using smaller bandwidths for increasing penalties this estimator converges to the additive smooth backfitting estimator of mammen linton and nielsen ann statist 27 1999 1443 1490 the structure of the estimator is investigated and two algorithms are provided a proposal for selection of tuning parameters is made and the respective properties are studied finally a finite sample evaluation is performed for simulated and ozone data

efficient estimation and inferences for varying coefficient models abstract this article deals with statistical inferences based on the varying coefficient models proposed by hastie and tibshirani local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established the standard error formulas for estimated coefficients are derived and are empirically tested a goodness of fit test technique based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying coefficient model are constant or whether any covariates are statistically significant in the model the null distribution of the test is estimated by a conditional bootstrap method our estimation techniques involve solving hundreds of local likelihood equations to reduce the computational burden a one step newton raphson estimator is proposed and implemented the resulting one step procedure is shown to save computational cost on an order of tens with no

one step local quasi likelihood estimation summary local quasi likelihood estimation is a useful extension of local least squares methods but its computational cost and algorithmic convergence problems make the procedure less appealing particularly when it is iteratively used in methods such as the back fitting algorithm cross validation and bootstrapping a one step local quasi likelihood estimator is introduced to overcome the computational drawbacks of the local quasi likelihood method we demonstrate that as long as the initial estimators are reasonably good the one step estimator has the same asymptotic behaviour as the local quasi likelihood method our simulation shows that the one step estimator performs at least as well as the local quasi likelihood method for a wide range of choices of bandwidths a data driven bandwidth selector is proposed for the one step estimator based on the pre asymptotic substitution method of fan and gijbels it is then demonstrated that the datadriven one step local quasi likelihood estimator performs as well as the maximum local quasilikelihood estimator by using the ideal optimal bandwidth

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

kardar parisi zhang equation in the weak noise limit pattern formation and upper critical dimension we extend the previously developed nonperturbative weak noise scheme applied to the noisy burgers equation in one dimension to the kardar parisi zhang equation for a growing interface in arbitrary dimensions by means of the cole hopf transformation we show that the growth morphology can be interpreted in terms of dynamically evolving textures of localized growth modes with superimposed diffusive modes in the cole hopf representation the growth modes are static solutions to the diffusion equation and the nonlinear schrodinger equation subsequently boosted to finite velocity by a galilei transformation we discuss the dynamics of the pattern formation and briefly the superimposed linear modes implementing the stochastic interpretation we discuss kinetic transitions and in particular the preliminary scaling properties pertaining to the pair mode or dipole sector in the dipole sector we obtain the hurst exponent h 3 d 4 d or dynamic exponent zdip 4 d 3 d for the random walk of growth modes below d 3 the dipole growth modes show anomalous diffusion above d 3 the dipole growth modes freeze finally applying derrick s theorem based on constrained minimization we show that the upper critical dimension is d 4 in the sense that growth modes cease to exist above this dimension

extremely large scale simulation of a kardar parisi zhang model using graphics cards the octahedron model introduced recently has been implemented onto graphics cards which permits extremely large scale simulations via binary lattice gases and bit coded algorithms we confirm scaling behavior belonging to the two dimensional kardar parisi zhang universality class and find a surface growth exponent 0 2415 15 on 2 17 2 17 systems ruling out 1 4 suggested by field theory the maximum speedup with respect to a single cpu is 240 the steady state has been analyzed by finite size scaling and a growth exponent 0 393 4 is found correction to scaling exponent are computed and the power spectrum density of the steady state is determined we calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered we provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width

identification and wavelet estimation of weighted ate under discontinuous and kink incentive assignment mechanisms abstract this paper studies identification estimation and inference of a weighted average treatment effect w ate parameter in a class of switching regime models where the agent s selection of treatment is affected by either a discontinuous or kink incentive assignment mechanism and some unobservable characteristic for each assignment mechanism we i establish identification and propose a local wavelet estimator of the w ate ii establish asymptotic properties of the local wavelet estimator including optimal convergence rate and asymptotic normality and iii investigate the finite sample performance of the local wavelet estimators and compare them with local polynomial estimators via an extensive simulation study we also propose an identification robust wavelet estimator of the w ate

nonperturbative renormalization group for the stationary kardar parisi zhang equation scaling functions and amplitude ratios in 1 1 2 1 and 3 1 dimensions we investigate the strong coupling regime of the stationary kardar parisi zhang equation for interfaces growing on a substrate of dimension d 1 2 and 3 using a nonperturbative renormalization group nprg approach we compute critical exponents correlation and response functions extract the related scaling functions and calculate universal amplitude ratios we work with a simplified implementation of the second order in the response field approximation proposed in a previous work phys rev e 84 061150 2011 and phys rev e 86 019904 e 2012 which greatly simplifies the frequency sector of the nprg flow equations while keeping a nontrivial frequency dependence for the two point functions the one dimensional scaling function obtained within this approach compares very accurately with the scaling function obtained from the full second order nprg equations and with the exact scaling function furthermore the approach is easily applicable to higher dimensions and we provide scaling functions and amplitude ratios in d 2 and d 3 we argue that our ansatz is reliable up to d symbol see text 3 5

critical exponents of the kpz equation via multi surface coding numerical simulations we study the kpz equation in d 2 3 and 4 spatial dimensions by using a restricted solid on solid discretization of the surface we measure the critical exponents very precisely and we show that the rational guess is not appropriate and that d 4 is not the upper critical dimension we are also able to determine very precisely the exponent of the sub leading scaling corrections that turns out to be close to unity in all cases we introduce and use a multi surface coding technique that allows a gain of the order of 30 fold over usual numerical simulations

finite sample variance of local polynomials analysis and solutions abstract fitting local polynomials in nonparametric regression has a number of advantages the attractive theoretical features are in a partial contradiction to variance properties for random design and to practical experience over a broad range of situations no upper bound can be given for the conditional variance the unconditional variance is infinite when using optimal weights with compact support properties are better for gaussian weights we analyze local polynomials for finite sample size both theoretically and numerically it turns out that difficulties arise in sparse regions in the realization of the design when the realization has locally a small variance and or a skew empirical distribution two small sample modifications of local polynomials are presented local increase of bandwidth in sparse regions of the design and local polynomial ridge regression both modifications combine a good finite sample behavior with the asymptotic advantages of local polynomials

a variable span smoother abstract a variable span smoother based on linear fits is described local cross validation is used to estimate the optimal span as a function of abscissa value computationally efficient algorithms making use of updating formulas are presented

proliferation assisted transport in a random environment we investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field numerical results in d 1 suggest that a new intermediate diffusion behaviour appears we introduce the idea of proliferation assisted barrier crossing and give a flory like argument to understand qualitatively this non trivial diffusive behaviour a renormalization group analysis close to the critical dimension dc 2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime

variable selection for the single index model summary we consider variable selection in the single index model we prove that the popular leave m out crossvalidation method has different behaviour in the single index model from that in linear regression models or nonparametric regression models a new consistent variable selection method called separated crossvalidation is proposed further analysis suggests that the method has better finite sample performance and is computationally easier than leave m out crossvalidation separated crossvalidation applied to the swiss banknotes data and the ozone concentration data leads to single index models with selected variables that have better prediction capability than models based on all the covariates

estimation and testing for partially linear single index models in partially linear single index models we obtain the semiparametrically efficient profile least squares estimators of regression coefficients we also employ the smoothly clipped absolute deviation penalty scad approach to simultaneously select variables and estimate regression coefficients we show that the resulting scad estimators are consistent and possess the oracle property subsequently we demonstrate that a proposed tuning parameter selector bic identifies the true model consistently finally we develop a linear hypothesis test for the parametric coefficients and a goodness of fit test for the nonparametric component respectively monte carlo studies are also presented

nonperturbative renormalization group study of the stochastic navier stokes equation we study the renormalization group flow of the average action of the stochastic navier stokes equation with power law forcing using galilean invariance we introduce a nonperturbative approximation adapted to the zero frequency sector of the theory in the parametric range of the holder exponent 4 2e of the forcing where real space local interactions are relevant in any spatial dimension d we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis kolmogorov s 5 3 law is thus recovered for e 2 as also predicted by perturbative renormalization at variance with the perturbative prediction the 5 3 law emerges in the presence of a saturation in the e dependence of the scaling dimension of the eddy diffusivity at e 3 2 when according to perturbative renormalization the velocity field becomes infrared relevant

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

convergence criteria of a new three step iteration with errors for nonexpansive nonself mappings a new three step iteration with errors for nonexpansive nonself mappings in banach spaces is introduced and studied weak and strong convergence theorems of such iterations are established the results obtained in this paper extend and improve the several recent results in this area

adaptive varying coefficient linear models varying coefficient linear models arise from multivariate nonparametric regression nonlinear time series modelling and forecasting functional data analysis longitudinal data analysis and others it has been a common practice to assume that the vary coefficients are functions of a given variable which is often called an index a frequently asked question is which variable should be used as the index in this paper we explore the class of the varying coefficient linear models in which the index is unknown and is estimated as a linear combination of regression and or other variables this will enlarge the modelling capacity substantially we search for the index such that the derived varying coefficient model provides the best approximation to the underlying unknown multi dimensional regression function in the least square sense the search is implemented through the newly proposed hybrid backfitting algorithm the core of the algorithm is the alternative iteration between estimating the index through a one step scheme and estimating coefficient functions through a one dimensional local linear smoothing the generalised cross validation method for choosing bandwidth is efficiently incorporated into the algorithm the locally significant variables are selected in terms of the combined use of t statistic and akaike information criterion we further extend the algorithm for the models with two indices simulation shows that the proposed methodology has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers the methods are further illustrated through the canadian mink muskrat data in 1925 1994 and the pound dollar exchange rates in 1974 1983

scaling of fluctuation for directed polymers with random interaction using a finite size scaling form for reunion probability we show numerically the existence of a binding unbinding transition for directed polymers with random interaction the cases studied are a1 two chains in 1 1 dimensions a2 two chains in 2 1 dimensions and b three chains in 1 1 dimensions a similar finite size scaling form for fluctuation establishes a disorder induced transition with identical exponents for cases a2 and b the length scale exponents in all the three cases are in agreement with previous exact renormalization group results

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

modelling sparse generalized longitudinal observations with latent gaussian processes summary in longitudinal data analysis one frequently encounters non gaussian data that are repeatedly collected for a sample of individuals over time the repeated observations could be binomial poisson or of another discrete type or could be continuous the timings of the repeated measurements are often sparse and irregular we introduce a latent gaussian process model for such data establishing a connection to functional data analysis the functional methods proposed are non parametric and computationally straightforward as they do not involve a likelihood we develop functional principal components analysis for this situation and demonstrate the prediction of individual trajectories from sparse observations this method can handle missing data and leads to predictions of the functional principal component scores which serve as random effects in this model these scores can then be used for further statistical analysis such as inference regression discriminant analysis or clustering we illustrate these non parametric methods with longitudinal data on primary biliary cirrhosis and show in simulations that they are competitive in comparisons with generalized estimating equations and generalized linear mixed models

variable bandwidth and local linear regression smoothers in this paper we introduce an appealing nonparametric method for estimating the mean regression function the proposed method combines the ideas of local linear smoothers and variable bandwidth hence it also inherits the advantages of both approaches we give expressions for the conditional mse and mise of the estimator minimization of the mise leads to an explicit formula for an optimal choice of the variable bandwidth moreover the merits of considering a variable bandwidth are discussed in addition we show that the estimator does not have boundary effects and hence does not require modifications at the boundary the performance of a corresponding plug in estimator is investigated simulations illustrate the proposed estimation method

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

towards a strong coupling theory for the kpz equation abstract after a brief introduction we review the nonperturbative weak noise approach to the kardar parisi zhang kpz equation in one dimension we argue that the strong coupling aspects of the kpz equation are related to the existence of localized propagating domain walls or solitons representing the growth modes the statistical weight of the excitations is governed by a dynamical action representing the generalization of the boltzmann factor to kinetics this picture is not limited to one dimension we thus attempt a generalization to higher dimensions where the strong coupling aspects presumably are associated with a cellular network of domain walls based on this picture we present arguments for the wolf kertez expression z 2d 1 d 1 for the dynamical exponent

interpolation methods for adapting to sparse design in nonparametric regression abstract we suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing these methods are based on simple rules determined by the kernel and bandwidth for deciding when and where pseudo design points should be added to augment the original design sequence new ordinates for the added design points are computed by simple interpolation then local linear smoothing is applied directly to the expanded dataset the method is competitive with alternatives e g those involving ridge regression in terms of both simplicity and performance

the amount of noise inherent in bandwidth selection for a kernel density estimator abstract any practical method of constructing a bandwidth must depend only on a statistical sample and should produce some sort of estimate of this bandwidth the purpose of this paper is to show that there a well defined limits to the accuracy of all data driven bandwidth estimates put another way there is an unbridgeable gap between the minimum integrated square error attained using a optimal bandwidth and the minimum achievable integrated square error using a data driven bandwidth estimate additional keywords stochastic processes cross validation and random variables

relative efficiencies of kernel and local likelihood density estimators summary local likelihood methods enjoy advantageous properties such as good performance in the presence of edge effects that are rarely found in other approaches to nonparametric density estimation however as we argue in this paper standard kernel methods can have distinct advantages when edge effects are not present we show that whereas the integrated variances of the two methods are virtually identical the integrated squared bias of a conventional kernel estimator is less than that of a local log linear estimator by as much as a factor of 4 moreover the greatest bias improvements offered by kernel methods occur when they are needed most i e when the effect of bias is particularly high similar comparisons can also be made when high degree local log polynomial fits are assessed against high order kernel methods for example although as is well known high degree local polynomial fits offer potentially infinite efficiency gains relative to their kernel competitors the converse is also true indeed the asymptotic value of the integrated squared bias of a local log quadratic estimator can exceed any given constant multiple of that for the competing kernel method in all cases the densities that suffer problems in the context of local log likelihood methods can be chosen to be symmetric either unimodal or bimodal either infinitely or compactly supported and to have arbitrarily many derivatives as functions on the real line they are not pathological however our results reveal quantitative differences between global performances of local log polynomial estimators applied to unimodal or multimodal distributions

effective action for stochastic partial differential equations stochastic partial differential equations spdes are the basic tool for modeling systems where noise is important spdes are used for models of turbulence pattern formation and the structural development of the universe itself it is reasonably well known that certain spdes can be manipulated to be equivalent to nonquantum field theories that nevertheless exhibit deep and important relationships with quantum field theory in this paper we systematically extend these ideas we set up a functional integral formalism and demonstrate how to extract all the one loop physics for an arbitrary spde subject to arbitrary gaussian noise it is extremely important to realize that gaussian noise does not imply that the field variables undergo gaussian fluctuations and that these nonquantum field theories are fully interacting the limitation to one loop is not as serious as might be supposed experience with quantum field theories qfts has taught us that one loop physics is often quite adequate to give a good description of the salient issues the limitation to one loop does however offer marked technical advantages because at one loop almost any field theory can be rendered finite using zeta function technology we can sidestep the complications inherent in the martin siggia rose formalism the spde analog of the becchi rouet stora tyutin formalism used in qft and instead focus attention on a minimalist approach that uses only the physical fields this direct approach is the spde analog of canonical quantization using physical fields after setting up the general formalism for the characteristic functional partition function we show how to define the effective action to all loops and then focus on the one loop effective action and its specialization to constant fields the effective potential the physical interpretation of the effective action and effective potential for spdes is addressed and we show that key features carry over from qft to the case of spdes an important result is that the amplitude of the two point function governing the noise acts as the loop counting parameter and is the analog of planck s constant in this spde context we derive a general expression for the one loop effective potential of an arbitrary spde subject to translation invariant gaussian noise and compare this with the one loop potential for qft

efficient local estimation for time varying coefficients in deterministic dynamic models with applications to hiv 1 dynamics recently deterministic dynamic models have become very popular in biomedical research and other scientific areas examples include modeling human immunodeficiency virus hiv dynamics pharmacokinetic pharmacodynamic analysis tumor cell kinetics and genetic network modeling in this article we propose estimation methods for the time varying coefficients in deterministic dynamic systems that are usually described by a set of differential equations three two stage local polynomial estimators are proposed and their asymptotic normality is established an alternative approach a discretization method that is widely used in stochastic diffusion models is also investigated we show that the discretization method that uses the simple euler discretization approach for the deterministic dynamic model does not achieve the optimal convergence rate compared with the proposed two stage estimators we use monte carlo simulations to study the finite sample performance and use a real data application to hiv dynamic

directed polymers on a cayley tree with spatially correlated disorder in this paper we consider directed walks on a tree with a fixed branching ratio k at a finite temperature t we consider the case where each site or link is assigned a random energy uncorrelated in time but correlated in the transverse direction i e within the shell in this paper we take the transverse distance to be the hierarchical ultrametric distance but other possibilities are discussed we compute the free energy for the case of quenched disorder and show that there is a fundamental difference between the case of short range spatial correlations of the disorder which behave similarly to the non correlated case considered previously by derrida and spohn and the case of long range correlations which have a totally different overlap distribution approaching a single delta function about q 1 for large l where l is the length of the walk in the latter case the free energy is not extensive in l for the intermediate and also relevant range of l values although in the true thermodynamic limit extensivity is restored we identify a crossover temperature which grows with l and whenever the system is always in the low temperature phase thus in the case of long ranged correlation as opposed to the short ranged case a phase transition is absent

two loop renormalization group analysis of the burgers kardar parisi zhang equation a systematic analysis of the burgers kardar parisi zhang equation in d 1 dimensions by dynamic renormalization group theory is described the fixed points and exponents are calculated to two loop order we use the dimensional regularization scheme carefully keeping the full d dependence originating from the angular parts of the loop integrals for dimensions less than mathit d mathit c 2 we find a strong coupling fixed point which diverges at d 2 indicating that there is nonperturbative strong coupling behavior for all d ensuremath ge 2 at d 1 our method yields the identical fixed point as in the one loop approximation and the two loop contributions to the scaling functions are nonsingular for dg2 dimensions there is no finite strong coupling fixed point in the framework of a 2 ensuremath epsilon expansion we find the dynamic exponent corresponding to the unstable fixed point which described the nonequilibrium roughening transition to be z 2 o mathrm ensuremath epsilon 3 in agreement with a recent scaling argument by doty and kosterlitz phys rev lett 69 1979 1992 similarly our result for the correlation length exponent at the transition is 1 ensuremath nu ensuremath epsilon o mathrm ensuremath epsilon 3 for the smooth phase some aspects of the crossover from gaussian to critical behavior are discussed

on the role of the shrinkage parameter in local linear smoothing it has been shown that local linear smoothing possesses a variety of very attractive properties not least being its mean square performance however such results typically refer only to asymptotic mean squared error meaning the mean squared error of the asymptotic distribution and in fact the actual mean squared error is often infinite see seifert and gasser 1996 this difficulty may be overcome by shrinking the local linear estimator towards another estimator with bounded mean square however that approach requires information about the size of the shrinkage parameter from at least a theoretical viewpoint very little is known about the effects of shrinkage in particular it is not clear how small the shrinkage parameter may be chosen without affecting first order properties or whether infinitely supported kernels such as the gaussian require shrinkage in order to achieve first order optimal performance in the present paper we provide concise and definitive answers to such questions in the context of general ridged and shrunken local linear estimators we produce necessary and sufficient conditions on the size of the shrinkage parameter that ensure the traditional mean squared error formula we show that a wide variety of infinitely supported kernels with tails even lighter than those of the gaussian kernel do not require any shrinkage at all in order to achieve traditional first order optimal mean square performance

on partial local smoothing rules for curve estimation summary we compare the performances of local and global rules for smoothing parameter choice in terms of asymptotic mean squared errors of the resulting estimators in some instances there is surprisingly little to choose between local and global approaches our analysis identifies contexts where the differences are small or large this work motivates development of smoothing rules that form a half way house between local and global smoothing there interpolation provides a basis for partial local smoothing a key result shows that interpolation on even a coarse grid can produce a very good approximation to full local smoothing our theoretical and numerical results lead us to suggest linear interpolation of a bandwidth obtained by integral approximations on discrete intervals

on the perturbation expansion of the kpz equation we present a simple argument to show that the function of the d dimensional kpz equation d 2 is to all orders in perturbation theory given by beta g r d 2 g r 2 8 pi d 2 text gamma 2 d 2 g r 2 neither the dynamical exponent z nor the roughness exponent have any correction in any order of perturbation theory this shows that standard perturbation theory cannot attain the strong coupling regime and in addition breaks down at d 4 we also calculate a class of correlation functions exactly

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

renormalization group analysis of a quivering string model of posture control scaling concepts and renormalization group methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces the string is driven by uncorrelated white gaussian noise intended to model the corrections of the physiological control system we find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space representing the dynamics with various nontrivial fixed points and basins of attraction the transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon and the robustness of the linear model with respect to weak nonlinearities is confirmed correlations in posture fluctuations are obtained in both time and space domains there is an attractive fixed point identified with falling the scaling of the correlations in the front back displacement which can be measured in the laboratory is predicted for both large separation along the string and long time regimes of posture control

a kpz cocktail shaken not stirred the stochastic partial differential equation proposed nearly three decades ago by kardar parisi and zhang kpz continues to inspire intrigue and confound its many admirers here we i pay debts to heroic predecessors ii highlight additional experimentally relevant aspects of the recently solved 1 1 kpz problem iii use an expanding substrates formalism to gain access to the 3d radial kpz equation and lastly iv examining extremal paths on disordered hierarchical lattices set our gaze upon the fate of d infty kpz clearly there remains ample unexplored territory within the realm of kpz and for the hearty much work to be done especially in higher dimensions where numerical and renormalization group methods are providing a deeper understanding of this iconic equation

field theoretic thermodynamic uncertainty relation general formulation exemplified with the kardar parisi zhang equation we propose a field theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a markovian dynamics on a discrete set of states and for overdamped langevin equations we first formulate a framework which describes quantities like current entropy production and diffusivity in the case of a generic field theory we will then apply this general setting to the one dimensional kardar parisi zhang equation a paradigmatic example of a non linear field theoretic langevin equation in particular we will treat the dimensionless kardar parisi zhang equation with an effective coupling parameter measuring the strength of the non linearity it will be shown that a field theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant the calculations show that the field theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the kardar parisi zhang equation due to an excess term stemming from its non linearity

growing surfaces with anomalous diffusion results for the fractal kardar parisi zhang equation in this paper i study a model for a growing surface in the presence of anomalous diffusion also known as the fractal kardar parisi zhang equation fkpz this equation includes a fractional laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a levy flight it is shown that for a specific choice of parameters of the fkpz equation the equation can be solved exactly in one dimension so that all the critical exponents which describe the surface that grows under fkpz can be derived for that case afterwards the self consistent expansion sce is used to predict the critical exponents for the fkpz model for any choice of the parameters and any spatial dimension it is then verified that the results obtained using sce recover the exact result in one dimension at the end a simple picture for the behavior of the fractal kpz equation is suggested and the upper critical dimension of this model is discussed

towards the evaluation of the relevant degrees of freedom in nonlinear partial differential equations we investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations the proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems we examine dynamical scaling characteristics in the short time and the long time evolution regime providing only a reduced number of degrees of freedom to the evolution process