on second order iterative monads abstract b courcelle studied algebraic trees as precisely the solutions of all recursive program schemes for a given signature in set he proved that the corresponding monad is iterative we generalize this to recursive program schemes over a given finitary endofunctor h of a suitable category a monad is called second order iterative if every guarded recursive program scheme has a unique solution in it we construct two second order iterative monads one called the second order rational monad s h is proved to be the initial second order iterative monad the other one called the context free monad c h is a quotient of s h and in the original case of a polynomial endofunctor h of set we prove that c h is the monad studied by b courcelle the question whether these two monads are equal is left open

unification of infinite sets of terms schematized by primal grammars abstract infinite sets of terms appear frequently at different places in computer science on the other hand several practically oriented parts of logic and computer science require the manipulated objects to be finite or finitely representable schematizations present a suitable formalism to manipulate finitely infinite sets of terms since schematizations provide a different approach to solve the same kind of problems as constraints do they can be viewed as a new type of constraints the paper presents a new recurrent schematization called primal grammars the main idea behind the primal grammars is to use primitive recursion as the generating engine of infinite sets the evaluation of primal grammars is based on substitution and rewriting hence no particular semantics for them is necessary this fact allows also a natural integration of primal grammars into prolog into functional languages or into other rewrite based applications primal grammars have a decidable unification problem and the paper presents a unification algorithm for them that produces finite results this unification algorithm is proved sound and complete and it terminates for every input

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

type inference for record concatenation and subtyping record concatenation multiple inheritance and multiple object cloning are closely related and part of various language designs for example in cardelli s untyped obliq language a new object can be constructed from several existing objects by cloning followed by concatenation an error is given in case of field name conflicts type systems for record concatenation have been studied by wand harper and pierce remy and others and type inference for the combination of record concatenation and subtyping has been studied by sulzmann and by pottier in this paper we present a type inference algorithm for record concatenation subtyping and recursive types our example language is the abadi cardelli object calculus extended with a concatenation operator our algorithm enables type checking of obliq programs without changing the programs at all we prove that the type inference problem is np complete

the effect of uncertainty of item parameter estimation on ability estimates the conventional method of measuring ability which is based on items with assumed true parameter values obtained from a pretest is compared to a bayesian method that deals with the uncertainties of such items computational expressions are presented for approximating the posterior mean and variance of ability under the three parameter logistic 3pl model a 1987 american college testing program act math test is used to demonstrate that the standard practice of using maximum likelihood or empirical bayes techniques may seriously underestimate the uncertainty in estimated ability when the pretest sample is only moderately large

the monadic second order logic of graphs ix machines and their behaviours abstract we establish that every monadic second order property of the behaviour of a machine transition systems and tree automata are typical examples of machines is a monadic second order property of the machine itself in this way we clarify the distinction between dynamic properties of machines i e properties of their behaviours and their static properties i e properties of the graphs or relational structures representing them it is important for program verification that the dynamic properties that one wants to verify can be formulated statically in the simplest possible way as a corollary of our main result we also obtain that the monadic theory of an algebraic tree is decidable

recursion over realizability structures abstract realizability structures play a major role in the metamathematics of intuitionistic systems and they are a basic tool in the extraction of the computational content of constructive proofs besides their rich categorical structure and effectiveness properties provide a privileged mathematical setting for the semantics of data types of programming languages in this paper we emphasize the modelling of recursive definitions of programs and types a realizability model for a language including girard s system f and an operator of recursion on types is given and some of its local properties are studied

fundamental properties of infinite trees infinite trees naturally arise in the formalization and the study of the semantics of programming languages this paper investigates some of their combinatorial and algebraic properties that are especially relevant to semantics

unique normal form property of compatible term rewriting systems a new proof of chew s theorem abstract we present a new and complete proof of chew s theorem which states that a compatible term rewriting system has the unique normal form property i e a b implies a b for any normal forms a b

tree based generation of languages of fractals the notion of p interpreted top down tree generators is introduced combining the nondeterministic nature of grammars as known from formal language theory with the infinite refinement of pictures studied in fractal geometry

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

the ordinal generated by an ordinal grammar is computable abstract a prefix grammar is a context free grammar whose nonterminals generate prefix free languages a prefix grammar g is an ordinal grammar if the language l g is well ordered with respect to the lexicographic ordering it is known that from a finite system of parametric fixed point equations over ordinals one can construct an ordinal grammar g such that the lexicographic order of g is isomorphic with the least solution of the system if this solution is well ordered in this paper we show that given an ordinal grammar one can compute the cantor normal form of the order type of the lexicographic order of its language yielding that least solutions of fixed point equation systems defining algebraic ordinals are effectively computable and thus their isomorphism problem is also decidable

simplifying subtyping constraints this paper offers a theoretical study of constraint simplification a fundamental issue for the designer of a practical type inference system with subtyping in the simpler case where constraints are equations a simple isomorphism between constrained type schemes and finite state automata yields a complete constraint simplification method using it as a guide for the intuition we move on to the case of subtyping and describe several simplification algorithms although no longer complete they are conceptually simple efficient and very effective in practice overall this paper gives a concise theoretical account of the techniques found at the core of our type inference system our study is restricted to the case where constraints are interpreted in a non structural lattice of regular terms nevertheless we highlight a small number of general ideas which explain our algorithms at a high level and may be applicable to a variety of other systems

functional coefficient instrumental variables models we consider estimation of nonparametric structural models under a functional coefficient representation for the regression function under this representation models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables a nonparametric generalization of random coefficient models the functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed and partially linear models over which they have appreciable flexibility we propose two step estimators that use local linear approximations in both steps the first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors our large sample results include consistency and asymptotic normality of the proposed estimators the high practical power of estimators is illustrated via both a monte carlo simulation study and an application to returns to education

macro tree transducers attribute grammars and mso definable tree translations a characterization is given of the class of tree translations definable in monadic second order logic mso in terms of macro tree transducers the first main result is that the mso definable tree translations are exactly those tree translations realized by macro tree transducers mtts with regular look ahead that are single use restricted for this the single use restriction known from attribute grammars is generalized to mtts since mtts are closed under regular look ahead this implies that every mso definable tree translation can be realized by an mtt the second main result is that the class of mso definable tree translations can also be obtained by restricting mtts with regular look ahead to be finite copying i e to require that each input subtree is processed only a bounded number of times the single use restriction is a rather strong static restriction on the rules of an mtt whereas the finite copying restriction is a more liberal dynamic restriction on the derivations of an mtt

bases for parametrized iterativity parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where recursion is allowed to use only some variables chosen as a parameter we show how such algebras can be introduced in an arbitrary category a by employing a base i e an operation interpreting objects of a as monads on a for every base we prove that free base algebras and free iterative base algebras exist the main result is a coalgebraic construction of the latter all equation morphisms form a diagram whose colimit is proved to be a free iterative base algebra

varietes d automates descendants d arbres infinis resume nous definissons deux varietes d automates descendants d arbres infinis la varietedes b i automates i e b variete et la varietedes m i automates i e m variete pour i 1 2 3 4 ces deux varietes decoulent de la generalisation des automates de buchi et des automates de mullerala reconnaissance des langages d arbres infinis nousetudions la puissance des xi automates dans la x variete x b m la difference entre le determinisme et le non determinisme et les differentes proprietes de fermeture des familles de langages d arbres infinis engendrees par la x variete x b m nous montrons que plusieurs versions du theoreme de mcnaughton ne s etendent pas aux langages d arbres infinis

l a l b decidability results from complete formal systems abstract the equivalence problem for deterministic pushdown automata is shown to be decidable we exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda m we then extend the result to deterministic pushdown transducers from a free monoid into an abelian group a general algebraic and logical framework inspired by harrison et al theoret comput sci 9 1979 173 205 conrcelle theoret comput sci 6 1978 255 279 and meitus kybernetika 5 1989 14 25 in russian is developed

a semiparametric quantile panel data model with an application to estimating the growth effect of fdi abstract this paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant a three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated a simple and easily implemented procedure for making inferences is proposed monte carlo simulation is conducted to examine the finite sample performance of the proposed estimators finally using the cross country panel data we find a strong empirical evidence of the existence of the absorptive capacity hypothesis together with another new finding that fdi has much stronger growth effects for countries with fast economic growth than for those with slow economic growth

functional coefficient autoregressive models in this article we propose a new class of models for nonlinear time series analysis investigate properties of the proposed model and suggest a modeling procedure for building such a model the proposed modeling procedure makes use of ideas from both parametric and nonparametric statistics a consistency result is given to support the procedure for illustration we apply the proposed model and procedure to several data sets and show that the resulting models substantially improve postsample multi step ahead forecasts over other models

investigating the impact of uncertainty about item parameters on ability estimation asymptotic expansions of the maximum likelihood estimator mle and weighted likelihood estimator wle of an examinee s ability are derived while item parameter estimators are treated as covariates measured with error the asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators a numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular mle or wle method

regular sets over extended tree structures we investigate notions of decidability and definability for the monadic second order logic over labeled tree structures and its relations with finite automata using oracles to test input prefixes a general framework is defined allowing to transfer some mso properties from a graph structure to a labeled tree structure transferred properties are the decidability of sentences and the existence of a definable model for every satisfiable formula a class of finite automata with prefix oracles is also defined recognizing exactly languages defined by mso formulas in any labeled tree structure applying these results the well known equivalence between languages recognized by finite automata sets of vertices mso definable in a tree structure and sets of pushdown contexts generated by pushdown automata is extended to k iterated pushdown automata

on final coalgebras of continuous functors continuous endofunctors f of locally finitely presentable categories carry a natural metric on their final coalgebra whenever f 0 has an element this metric is proved to be a cauchy completion of the initial algebra of f this is illustrated on the poset of real numbers represented as a final coalgebra of an endofunctor of pos by pavlovic and pratt under additional assumptions on the locally finitely presentable category all finitary endofunctors are proved to have a final coalgebra constructed in steps of the natural iteration construction

modeling and testing smooth structural changes with endogenous regressors abstract modeling and detecting parameter stability of econometric models is a long standing problem most existing estimation and testing methods are designed for models without endogeneity little attention has been paid to models with endogeneous regressors which may arise in many scenarios in economics in this paper we first consider a time varying coefficient time series model with potential time varying endogeneity a local linear two stage least squared estimation is developed to estimate coefficient functions the consistency and asymptotic normality of the estimator are derived furthermore a nonparametric test is proposed to check smooth structural changes as well as abrupt structural breaks with possibly unknown change points in regression models with potential endogeneity the idea is to compare the fitted values of the unrestricted nonparametric time varying coefficient model and the restricted constant parameter model the test has an asymptotic n 0 1 distribution and does not require any prior information about the alternatives a simulation study highlights the merits of the proposed estimator and test in an application we estimate the new keynesian phillips curve for the us nonparametrically and find strong evidence against its stability

an investigation of hierarchical bayes procedures in item response theory hierarchical bayes procedures for the two parameter logistic item response model were compared for estimating item and ability parameters simulated data sets were analyzed via two joint and two marginal bayesian estimation procedures the marginal bayesian estimation procedures yielded consistently smaller root mean square differences than the joint bayesian estimation procedures for item and ability estimates as the sample size and test length increased the four bayes procedures yielded essentially the same result

infinite hypergraphs i basic properties abstract basic properties of the category of infinite directed hyperedge labelled hypergraphs are studied an algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions it is then shown that two expressions define the same hypergraphs if and only if they are congruent with respect to some rewriting system these results will be used in the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions

the evaluation of first order substitution is monadic second order compatible we denote first order substitutions of finite and infinite terms by function symbols indexed by the sequences of first order variables to which substitutions are made we consider the evaluation mapping from infinite terms to infinite terms that evaluates these substitution operations this mapping may perform infinitely many nested substitutions so that a term which has the structure of an infinite string can be transformed into one isomorphic to an infinite binary tree we prove that this mapping is monadic second order compatible which means that a monadic second order formula expressing a property of the output term produced by the evaluation mapping can be translated into a monadic second order formula expressing this property over the input term this implies that deciding the monadic second order theory of the output term reduces to deciding that of the input term as an application we obtain another proof that the monadic second order properties of the algebraic trees which represent the behaviours of recursive applicative program schemes are decidable this proof extends to hyperalgebraic trees these infinite trees correspond to certain recursive program schemes with functional parameters of arbitrary high type

macro tree translations of linear size increase are mso definable the first main result is that if a macro tree translation is of linear size increase i e if the size of every output tree is linearly bounded by the size of the corresponding input tree then the translation is mso definable i e definable in monadic second order logic this gives a new characterization of the mso definable tree translations in terms of macro tree transducers they are exactly the macro tree translations of linear size increase the second main result is that given a macro tree transducer it can be decided whether or not its translation is mso definable and if it is then an equivalent mso transducer can be constructed similar results hold for attribute grammars which define a subclass of the macro tree translations

equational logic of circular data type specification abstract iteration theories introduced by bloom elgot and wright in 1980 formalize the equational properties of the strong behaviors of flowchart algorithms we show that the same equational properties are shared by the functors used to specify circular data types lehmann and smyth 1981 have shown how to specify circular data types such as stacks as fixed points of certain functors the called gw functors for example the set of stacks of elements in the set a is a solution to the equation in the variable x x f a x where f x x 1 a x is the functor on set taking the pair a x to the disjoint union of the singleton set 1 and the product a x such equations have initial solutions f a which in turn determine a solution functor f the equational properties of the operation f f are precisely captured by the axioms for iteration theories more precisely we show how the structure th c of all functors c n c p n p 0 on the category c forms an iteration theory and conversely any identity valid in all such structures is valid in the class of all iteration theories

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

a mezei wright theorem for categorical algebras the main result of this paper is a generalization of the mezei wright theorem a result on solutions of a system of fixed point equations in the typical setting one solves a system of fixed point equations in an algebra equipped with a suitable partial order there is a least element suprema of w chains exist the operations preserve the ordering and least upper bounds of w chains in this setting one solution of this kind of system is provided by least fixed points the mezei wright theorem asserts that such a solution is preserved by a continuous order preserving algebra homomorphism in several settings such as countable words or synchronization trees there is no well defined partial order but one can naturally introduce a category by considering morphisms between the elements the generalization of this paper consists in replacing ordered algebras by categorical algebras the least element is replaced by an initial element and suprema of w chains are replaced by colimits of w diagrams then the mezei wright theorem for categorical algebras is that initial solutions are preserved by continuous morphisms we establish this result for initial solutions of parametric fixed point equations one use of the theorem is to characterize an algebraic element as one that can arise as a solution of some system of fixed point equations in familiar examples an algebraic element is one that is context free regular or rational then if h a b is a continuous morphism of categorical algebras the algebraic objects in b are those isomorphic to h images of algebraic objects in a

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

dpda s in atomic normal form and applications to equivalence problems abstract in this paper we introduce a new normal form for dpda s the atomic normal form as an application using also the concept of address language due to gorn 19 20 we give alternate and more direct proofs of results of courcelle 3 4 relating recursion schemes and dpda s address languages enable us to encode trees even when they are not locally finite as a consequence the decidability of a new class of schemes corresponding to the stateless dpda s of 26 is obtained

fundamental study the modular decomposition of countable graphs definition and construction in monadic second order logic we consider the notion of modular decomposition for countable graphs the modular decomposition of a graph given with an enumeration of its set of vertices can be defined by formulas of monadic second order logic another result is the definition of a representation of modular decompositions by low degree relational structures such relational structures can also be defined in the considered graph by monadic second order formulas

equivalences and transformations of regular systems applications to recursive program schemes and grammars abstract this work presents a unified theory of recursive program schemes context free grammars grammars on arbitrary algebraic structures and in fact recursive definitions of all kind by means of regular systems the equivalences of regular systems associated with either all their solutions or their least solutions in all domains of appropriate type satisfying a set of algebraic laws expressed by equations are systematically investigated and characterized in some cases in terms of system transformations by folding unfolding and rewriting according to the equational algebraic laws grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union and the same questions are raised for them we also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system this theory applies to grammars of many kinds which generate trees graphs etc we formulate some classical transformations of context free grammars in terms of correct transformations which only use folding unfolding and algebraic laws and we immediately obtain their correctness

sieve instrumental variable quantile regression estimation of functional coefficient models abstract in this paper we consider sieve instrumental variable quantile regression ivqr estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates we estimate the functional coefficients by the sieve ivqr technique and establish the uniform consistency and asymptotic normality of the estimators based on the sieve estimates we propose a nonparametric specification test for the constancy of the functional coefficients and study its asymptotic we conduct simulations to evaluate the finite sample behavior of our estimator and test statistic and apply our method to study the estimation of quantile engel curves

infinitary combinatory reduction systems we define infinitary combinatory reduction systems icrss thus providing the first notion of infinitary higher order rewriting the systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary l calculus are special cases furthermore we generalise a number of known results from first order infinitary rewriting and infinitary l calculus to icrss in particular for fully extended left linear icrss we prove the well known compression property and for orthogonal icrss we prove that 1 if a set of redexes u has a complete development then all complete developments of u end in the same term and that 2 any tiling diagram involving strongly convergent reductions s and t can be completed iff at least one of s t and t s is strongly convergent we also prove an ancillary result of independent interest a set of redexes in an orthogonal icrs has a complete development iff the set has the so called finite jumps property

an algebraic semantics approach to the effective resolution of type equations abstract this article presents a syntactic calculus of partially ordered data type structures and its application to computation a syntax of record like terms and a type subsumption ordering are defined and shown to form a lattice structure a simple type as set interpretation of these term structures extends this lattice to a distributive one and in the case of finitary terms to a complete brouwerian lattice as a result a method for solving systems of type equations by iterated rewriting of type symbols is proposed which defines an operational semantics for kbl a knowledge base language it is shown that a kbl program can be seen as a system of equations thanks to the lattice properties of finite structures systems of simultaneous type equations are shown to admit least fixed point solutions an operational semantics for kbl is described as term rewriting fan out rewriting a particular rewriting computation order related to the conventional outermost term rewriting which rewrites symbols closer to the root first is defined and shown to be maximal correctness with respect to least fixed point semantics of kbl s operational semantics as defined by fan out rewriting is discussed finally extensions and further research directions are sketched

on the existence of nonterminating queries for a restricted class of prolog clauses abstract this work studies the existence of nonterminating queries for a restricted class of recursive predicates the class is restricted to predicates defined by a set of clauses containing only one direct recursive clause moreover this clause must be of the form p p for this restricted class of predicates we prove a necessary and sufficient condition for the existence of a query which is nonterminating in the absence of the occur check the condition is based upon concepts from rational trees

posterior convergence given the mean for various applications one wants to know the asymptotic behavior of x the posterior density of a parameter given the mean x of the data rather than the full data set here we show that x is asymptotically normal in an l 1 sense and we identify the mean of the limiting normal and its asymptotic variance the main results are first proved assuming that x 1 x n are independent and identical suitable modifications to obtain results for the nonidentical case are given separately our results may be used to construct approximate hpd highest posterior density sets for the parameter which is of use in the statistical theory of standardized educational tests they may also be used to show the covariance between two test items conditioned on the mean is asymptotically nonpositive this has implications for constructing tests of item independence

infinite hypergraphs ii systems of recursive equations abstract the results and tools which were developed in part i of this paper 4 are used to solve systems of recursive equations on hypergraphs and to characterize their solutions completely a hypergraph s initial solutions are called equational hypergraphs it is then shown that the context free graphs of muller and schupp 15 are equational

infinite labeled trees from rational to sturmian trees this paper studies infinite unordered d ary trees with nodes labeled by 0 1 we introduce the notions of rational and sturmian trees along with the definitions of strongly balanced trees and mechanical trees and study the relations among them in particular we show that strongly balanced trees exist and coincide with mechanical trees in the irrational case providing an effective construction such trees also have a minimal factor complexity hence are sturmian we also give several examples illustrating the inclusion relations between these classes of trees

a coinductive completeness proof for the equivalence of recursive types we prove that the equivalence of recursive types induced by the equality of their infinite unfoldings coincides with the equality of their interpretations as closures over the model p

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

decidability of the existential theory of infinite terms with subterm relation we examine the problem of solving equations inequalities and atomic formulas built on the subterm relation in algebras of rational and infinite terms trees we prove that this problem is decidable for any such algebra in a finite signature s with possible new free constants moreover even in presence of subterm relation the existential theory of rational trees is the same as the existential theory of infinite trees we leave out the easier case where s has no symbols of arity greater than one when s has only a symbol of arity greater than one the decision procedure is different in the two cases where the algebra of rational or infinite trees does or does not contain new free constants

automata on infinite objects and their applications to logic and programming abstract we introduce various types of automata top down automata and bottom up automata on infinite trees we study the power of determinstic and nondeterministic tree automata and prove that deterministic and non deterministic bottom up tree automata accept the same infinite tree sets we establish a relationship between tree automata logic programs recursive program schemes and the monadic second order theory of the tree we prove that the equivalence of two rational logic programs is decidable

model checking higher order programs we propose a novel verification method for higher order functional programs based on higher order model checking or more precisely model checking of higher order recursion schemes recursion schemes for short the most distinguishing feature of our verification method for higher order programs is that it is sound complete and automatic for the simply typed calculus with recursion and finite base types and for various program verification problems such as reachability flow analysis and resource usage verification we first show that a variety of program verification problems can be reduced to model checking problems for recursion schemes by transforming a program into a recursion scheme that generates a tree representing all the interesting possible event sequences of the program we then develop a new type based model checking algorithm for recursion schemes and implement a prototype recursion scheme model checker to our knowledge this is the first implementation of a recursion scheme model checker experiments show that our model checker is reasonably fast despite the worst case time complexity of recursion scheme model checking being hyperexponential in general altogether the results provide a new promising approach to verification of higher order functional programs

type inference with recursive types syntax and semantics abstract in this paper we study type inference systems for calculus with a recursion operator over types the main syntactical properties notably the existence of principal type schemes are proved to hold when recursive types are viewed as finite notations for infinite regular type expressions representing their infinite unfoldings exploiting the approximation structure of a model for the untyped language of terms types are interpreted as limits of sequences of their approximations we show that the interpretation is essentially unique and that two types have equal interpretation if and only if their infinite unfoldings are identical finally a completeness theorem is proved to hold w r t the specific model we consider for a natural infinitary extension of the type inference system

a person fit test for irt models for polytomous items a person fit test based on the lagrange multiplier test is presented for three item response theory models for polytomous items the generalized partial credit model the sequential model and the graded response model the test can also be used in the framework of multidimensional ability parameters it is shown that the lagrange multiplier statistic can take both the effects of estimation of the item parameters and the estimation of the person parameters into account the lagrange multiplier statistic has an asymptotic 2 distribution the type i error rate and power are investigated using simulation studies results show that test statistics that ignore the effects of estimation of the persons ability parameters have decreased type i error rates and power incorporating a correction to account for the effects of the estimation of the persons ability parameters results in acceptable type i error rates and power characteristics incorporating a correction for the estimation of the item parameters has very little additional effect it is investigated to what extent the three models give comparable results both in the simulation studies and in an example using data from the neo personality inventory revised

generalized automata on infinite trees and muller mcnaughton s theorem abstract we introduce various types of top down and bottom up generalized automata on infinite trees we study the power of deterministic and nondeterministic generalized tree automata and prove that deterministic and nondeterministic bottom up automata accept the same class we prove also that nondeterministic top down and bottom up generalized automata have the same power we give various characterizations of the monadic second order theory of the tree in terms of tree automata and tree grammars we consider different types of extensions of muller mcnaughton s theorem but unfortunately not all the extensions of it are possible

axiomatisations of functional dependencies in the presence of records lists sets and multisets we investigate functional dependencies in databases that support complex values such as records lists sets anu multisets therefore an abstract algebraic framework is proposed that classifies data models according to the underlying types they support this allows to emphasise the impact of the data types rather than the specifics of a particular data model the main results are finite minimal sound and complete sets of inference rules for the implication of functional dependencies in the presence of records and all combinations of lists sets and multisets the inference rules are similar to armstrong s original axioms for the relational data model thanks to the algebraic framework the completeness result however requires a deep analysis in the case of sets and in particular multisets

the io and oi hierarchies abstract an analysis of recursive procedures in algol 68 with finite modes shows that a denotational semantics of this language can be described on the level of program schemes using a typed calculus with fixed point operators in the first part of this paper we derive classical schematological theorems for the resulting class of level n schemes in part two we investigate the language families obtained by call by value and call by name interpretation of level n schemes over the algebra of formal languages it is proved that differentiating according to the functional level of recursion leads to two infinite hierarchies of recursive languages the io and oi hierarchies which can be characterized as canonical extensions of the regular context free and io and oi macro languages respectively sufficient conditions are derived to establish strictness of io like hierarchies finally we derive that recursion on higher types induces an infinite hierarchy of control structures by proving that level n schemes are strictly less powerful than level n 1 schemes

varying coefficient panel data model in the presence of endogenous selectivity and fixed effects this paper considers a exible panel data sample selection model in which i the outcome equation is permitted to take a semiparametric varying coecient form to capture potential parameter heterogeneity in the relationship of interest ii both the outcome and parametric selection equations contain unobserved xed eects and iii selection is generalized to a polychotomous case we propose a two stage estimator given consistent parameter estimates from the selection equation obtained in the rst stage we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time the selection bias term is then asymptotically removed from the equation along with xed eects using kernel based weights the proposed estimator is consistent and asymptotically normal we rst investigate the nite sample properties of the estimator in a small monte carlo study and then apply it to study production technologies of u s retail credit unions from 2002 to 2006

a characterisation of deterministic context free languages by means of right congruences we study here a kind of rewriting systems called controlled rewriting systems c systems for short which generalise the notion of regular semi thue systems we show that the deterministic context free languages are exactly the sets of the form r s where r is a rational set and s is the right congruence generated by a c system of s of a restricted type s is basic and confluent

algebras with parametrized iterativity iterative algebras as studied by nelson and tiuryn are generalized to algebras whose iterativity is parametrized in the sense that only some variables can be used for iteration for example in the case of one binary operation the free iterative algebra is the algebra of all rational binary trees if only the left hand variable is allowed to be iterated then the free iterative algebra is the algebra of all right well founded rational binary trees in order to express such parametrized iterativity we work with parametrized endofunctors of set i e finitary endofunctors h setxset set and introduce the concept of iterativity for algebras for the endofunctor email protected h x x we then describe free iterative h algebras

a new foundation for finitary corecursion and iterative algebras abstract this paper contributes to a generic theory of behaviour of finite state systems systems are coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category their behaviour gives rise to the locally finite fixpoint lff a new fixpoint of the endofunctor the lff exists provided that the endofunctor is finitary and preserves monomorphisms is a subcoalgebra of the final coalgebra i e it is fully abstract w r t behavioural equivalence and it is characterized by two universal properties as the final locally finitely generated coalgebra and as the initial fg iterative algebra instances of the lff are regular languages rational streams rational formal power series regular trees etc moreover we obtain e g realtime deterministic resp non deterministic context free languages constructively s algebraic formal power series in general the behaviour of finite coalgebras under the coalgebraic language semantics arising from the generalized powerset construction by silva bonchi bonsangue and rutten and the monad of courcelle s algebraic trees

infinite normal forms for non linear term rewriting systems abstract nonterminating rewrite relations have recently been studied in order to set a framework within which infinite terms can be seen as limits of infinite converging derivations results about the existence of infinite normal forms have been given only for orthogonal term rewriting systems namely left linear and nonoverlapping systems in this paper we show that some of those results can be extended to a particular class of nonorthogonal term rewriting systems we deal with systems in which the nonterminating rules are unfolding rules that model the operational semantics of a recursive operator the left linearity requirement is replaced by a retraction property of the supporting term algebra that allows the definition of a rewrite relation modulo a congruence relation induced on the set of terms by the unfolding rules

the bisimulation problem for equational graphs of finite out degree the bisimulation problem for equational graphs of finite out degree is shown to be decidable we reduce this problem to the eta bisimulation problem for deterministic rational vectors of boolean series on the alphabet of a deterministic pushdown automaton cal m we then exhibit a complete formal system for deducing equivalent pairs of such vectors

base modules for parametrized iterativity the concept of a base that is a parametrized finitary monad which we introduced earlier followed the footsteps of tarmo uustalu in his attempt to formalize parametrized recursion we proved that for every base free iterative algebras exist and we called the corresponding monad the rational monad of the base here we introduce modules for a base and we prove that the rational monad of a base gives rise to a canonical module that is characterized as the free iterative module on the given base this generalizes the classical nonparametric case of iterative s algebras whose rational monad is the monad of rational s trees and that was characterized by calvin elgot et al as the free iterative monad on s a basic parametrized example is the base assigning to every parameter set x the monad a x xa whose rational monad is the monad of all right wellfounded rational binary trees the rational module for this base is the natural transformation x xx xa x xa given by parametrized concatenation

completely iterative algebras and completely iterative monads completely iterative theories of calvin elgot formalize potentially infinite computations as solutions of recursive equations one of the main results of elgot and his coauthors is that infinite trees form a free completely iterative theory their algebraic proof of this result is extremely complicated we present completely iterative algebras as a new approach to the description of free completely iterative theories examples of completely iterative algebras include algebras on complete metric spaces it is shown that a functor admits an initial completely iterative algebra iff it has a final coalgebra the monad given by free completely iterative algebras is proved to be the free completely iterative monad on the given endofunctor this simplifies substantially all previous descriptions of these monads moreover the new approach is much more general than the classical one of elgot et al a necessary and sufficient condition for the existence of a free completely iterative monad is proved

additions and corrections to terminal coalgebras in well founded set theory abstract this note is to correct certain mistaken impressions of the author s that were in the original paper terminal coalgebras in well founded set theory which appeared in theoretical computer science 114 1993 299 315

the impact of fallible item parameter estimates on latent trait recovery in this paper we propose an upward correction to the standard error se estimation of ml the maximum likelihood ml estimate of the latent trait in item response theory irt more specifically the upward correction is provided for the se of ml when item parameter estimates obtained from an independent pretest sample are used in irt scoring when item parameter estimates are employed the resulting latent trait estimate is called pseudo maximum likelihood pml estimate traditionally the se of ml is obtained on the basis of test information only as if the item parameters are known the upward correction takes into account the error that is carried over from the estimation of item parameters in addition to the error in latent trait recovery itself our simulation study shows that both types of se estimates are very good when is in the middle range of the latent trait distribution but the upward corrected ses are more accurate than the traditional ones when takes more extreme values

p calculus internal mobility and agent passing calculi abstract the calculus is a process algebra which originates from ccs and permits a natural modelling of mobility i e dynamic reconfigurations of the process linkage using communication of names previous research has shown that the calculus has a much greater expressiveness than ccs but it also has a much more complex mathematical theory the primary goal of this work is to understand the reasons for this gap another goal is to compare the expressiveness of name passing calculi i e calculi like calculus where mobility is achieved via exchange of names and that of agent passing calculi i e calculi where mobility is achieved via exchange of agents we divide the mobility mechanisms of the calculus into internal and external mobility mechanisms the study of the subcalculus which only uses internal mobility called i suggests that internal mobility is responsible for much of the expressiveness of the calculus whereas external mobility is responsible for many of the semantic complications a pleasant property of i is the full symmetry between input and output constructs internal mobility is strongly related to agent passing mobility by imposing bounds on the order of the types of i and of the higher order calculus sangiorgi 1992 we define a hierarchy of name passing calculi based on internal mobility and one of agent passing calculi we show that there is an exact correspondence in terms of expressiveness between the two hierarchies

instrumental variables estimators of nonparametric models with discrete endogenous regressors this paper discusses estimation of nonparametric models whose regressor vectors consist of a vector of exogenous variables and a univariate discrete endogenous regressor with finite support both identification and estimators are derived from a transform of the model that evaluates the nonparametric structural function via indicator functions in the support of the discrete regressor a two step estimator is proposed where the first step constitutes nonparametric estimation of the instrument and the second step is a nonparametric version of two stage least squares linear functionals of the model are shown to be asymptotically normal and a consistent estimator of the asymptotic covariance matrix is described for the binary endogenous regressor case it is shown that one functional of the model is a conditional on covariates local average treatment effect that permits both unobservable and observable heterogeneity in treatments finite sample properties of the estimators from a monte carlo simulation study illustrate the practicability of the proposed estimators

the solutions of two star height problems for regular trees abstract regular trees can be defined by two types of rational expressions for these two types we solve the star height problem i e we show how to construct a rational expression of minimal star height from the minimal graph of the given tree i e the analogue of the minimal deterministic automation for regular languages in one case the minimal starheight is the rank in the sense of eggan of the minimal graph there corresponds a characterization of the star height of a prefix free regular language w r t rational expressions of a special kind called deterministic as the rank of its minimal deterministic automaton considered as a graph

identification and sequential estimation of panel data models with insufficient exclusion restrictions abstract this paper presents estimators for nonparametric panel data models with additive fixed effects we analyze a model in which the entire regressor vector consisting of time varying as well as time invariant regressors is correlated with the individual fixed effect but there are insufficient exclusion restrictions to permit direct instrumental variables estimation of the model it is shown that when the model satisfies the additive interactive regression air representation of andrews and whang economic theory 6 1990 466 480 a sequential estimator consistently estimates the model the limiting distribution of scalar nonlinear functionals of the model is shown to be standard normal finite sample properties of the estimator are considered in a monte carlo simulation study and used to estimate the returns to education in a cohort of mature men from the national longitudinal survey

functional coefficient regression models for nonlinear time series abstract the local linear regression technique is applied to estimation of functional coefficient regression models for time series data the models include threshold autoregressive models and functional coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross validatory estimation for the expected forecasting errors the proposed methodology is data analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality the asymptotic properties of the proposed estimators are investigated under the mixing condition both simulated and real data examples are used for illustration

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

terminal coalgebras and free iterative theories every finitary endofunctor h of set can be represented via a finitary signature and a collection of equations called basic we describe a terminal coalgebra for h as the terminal coalgebra of all trees modulo the congruence of applying the basic equations potentially infinitely often as an application we describe a tree iterative theory on h in the sense of calvin elgot as the theory of all rational trees modulo the analogous congruence this yields a number of new examples of iterative theories e g the theory of all strongly extensional rational finitely branching trees free on the finite power set functor or the theory of all binary rational unordered trees free on one commutative binary operation

stochastic order in dichotomous item response models for fixed adaptive and multidimensional tests dichotomous irt models can be viewed as families of stochastically ordered distributions of responses to test items this paper explores several properties of such distributions in particular it is examined under what conditions stochastic order in families of conditional distributions is transferred to their inverse distributions from two families of related distributions to a third family or from multivariate conditional distributions to a marginal distribution the main results are formulated as a series of theorems and corollaries which apply to dichotomous irt models one part of the results holds for unidimensional models with fixed item parameters the other part holds for models with random item parameters as used for example in adaptive testing or for tests with multidimensional abilities

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size