conformal invariance in 2 1 dimensional stochastic systems stochastic partial differential equations can be used to model second order thermodynamical phase transitions as well as a number of critical out of equilibrium phenomena in 2 1 dimensions many of these systems are conjectured and some are indeed proved to be described by conformal field theories we advance in the framework of the martin siggia rose field theoretical formalism of stochastic dynamics a general solution of the translation ward identities which yields a putative conformal energy momentum tensor even though the computation of energy momentum correlators is obstructed in principle by dimensional reduction issues these are bypassed by the addition of replicated fields to the original 2 1 dimensional model the method is illustrated with an application to the kardar parisi zhang kpz model of surface growth the consistency of the approach is checked by means of a straightforward perturbative analysis of the kpz ultraviolet region leading as expected to its c 1 conformal fixed point

influences of large height differences and overhangs on the dynamic scaling behavior of discrete models abstract in order to investigate the influences of large height differences and overhangs on the dynamic scaling behavior of discrete models meanwhile reducing the finite size effects the etching model is modified to reduce large height differences and the overhangs in ballistic deposition surfaces are removed under certain principles numerical simulations are carried out for the modified models and the results show that the modified surfaces lead to good dynamic scaling behavior even on small system length scales the values of the dynamic scaling exponents are in excellent agreement with theoretical predictions of the kardar parisi zhang equation in 1 1 dimensions

conformal invariance of isoheight lines in a two dimensional kardar parisi zhang surface the statistics of isoheight lines in the 2 1 dimensional kardar parisi zhang kpz model is shown to be conformally invariant and equivalent to those of self avoiding random walks this leads to a rich variety of exact analytical results for the kpz dynamics we present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called schramm loewner evolution or sle with diffusivity 8 3 it is shown that the absence of the nonlinear term in the kpz equation will change the diffusivity from 8 3 to 4 indicating that the isoheight lines of the edwards wilkinson surface are also conformally invariant and belong to the universality class of domain walls in the o2 spin model

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

instability intermittency and multiscaling in discrete growth models of kinetic roughening we show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations such as the kardar parisi zhangequation and the lai das sarma villain equation and related atomistic models of epitaxial growth have a generic instability in which isolated pillars or grooves on an otherwise flat interface grow in time when their height or depth exceeds a critical value depending on the details of the model the instability found in the discretized version may or may not be present in the truly continuum growth equation indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts this instability can be controlled either by the introduction of higher order nonlinear terms with appropriate coefficients or by restricting the growth of pillars or grooves by other means a number of such controlled instability models are studied by simulation for appropriate choice of the parameters used for controlling the instability these models exhibit intermittent behavior characterized by multiexponent scaling of height fluctuations over the time interval during which the instability is active the behavior found in this regime is very similar to the turbulent behavior observed in recent simulations of several one and two dimensional atomistic models of epitaxial growth

a random rule model of surface growth abstract stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps as in the etching model mello et al 2001 5 in this paper i modify the etching model to perform sequential instead of random substrate scan the randomicity is introduced not in the site selection but in the choice of the rule to be followed in each site the change positively affects the study of dynamic and asymptotic properties by reducing the finite size effect and the short time anomaly and by increasing the saturation time it also has computational benefits better use of the cache memory and the possibility of parallel implementation

definition of percolation thresholds on self affine surfaces we study the percolation transition on a two dimensional substrate with long range self affine correlations we find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed numerical results are provided for spanning across the lattice in specified horizontal or vertical either or both directions

nonparametric identification in nonseparable panel data models with generalized fixed effects abstract this paper extends the familiar notion of fixed effects to nonlinear structures with infinite dimensional unobservables like preferences the main result is that a generalized version of differencing identifies local average responses lars in nonseparable structures in contrast to existing results this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest and it requires only two time periods on the other hand the results are confined to the subpopulation of stayers chamberlain 1982 i e the population for which the explanatory variables do not change over time we extend the basic framework to include time trends and dynamics in the explanatory variables and we show how distributional effects as well as average partial effects are identified our approach also allows endogeneity in the transitory unobservables furthermore we show that this new identification principle can be applied to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects finally we suggest estimators for the local average response and average partial effect and we analyze their large and finite sample behavior

percolation through self affine surfaces we study the percolation transition in a long range correlated system a self affine surface for all relevant physical cases i e positive roughness exponents it is found that the onset of percolation is governed by the largest wavelength of the height distribution and thus self averaging breaks down self averaging is recovered for negative roughness exponents i e power law decay of the height pair correlation function and in this case the critical exponents that characterize the transition are explicitly dependent on the roughness exponent above a threshold value below this threshold the spatial correlations are no longer relevant the problem is analytically investigated for a hierarchical network and by means of numerical simulations in two dimensions finally we discuss the application of those properties to mercury porosimetry in cracks

root n consistent semiparametric estimators of a dynamic panel sample selection model abstract this paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possibly predetermined variables lags of the dependent variables and unobserved individual effects the selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations we derive a set of conditional moment restrictions that are then exploited to construct a three step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term in the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of berkson s minimum chi square sieve method and a first step kernel estimator for the selection probability this second step estimator is of interest in its own right it can be used to semiparametrically estimate a panel data binary response model with a nonparametric individual specific effect without making any other distributional assumptions we show that both estimators second and third stage are n consistent and asymptotically normal

universality in sandpile models a classification of sandpile models into universality classes is presented on the basis of extensive numerical simulations in which we measure an extended set of exponents the manna two state model s s manna j phys a 24 l363 1991 is found to belong to a universality class of random neighbor models which is distinct from the universality class of the original model of bak tang and wiesenfeld p bak c tang and k wiesenfeld phys rev lett 59 381 1987 directed models are found to belong to a universality class which includes the directed model introduced and solved by dhar and ramaswamy d dhar and r ramaswamy phys rev lett 63 1659 1989

experientia docet professionals play minimax in laboratory experiments we study how professional players and college students play zero sum twoperson strategic games in a laboratory setting we first ask professionals to play a 2x2 game that is formally identical to a strategic interaction situation that they face in their natural environment we find that these subjects play in the laboratory exactly as in the field that is as the equilibrium of the game dictates i their distribution of play is statistically no different from the equilibrium distribution and ii they generate sequences of choices that are serially independent in sharp contrast with them however we also find that college students play the game far from the equilibrium predictions we then study the behavior of professional players and college students in the classic o neill s 4x4 zero sum game a game that none of the subjects have encountered previously and fi nd the same drastic differences in behavior between these two subject pools the transfer of skills and experience from the familiar field to the unfamiliar laboratory observed for professional players is relevant from a methodological perspective to evaluate the circumstances under which behavior in a laboratory setting may be a reliable indicator of behavior in a naturally occurring setting from a cognitive perspective it is useful for research on recognition processes intuition and similarity as a basis for inductive reasoning

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

linear regression after selection abstract we study the effect upon linear regression of explicit selection on the dependent variable if the explanatory variables are multinormally distributed along with the dependent variable then the regression coefficient vector in the selected population is a scalar multiple of that in the original population

estimation of a nonlinear panel data model with semiparametric individual effects abstract this paper investigates identification and estimation of a class of nonlinear panel data single index models the model allows for unknown time specific link functions and semiparametric specification of the individual specific effects we develop an estimator for the parameters of interest and propose a powerful new kernel based modified backfitting algorithm to compute the estimator we derive uniform rates of convergence results for the estimators of the link functions and show the estimators of the finite dimensional parameters are root n consistent with a gaussian limiting distribution we study the small sample properties of the estimator via monte carlo techniques

contour lines of the discrete scale invariant rough surfaces we study the fractal properties of the two dimensional 2d discrete scale invariant dsi rough surfaces the contour lines of these rough surfaces show clear dsi in the appropriate limit the dsi surfaces converge to the scale invariant rough surfaces the fractal properties of the 2d dsi rough surfaces apart from possessing the discrete scale invariance property follow the properties of the contour lines of the corresponding scale invariant rough surfaces we check this hypothesis by calculating numerous fractal exponents of the contour lines by using numerical calculations apart from calculating the known scaling exponents some other new fractal exponents are also calculated

nonlinear measures for characterizing rough surface morphologies we develop an approach for characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops i e loops of constant height given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops and the exponent that characterizes their size distribution scaling formulas are derived and used to relate these two geometrical exponents to the roughness exponent of a self affine surface thus providing independent measurements of this important quantity furthermore we define the scale dependent curvature and demonstrate that by measuring its third moment departures of the height fluctuations from gaussian behavior can be ascertained these nonlinear measures are used to characterize the morphology of computer generated gaussian rough surfaces surfaces obtained in numerical simulations of a simple growth model and surfaces observed by scanning tunneling microscopes for experimentally realized surfaces the self affine scaling is cut off by a correlation length and we generalize our theory of contour loops to take this into account

dependency of percolation critical exponents on the exponent of power law size distribution abstract the standard percolation theory uses objects of the same size moreover it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently the universality of the percolation theory is still valid in this study the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated two different object shapes i e stick shaped and square are considered these two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs the finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent in particular the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically as a result this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution

moment analysis of the probability distribution of different sandpile models we reconsider the moment analysis of the bak tang wiesenfeld and the stochastic sandpile model introduced by manna j phys a 24 l363 1991 in two and three dimensions in contrast to recently performed investigations our analysis reveals that the models are characterized by different scaling behavior i e they belong to different universality classes

dissipative sandpile models with universal exponents we consider a dissipative variant of the stochastic abelian sandpile model on a two dimensional lattice the boundaries are closed and the dissipation is due to the fact that each toppled grain is removed from the lattice with probability epsilon it is shown that the scaling properties of this model are in the universality class of the stochastic abelian models with conservative dynamics and open boundaries in particular the dissipation rate epsilon can be adjusted according to a suitable function epsilon f l such that the avalanche size distribution will coincide with that of the conservative model on a finite lattice of size l

bias corrections for two step fixed effects panel data estimators this paper introduces large t bias corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity these models include systems of equations with limited dependent variables and unobserved individual effects and sample selection models with unobserved individual effects our two step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity selection bias we then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable the fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem this problem is exacerbated by the two step nature of the procedure as these two step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large t bias adjustments to an important class of models simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator

invasion percolation in fractal fractures abstract invasion percolation ip with trapping was studied on two dimensional substrates with a correlated distribution of invasion thresholds the substrates represented the void spaces of variable aperture fracture models that were formed by 2 1 dimensional self affine rough surfaces and their replicas displaced relative to each other void spaces generated in this manner were self affine on length scales less than the horizontal displacement rd and uncorrelated on larger length scales the geometry of the ip clusters reflected the void space geometry with different scaling behavior on length scales below and beyond rd

classification of 2 1 dimensional growing surfaces using schramm loewner evolution statistical behavior and scaling properties of isoheight lines in three different saturated two dimensional grown surfaces with controversial universality classes are investigated using ideas from schramm loewner evolution text sle ensuremath kappa we present some evidence that the isoheight lines in the ballistic deposition bd eden and restricted solid on solid rsos models have conformally invariant properties all in the same universality class as the self avoiding random walk saw equivalently text sle 8 3 this leads to the conclusion that all these discrete growth models fall into the same universality class as the kardar parisi zhang kpz equation in two dimensions

geometrical exponents of contour loops on synthetic multifractal rough surfaces multiplicative hierarchical cascade p model in this paper we study many geometrical properties of contour loops to characterize the morphology of synthetic multifractal rough surfaces which are generated by multiplicative hierarchical cascading processes to this end two different classes of multifractal rough surfaces are numerically simulated as the first group singular measure multifractal rough surfaces are generated by using the p model the smoothened multifractal rough surface then is simulated by convolving the first group with a so called hurst exponent h the generalized multifractal dimension of isoheight lines contours d q correlation exponent of contours x l cumulative distributions of areas and perimeters are calculated for both synthetic multifractal rough surfaces our results show that for both mentioned classes hyperscaling relations for contour loops are the same as that of monofractal systems in contrast to singular measure multifractal rough surfaces h plays a leading role in smoothened multifractal rough surfaces all computed geometrical exponents for the first class depend not only on its hurst exponent but also on the set of p values but in spite of multifractal nature of smoothened surfaces second class the corresponding geometrical exponents are controlled by h the same as what happens for monofractal rough surfaces

on the geometric approach to multivariate selection multivariate selection can be represented as a linear transformation in a geometric framework this approach has led to considerable simplification in the study of the effects of selection on factor analysis in this note this approach is extended to describe the effects of selection on regression analysis and to adjust for the effects of selection using the inverse of the linear transformation

correlation estimation with singly truncated bivariate data correlation coefficient estimates are often attenuated for truncated samples in the sense that the estimates are biased towards zero motivated by real data collected in south sudan we consider correlation coefficient estimation with singly truncated bivariate data by considering a linear regression model in which a truncated variable is used as an explanatory variable a consistent estimator for the regression slope can be obtained from the ordinary least squares method a consistent estimator of the correlation coefficient is then obtained by multiplying the regression slope estimator by the variance ratio of the two variables results from two limited simulation studies confirm the validity and robustness of the proposed method the proposed method is applied to the south sudanese children s anthropometric and nutritional data collected by world vision copyright 2017 john wiley sons ltd

panel data discrete choice models with lagged dependent variables in this paper we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables lags of the endogenous dependent variable as well as unobservable individual specific effects for the binary logit model with the dependent variable lagged only once chamberlain 1993 gave conditions under which the model is not identified we present a stronger set of conditions under which the parameters of the model are identified the identification result suggests estimators of the model and we show that these are consistent and asymptotically normal although their rate of convergence is slower than the inverse of the square root of the sample size we also consider identification in the semiparametric case where the logit assumption is relaxed we propose an estimator in the spirit of the conditional maximum score estimator manski 1987 and we show that it is consistent in addition we discuss an extension of the identification result to multinomial discrete choice models and to the case where the dependent variable is lagged twice finally we present some monte carlo evidence on the small sample performance of the proposed estimators for the binary response model

on the connectivity of three dimensional fault networks natural fault networks involve a very broad range of fault lengths modeled in general by a power law length distribution n l al such a scaling law does not allow to define any a priori pertinent scale of observation for hydraulic field experiments in fractured media to investigate the relative effects of faults depending on their length we undertake in the spirit of percolation theory a theoretical and numerical study of the connectivity of three dimensional fault networks following power law length distributions we first establish the correct analytical expression of a percolation parameter p which describes the connectivity of the system the parameter p is found to be dependent on the third moment of the length distribution for fault planes it allows us to identify different regimes of connectivity depending on a the exponent of the fault length distribution the geometrical properties of the infinite cluster which partly control transport properties are also established at the percolation threshold for natural fault networks our theoretical analysis suggests that faults larger than a critical length scale may form a well connected network while smaller faults may be not connected on average this result which implies an increase of the connectivity with scale is consistent with scaling effects observed on permeability measurements

steady state of stochastic sandpile models we study the steady state of the abelian sandpile models with stochastic toppling rules the particle addition operators commute with each other but in general these operators need not be diagonalizable we use their abelian algebra to determine their eigenvalues and the jordan block structure these are then used to determine the probability of different configurations in the steady state we illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional example for systems of size 12 and also study the density profile in the steady state

characteristics of deterministic and stochastic sandpile models in a rotational sandpile model rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena in order to study the effect of rotational bias in an out of equilibrium situation like self organized criticality a two state quasideterministic rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains an extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium steady state of the model the probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves the model exhibits characteristics of both deterministic and stochastic sandpile models

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

attracted diffusion limited aggregation in this paper we present results of extensive monte carlo simulations of diffusion limited aggregation dla with a seed placed on an attractive plane as a simple model in connection with the electrical double layers we compute the fractal dimension of the aggregated patterns as a function of the attraction strength for the patterns grown in both two and three dimensions the fractal dimension shows a significant dependence on the attraction strength for small values of and approaches that of the ordinary two dimensional 2d dla in the limit of large for the nonattracting case with 1 our results in three dimensions reproduce the patterns of 3d ordinary dla while in two dimensions our model leads to the formation of a compact cluster with dimension 2 for intermediate the 3d clusters have a quasi 2d structure with a fractal dimension very close to that of the ordinary 2d dla this allows one to control the morphology of a growing cluster by tuning a single external parameter

critical behavior of a one dimensional fixed energy stochastic sandpile we study a one dimensional fixed energy version that is with no input or loss of particles of manna s stochastic sandpile model the system has a continuous transition to an absorbing state at a critical value of the particle density and exhibits the hallmarks of an absorbing state phase transition including finite size scaling critical exponents are obtained from extensive simulations which treat stationary and transient properties and an associated interface representation these exponents characterize the universality class of an absorbing state phase transition with a static conserved density in one dimension they differ from those expected at a linear interface depinning transition in a medium with point disorder and from those of directed percolation

consistent estimation of limited dependent variable models despite misspecification of distribution abstract by exploiting conditions on the behavior of regressors estimators are developed which are consistent up to a factor of proportionality for the slope coefficients of the regression function of a imperfectly observed dependent variable limited dependent variables are a special case of interest the consistency is robust to misspecification of the distribution of the latent dependent variable the estimators are weighted pseudo maximum likelihood estimators which can be readily computed using popular methods and software

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is

binary choice panel data models with predetermined variables we present a class of binary choice models for panel data with the following features i the explanatory variables are predetermined but not strictly exogenous this includes lagged dependent variables as well as other forms of unspecified feedback ii individual effects are allowed to be correlated with the explanatory variables dependence is specified through the conditional expectation of the effects which is let to be non parametric we also present a gmm estimator for these models which is consistent and asymptotically normal for fixed t and large n we study its finite sample properties in an autoregressive model by means of monte carlo simulations finally as an empirical illustration we estimate a female labour force participation equation with predetermined children using psid data

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

bounds on parameters in panel dynamic discrete choice models identification of dynamic nonlinear panel data models is an important and delicate problem in econometrics in this paper we provide insights that shed light on the identification of parameters of some commonly used models using these insights we are able to show through simple calculations that point identification often fails in these models on the other hand these calculations also suggest that the model restricts the parameter to lie in a region that is very small in many cases and the failure of point identification may therefore be of little practical importance in those cases although the emphasis is on identification our techniques are constructive in that they can easily form the basis for consistent estimates of the identified sets

hydraulic properties of two dimensional random fracture networks following a power law length distribution 1 effective connectivity natural fracture networks involve a very broad range of fractures of variable lengths and apertures modeled in general by a power law length distribution and a lognormal aperture distribution the objective of this two part paper is to characterize the permeability variations as well as the relevant flow structure of two dimensional isotropic models of fracture networks as determined by the fracture length and aperture distributions and by the other parameters of the model such as density and scale in this paper we study the sole influence of the fracture length distribution on permeability by assigning the same aperture to all fractures in the following paper de dreuzy et al this issue we study the more general case of networks in which fractures have both length and aperture distributions theoretical and numerical studies show that the hydraulic properties of power law length fracture networks can be classified into three types of simplified model if a power law length distribution n l l a is used in the network design the classical percolation model based on a population of small fractures is applicable for a power law exponent a higher than 3 for a lower than 2 on the contrary the applicable model is the one made up of the largest fractures of the network between these two limits i e for a in the range 2 3 neither of the previous simplified models can be applied so that a simplified two scale structure is proposed for this latter model the crossover scale is the classical correlation length defined in the percolation theory above which networks can be homogenized and below which networks have a multipath multisegment structure moreover the determination of the effective fracture length range within which fractures significantly contribute to flow corroborates the relevance of the previous models and clarifies their geometrical characteristics finally whatever the exponent a the sole significant scale effect is a decrease of the equivalent permeability for networks below or at percolation threshold

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

sandpile models and random walkers on finite lattices abelian sandpile models both deterministic such as the bak tang wiesenfeld btw model p bak c tang and k wiesenfeld phys rev lett 59 381 1987 and stochastic such as the manna model s s manna j phys a 24 l363 1991 are studied on finite square lattices with open boundaries the avalanche size distribution p l n is calculated for a range of system sizes l the first few moments of this distribution are evaluated numerically and their dependence on the system size is examined the sandpile models are conservative in the sense that grains are conserved in the bulk and can leave the system only through the boundaries it is shown that the conservation law provides an interesting connection between the sandpile models and random walk models using this connection it is shown that the average avalanche sizes l for the btw and manna models are equal to each other and both are equal to the average path length of a random walker starting from a random initial site on the same lattice of size l this is in spite of the fact that the sandpile models with deterministic btw and stochastic manna toppling rules exhibit different critical exponents indicating that they belong to different universality classes

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

evidence for universality within the classes of deterministic and stochastic sandpile models recent numerical studies have provided evidence that within the family of conservative undirected sandpile models with short range dynamic rules deterministic models such as the bak tang wiesenfeld model p bak c tang and k wiesenfeld phys rev lett 59 381 1987 and stochastic models such as the manna model s s manna j phys a 24 l363 1991 belong to different universality classes in this paper we examine the universality within each of the two classes in two dimensions by numerical simulations to this end we consider additional deterministic and stochastic models and use an extended set of critical exponents scaling functions and geometrical features universal behavior is found within the class of deterministic abelian models as well as within the class of stochastic models which includes both abelian and non abelian models in addition it is observed that deterministic but non abelian models exhibit critical exponents that depend on a parameter namely they are nonuniversal

sticky grains do not change the universality class of isotropic sandpiles we revisit the sandpile model with sticky grains introduced by mohanty and dhar phys rev lett 89 104303 2002 whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models while for directed models this conclusion is unquestionable for isotropic models we present strong evidence that the asymptotic scaling in the self organized regime in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate is like other stochastic sandpiles generically in the manna universality class this conclusion is drawn from extensive monte carlo simulations and is strengthened by the analysis of the langevin equations proposed by the same authors to account for this problem argued to converge upon coarse graining to the well established set of langevin equations for the manna class

sandpile models with and without an underlying spatial structure we present a simple mean field model for the sandpile model introduced by bak tang and wiesenfeld btw phys rev lett 59 381 1987 in the mean field model we are able to pinpoint the process of self organization as well as the emerging scale invariance displayed as a power law distribution of avalanche sizes we discuss the btw sandpile model on a lattice and show that the dynamical behavior can be expressed as a transport problem this implies that the average avalanche size scales with the system size and additional heuristic arguments related to the transport properties more than indicate the origin of the power law behavior we review recent work in which scaling relations and additional constraints between the various critical exponents are addressed we demonstrate that some of the proposed relations are inconsistent we present a coherent theory in which the scaling relations along with additional constraints leave only one exponent unknown

flooding transition in the topography of toppling surfaces of stochastic and rotational sandpile models a continuous phase transition occurs in the topography of toppling surfaces of stochastic and rotational sandpile models when they are flooded with liquid say water the toppling surfaces are extracted from the sandpile avalanches that appear due to sudden burst of toppling activity in the steady state of these sandpile models though a wide distribution of critical flooding heights exists a critical point is defined by merging the flooding thresholds of all the toppling surfaces the criticality of the transition is characterized by power law distributionofislandareainthecriticalregime afinitesizescalingtheoryisdevelopedandverifiedbycalculating several new critical exponents the flooding transition is found to be an interesting phase transition and does not belong to the percolation universality class the universality class of this transition is found to depend on the degree of self affinity of the toppling surfaces characterized by the hurst exponent h and the fractal dimension df of critical spanning islands the toppling surfaces of different stochastic sandpile models are found to have a single hurst exponent whereas those of different rotational sandpile models have another hurst exponent as a consequence the universality class of different sandpile models remains preserved within the same symmetry of the models

on the asymptotic bias of the ordinary least squares estimator of the tobit model this paper presents a precise characterization of the bias of least squares in two limited dependent variable models the tobit model and the truncated regression model for the cases considered the method of moments can be used to correct the bias of ols for more general cases the results provide approximations which appear to be relatively robust 13 and o in this paper we present a precise characterization of that bias for the particular case in which xt as well as is normally distributed we also show that the bias of the ols slope estimator can be corrected by dividing each estimate by the sample proportion of nonlimit observations other structural parameters can be consistently estimated in a similar fashion we present some evidence on the effect of nonnormality with respect to the predictions obtained in the normal model the case in which the sample contains only nonlimit observation the truncated regression model is considered elsewhere olsen 7 we analyze the relationship between his results and ours and derive some predictions of the normal model with respect to the seriousness of truncation bias

estimation of limited dependent variable models by ordinary least squares and the method of moments abstract under certain conditions a broad class of qualitative and limited dependent variable models can be consistently estimated by the method of moments using a non iterative correction to the ordinary least squares estimator with only a small loss of efficiency compared to maximum likelihood estimation the class of models is that obtained from a classical multinormal regression by any type of censoring or truncation and includes the tobit probit two limit probit truncated regression and some variants of the sample selection models the paper derives the estimators and their asymptotic covariance matrices

a nonparametric approach to the truncated regression problem abstract a description is given of a new method of estimating the regression parameters in the linear regression model from data where the dependent variable is subject to truncation the residual distribution is allowed to be unspecified the method is iterative and involves estimation of the residual distribution under the truncated sampling scheme the technique can be interpreted as an iterative bias adjustment of the observations in order to correct the regression relationship in the sampled population to match that of the model a simulation study compares the performance of various estimators including one suggested by bhattacharya chernoff and yang 1983 this truncation regression problem arises in many contexts of scientific and social research in economics tobin 1958 analyzed household expenditure on durable goods using a regression model that took account of the fact that the expenditure is always nonnegative a more general situation was studied by hausman and wise 1976 1977 in conn

estimation of dynamic models with error components abstract observations on n cross section units at t time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit different assumptions about the initial conditions are a initial state fixed b initial state random c the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed and d the unobserved individual effect independent of the unobserved dynamic process with initial value random asymptotic properties of the maximum likelihood and covariance estimators are obtained when t and when n the relationship between the pseudo and conditional maximum likelihood estimators is clarified a simple consistent estimator that is independent of the initial conditions and the way in which t or n is also suggested

adjusted least squares estimates for the scaled regression coefficients with censored data abstract the ordinary least squares ols method is popular for analyzing linear regression models because of its simplicity in computation suppose that the regressor variables are stochastic and the dependent observations are censored we can prove that under very general design conditions the least squares ls method can still be useful in estimating the scaled regression coefficients of the general regression model y q xi i i 1 2 n provided that the censored response observations are properly weighted here is a constant is a 1 p row vector x i are p 1 column vectors of explanatory variables i are unobserved random errors and q is an arbitrary unknown function particularly we shall see that under stronger design conditions such as assuming that the regressor variables have elliptically symmetric distribution the ols estimator consistently estimates the scaled when the response observations are complete the model discussed here is not the usual nonlinear re

generation of percolation cluster perimeters by a random walk a type of self avoiding random walk whish generates the perimeter of two dimensional lattice percolation clusters is given the algorithm has been simulated on a computer yielding the mean perimeter length as a function of occupation probability

semiparametric binary choice panel data models without strictly exogeneous regressors previous estimators of binary choice panel data models with fixed effects require strong parametric error asumptions strictly exogeneous regressors or both this is because nonlinearity of the model precludes the use of the moment conditions on differences based estimators that are generally employed for linear models without strictly exogeneous regressors based on the cross section binary choice estimator in lewbel 2000a we show how discrete choice panel data models with fixed effects can be estimated with only predetermined regressors the estimator is semiparametric in that the error distribution is not specified it allows for some general forms of heteroskedasticity and converges at rate root n this abstract was borrowed from another version of this item

conformal invariance of isoheight lines of the 2 1 dimensional wolf villain surfaces in order to learn more about the statistical properties of the surface fluctuations of the wolf villain wv model and confirm the applicability of the schramm loewner evolution theory sle to wv surfaces the contour lines of the 2 1 dimensional saturated surfaces of the wv model are investigated numerically the results obtained show that the isoheight lines of the wv surfaces are conformally invariant and can also be described in the frame of the sle theory with the diffusivity 4 the calculated fractal dimension of the contours is df 1 31 0 02

the abelian sandpile and related models abstract the abelian sandpile model is the simplest analytically tractable model of self organized criticality this paper presents a brief review of known results about the model the abelian group structure of the algebra of operators allows an exact calculation of many of its properties in particular when there is a preferred direction one can calculate all the critical exponents characterizing the distribution of avalanche sizes in all dimensions for the undirected case the model is related to q 0 state potts model this enables exact calculation of some exponents in two dimensions and there are some conjectures about others we also discuss a generalization of the model to a network of communicating reactive processors this includes sandpile models with stochastic toppling rules as a special case we also consider a nondashabelian stochastic variant which lies in a different universality class related to directed percolation

distribution free and link free estimation for the sample selection model abstract the prevalent estimation methods for the sample selection model rely heavily on parametric assumptions and are sensitive to departures from the underlying parametric assumptions see e g goldberger 1983 we propose an alternative estimation method the corrected maximum likelihood estimate which is consistent for the slope vector in the outcome equation up to a multiplicative scalar even through the parametric model on which the estimate is based might be misspecified as an important corollary it follows from our result that olsen s 1980 corrected ordinary least squares estimate is consistent if the outcome equation is linear without requiring olsen s assumptions on the joint error distribution

some results and a conjecture for manna s stochastic sandpile model we present some analytical results for the stochastic sandpile model studied earlier by manna in this model the operators corresponding to particle addition at different sites commute the eigenvalues of operators satisfy a system of coupled polynomial equations for an l l square we construct a nontrivial toppling invariant and hence a ladder operator which acting on eigenvectors of the evolution operator gives new eigenvectors with different eigenvalues for periodic boundary conditions in one direction one more toppling invariant can be constructed we show that there are many forbidden subconfigurations and only an exponentially small fraction of all stable configurations are recurrent we obtain rigorous lower and upper bounds for the minimum number of particles in a recurrent configuration and conjecture a formula for its exact value for finite size rectangles

experimental study of the roughness of crumpled surfaces abstract we report on the experimental study of the roughness of randomly crumpled surfaces which are unfolded this system provides a natural example of random surfaces which exhibit long range correlations it is shown that such rough surfaces are self affine with a hurst exponent h 0 9 a simple one dimensional model illustrates the way long range correlations may naturally occur in the crumpling process

the adjoint projection pursuit regression abstract consider a projection pursuit regression model y g x e with an arbitrary monotonic link function g we assume the link function is unknown thus we can only estimate the direction of that is the ratios among the components of say 1 2 the direction of is a useful estimand that measures say how many units of x 2 is equivalent to one unit of x 1 in terms of potency in affecting the outcome y projection pursuit regression usually solves the equation cov x y e y x 0 as an alternative we propose to solve the adjoint equation cov x e x x y 0 the adjoint equation has the advantage that e x x might be easier to estimate than e y x we establish two main results for the population case first is the unique solution up to a multiplicative scalar to the adjoint equation second satisfies a fixed point property based on a modified least squares regression derived from the adjoint equation we apply the population results to two important

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional das sarma tamborenea model abstract a mass of theoretical analysis and numerical calculation on 2 1 dimensional das sarma tamborenea model have been carried out over the years a problem about asymptotical behaviors that this model belongs to which universality classes is still interesting and controversial the schramm loewner evolution theory is an innovative point of view to describe the conformal invariance of contour lines of saturated rough surfaces in this paper we used sle theory to analyze the conformal invariance of the 2 1 dimensional dt model a noise reduction technique was also utilized to get better scaling behavior the results show that the contour lines of 2 1 dimensional dt model satisfy the property of conformal invariance and belongs to 4 universality class the relation d f 1 8 is also satisfied for the fractal dimension and diffusion coefficient of the contour lines

numerical determination of the avalanche exponents of the bak tang wiesenfeld model we consider the bak tang wiesenfeld sandpile model on a two dimensional square lattice of lattice sizes up to l 4096 a detailed analysis of the probability distribution of the size area duration and radius of the avalanches will be given to increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite size effects of the measurements the exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach

controlled instability and multiscaling in models of epitaxial growth we show that discretized versions of commonly studied nonlinear growth equations have a generic instability in which isolated pillars or grooves on an otherwise flat interface grow in time when their height or depth exceeds a critical value controlling this instability by the introduction of higher order nonlinear terms leads io intermittent behavior characterized by multiexponent scaling of height fluctuations similar to the turbulent behavior found in recent simulations of one dimensional atomistic models of epitaxial growth

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

scaling of clusters and winding angle statistics of isoheight lines in two dimensional kardar parisi zhang surfaces we investigate the statistics of iso height lines of 2 1 dimensional kardar parisi zhang model at different level sets around the mean height in the saturation regime we find that the exponent describing the distribution of the height cluster size behaves differently for level cuts above and below the mean height while the fractal dimensions of the height clusters and their perimeters remain unchanged the winding angle statistics also confirms again the conformal invariance of these contour lines in the same universality class of self avoiding random walks saws the study of surfaces their static statistical properties as well as growth and evolution dynamics and their morphological properties has been attracting an ever increasing amount of interest over the last two decades a method of characterizing surfaces is by looking at their iso height contour lines and the islands that are generated by a cut through the surface at a certain constant height such a situation can be found in the patterns exhibited by topographical islands and continents these islands and their coastlines have some fractal features with a fractal dimension related to the roughness exponent given by the structure function h h x h x r 2 i r 2 where h x is the height of interface as a function of its position theoretical modeling of the growth processes started with the work by edwards and wilkinson ew 1 who suggested that one might describe the dynamics of the height fluctuations by a simple linear diffusion equation kardar parisi and zhang kpz 2 realized that there is a relevant term proportional to the square of the height gradient which represents a correction for lateral growth the kpz equation is given by

nonparametric and semiparametric estimation with discrete regressors this note is concerned with nonparametric and semiparametric inference in regression models where regressors are not continuous when regressors are discrete with finite support a mere average of those observations of the dependent variable with the same regressor value will yield a root n consistent conditional expectation estimate we show that sequences of weights constructed in this way are consistent in the sense of stone 1977 even when the discrete regressors have infinite support the results are applied to the estimation of semiparametric models

critical properties of island perimeters in the flooding transition of stochastic and rotational sandpile models critical properties of external perimeters of islands that appear at the flooding transition in the toppling surfaces defined by the toppling number si of each sand column of stochastic and rotational sandpile models are studied a set of new critical exponents are estimated by extensive numerical simulation and finite size scaling analysis the values of the critical exponents are found different for these sandpile models several scaling relations among the critical exponents and the hurst exponent describing the self affinity of the toppling surfaces are established and verified the critical exponents obtained here are also found connected to the exponents describing the avalanche size distribution

theoretical studies of self organized criticality these notes are intended to provide a pedagogical introduction to the abelian sandpile model of self organized criticality and its related models the abelian group the algebra of particle addition operators the burning test for recurrent states equivalence to the spanning trees problem are described the exact solution of the directed version of the model in any dimension is explained the model s equivalence to scheidegger s model of river basins takayasu s aggregation model and the voter model is discussed for the undirected case the solution for one dimensional lattices and the bethe lattice is briefly described known results about the two dimensional case are summarized generalization to the abelian distributed processors model is discussed time dependent properties and the universality of critical behavior in sandpiles are briefly discussed i conclude by listing some still unsolved problems

bond percolation of polymers we study bond percolation of n non interacting gaussian polymers of l segments on a 2d square lattice of size l with reflecting boundaries through simulations we find the fraction of configurations displaying no connected cluster which span from one edge to the opposite edge from this fraction we define a critical segment density lc l and the associated critical fraction of occupied bonds plc l so that they can be identified as the percolation threshold in the l limit whereas plc l is found to decrease monotonically with l for a wide range of polymer lengths lc l is non monotonic we give physical arguments for this intriguing behaviour in terms of the competing effects of multiple bond occupancies and polymerization

fixed effects estimation of structural parameters and marginal effects in panel probit models fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem in this paper i characterize the leading term of a large t expansion of the bias of the mle and estimators of average marginal effects in parametric fixed effects panel binary choice models for probit index coefficients the former term is proportional to the true value of the coefficients being estimated this result allows me to derive a lower bound for the bias of the mle i then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity i subsequently propose new bias corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors

universality in sandpiles we perform extensive numerical simulations of different versions of the sandpile model we find that previous claims about universality classes are unfounded since the method previously employed to analyze the data suffered from a systematic bias we identify the correct scaling behavior and provide evidences suggesting that sandpiles with stochastic and deterministic toppling rules belong to the same universality class