nonparametric inference based on conditional moment inequalities abstract this paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and or equalities the parameters need not be identified confidence sets and tests are introduced the correct uniform asymptotic size of these procedures is established the false coverage probabilities and power of the cs s and tests are established for fixed alternatives and some local alternatives finite sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model the recommended cs test uses a cramer von mises type test statistic and employs a generalized moment selection critical value

bootstrap inference in partially identified models defined by moment inequalities coverage of the identified set this paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identi ed econometric models we consider econometric models de ned by nitely many weak moment inequalities y which encompass many applications of economic interest the objective of our inferential procedure is to cover the identi ed set with a prespeci ed probability z we compare our bootstrap procedure a competing asymptotic approximation and subsampling proce dures in terms of the rate at which they achieve the desired coverage level also known as the error in the coverage probability under certain conditions we show that our bootstrap procedure and the asymp totic approximation have the same order of error in the coverage probability which is smaller than the one obtained by using subsampling this implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling a monte carlo study con rms this nding in a small sample simulation

efficient discrete approximations of quantum gates quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set it has been shown that this is possible for almost all choices of base sets and furthermore that the number of gates required for precision e is only polynomial in log 1 e here we prove that using certain sets of base gates quantum compiling requires a string length that is linear in log 1 e a result which matches the lower bound from counting volume up to constant factor

chow s theorem and universal holonomic quantum computation a theorem from control theory relating the lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to holonomic quantum computation conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated with a non abelian gauge connection when applied to the optical holonomic computer these conditions determine that the holonomy group of the two qubit interaction model contains su 2 su 2 in particular a universal two qubit logic gate is attainable for this model

medical image interpolation based on multi resolution registration abstract we present a novel registration based image interpolation approach in this paper the proposed method is divided into two steps image registration and intensity interpolation an image registration method is developed to construct a corresponding transformation which is represented by the bicubic b spline vector valued function between the given images so that the image features are well matched to match features from coarse to fine a multi resolution strategy is applied with different numbers of b spline control points adopted at various resolution levels after registration the intensity values of in between images are calculated by linear cubic interpolation along the matching lines experimental results demonstrate that our interpolation approach is effective robust and capable of producing continuously deformed in between images with clear shape features

posterior consistency of gaussian process prior for nonparametric binary regression consider binary observations whose response probability is an unknown smooth function of a set of covariates suppose that a prior on the response probability function is induced by a gaussian process mapped to the unit interval through a link function in this paper we study consistency of the resulting posterior distribution if the covariance kernel has derivatives up to a desired order and the bandwidth parameter of the kernel is allowed to take arbitrarily small values we show that the posterior distribution is consistent in the l 1 distance as an auxiliary result to our proofs we show that under certain conditions a gaussian process assigns positive probabilities to the uniform neighborhoods of a continuous function this result may be of independent interest in the literature for small ball probabilities of gaussian processes

the bm l _ mathbf 1 norm density estimator process the notion of an l1 norm density estimator process indexed by a class of kernels is introduced then a functional central limit theorem and a glivenko cantelli theorem are established for this process while assembling the necessary machinery to prove these results a body of poissonization techniques and restricted chaining methods is developed which is useful for studying weak convergence of general processes indexed by a class of functions none of the theorems imposes any condition at all on the underlying lebesgue density f also somewhat unexpectedly the distribution of the limiting gaussian process does not depend on f

unified approach to testing functional hypotheses in semiparametric contexts abstract we suggest a new method with very wide applicability for testing semiparametric hypotheses about functions such as regression means and probability densities the technique is based on characterising hypotheses in terms of functionals which can be estimated root n consistently and constructing test statistics in terms of estimators of the functionals since the tests are semiparametric it is appropriate to assess them on the basis of their ability to detect departures of size n 1 2 from the null hypothesis we show that they do indeed have this property unlike tests constructed in a nonparametric setting their power does not depend critically on choice of a bandwidth and in particular smoothing parameter selection is not an issue that has to be addressed by users of the tests bootstrap methods are suggested for calibrating the tests in a regression setting applications include tests of specification such as partial linear and index models against nonparametric or semiparametric alternatives and tests of monotonicity concavity separability equality of regression functions and base independence of equivalence scales in a density setting they include tests of radial symmetry and stochastic dominance

scalable programmable quantum gates and a new aspect of the additivity problem for the classical capacity of quantum channels we consider two apparently separated problems in the first part of the article we study the concept of a scalable approximate programmable quantum gate spqg these are special approximate programmable quantum gates with nice properties that could have implications on the theory of universal computation unfortunately as we prove such objects do not exist in the domain of usual quantum theory in the second part the problem of noisy dense coding and generalizations is addressed we observe that the additivity problem for the classical capacity obtained is of apparently greater generality than for the usual quantum channel completely positive maps i e the latter occurs as a special case of the former but as we shall argue with the help of the nonexistence result of the first part the former cannot be reduced to an instance of the latter we conclude by suggesting that the additivity problem for the classical capacity of quantum channels as posed until now may conceptually not be in its appropriate generality

on the universality of almost every quantum logic gate lloyd phys rev lett 75 346 1995 showed that almost every quantum logic gate is universal in the sense that it can be used to approximate any unitary transformation the argument relied on a more general fact whose proof was not given in detail we give a complete proof of this more general fact

joint image segmentation and registration based on a dynamic level set approach using truncated hierarchical b splines abstract we present a novel approach for joint image segmentation and nonrigid registration using bidirectional composition based level set formulation this efficient framework incorporates automatic structural analysis from image segmentation into the registration framework this method has shown an improved performance as compared to carrying out segmentation and registration separately unlike previous approaches the implicit level set function defining the segmentation contour and the spatial transformation function that maps the deformation for image registration are both defined using b splines this joint level set framework uses a variational form of an atlas based segmentation together with large deformation based nonrigid registration in addition a bidirectional composition framework is introduced to incorporate a more symmetric update the minimization of the variational form is accomplished by dynamic evaluations on a set of successively refined adaptive grids at multiple image resolutions the improvement in the description of the segmentation result using higher order splines leads to a better accuracy of both the image segmentation and registration process the performance of the proposed method is demonstrated on synthetic and medical images to show the improvement as compared to other registration methods

brief paper discrete time controllability for feedback quantum dynamics controllability properties for discrete time markovian quantum dynamics are investigated we find that while in general the controlled system is not finite time controllable feedback control allows for arbitrary asymptotic state to state transitions under further assumptions on the form of the measurement we show that finite time controllability can be achieved in a time that is twice the dimension of the system and we provide an iterative procedure to design the unitary control actions

a test of non identifying restrictions and confidence regions for partially identified parameters abstract we propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables which do not necessarily identify the data generating process the restrictions can be derived from any model of interactions allowing censoring and multiple equilibria when the restrictions are parameterized the test can be inverted to yield confidence regions for partially identified parameters thereby complementing other proposals primarily chernozhukov et al chernozhukov v hong h tamer e 2007 estimation and confidence regions for parameter sets in econometric models econometrica 75 1243 1285

a subdivision based implementation of the hierarchical b spline finite element method abstract a novel technique is presented to facilitate the implementation of hierarchical b splines and their interfacing with conventional finite element implementations the discrete interpretation of the two scale relation as common in subdivision schemes is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b spline basis the subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same level basis functions their subsequent multiplication with subdivision matrices projects them during the assembly stage to the correct levels of the hierarchical b spline basis the proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one two and three space dimensions

noncommutative tori and universal sets of nonbinary quantum gates we address the problem of universality in simulation of evolution of quantum system and in theory of quantum computations related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific unitary transformations quantum gates from given set in an earlier paper application of clifford algebras to constructions of universal sets of binary quantum gates uk u 2n was shown for application of a similar approach to nonbinary quantum gates uk u ln in present work we used rational noncommutative torus t1 l2n a set of universal nonbinary two gates is presented here as one example

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

optimal aggregation of classifiers in statistical learning classification can be considered as nonparametric estimation of sets where the risk is defined by means of a specific distance between sets associated with misclassification error it is shown that the rates of convergence of classifiers depend on two parameters the complexity of the class of candidate sets and the margin parameter the dependence is explicitly given indicating that optimal fast rates approaching o n 1 can be attained where n is the sample size and that the proposed classifiers have the property of robustness to the margin the main result of the paper concerns optimal aggregation of classifiers we suggest a classifier that automatically adapts both to the complexity and to the margin and attains the optimal fast rates up to a logarithmic factor

boundedly pivotal structural change tests in continuous updating gmm with strong weak identification and completely unidentified cases abstract this paper develops structural change tests in the continuous updating gmm framework that are robust to weak identification we propose likelihood ratio like anderson rubin 1949 estimation of the parameters of a single equation in a complete system of stochastic equations annals of mathematical statistics 20 46 63 and kleinbergen 2005 testing parameters in gmm without assuming that they are identified manuscript brown university types of tests since the limits of the test statistics are not nuisance parameter free bounds for the limit of the test statistics are derived the bounds are nuisance parameter free and robust to identification problems simulations show that the anderson rubin 1949 and kleinbergen 2005 testing parameters in gmm without assuming that they are identified manuscript brown university type of tests have very good small sample properties in the case of weak instruments the sup lm test of andrews 1993a tests for parameter instability and structural change with unknown change point econometrica 61 821 856 rejects the true null of parameter stability more than the nominal level and also has low power in the weak instrument setup

quantum computational networks the theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines quantum gates are the generalization of classical logic gates a single type of gate the universal quantum gate together with quantum unit wires is adequate for constructing networks with any possible quantum computational property

phase space dynamical model of an open system of interacting q bits the path integral form of the propagator for a stochastic schrodinger equation is used to derive stochastic differential equations on the quantum phase space of interacting q bits in a random environment the equations can be considered as an approximate classical model of the quantum system predictions of the model are compared with that of the exact quantum equations for various examples of the environment operators

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

on the bootstrap of the maximum score estimator this paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator the theory developed also applies to other estimators within a cube root convergence class for some single parameter estimators in this class the results suggest a simple method for inference based upon the bootstrap

convex clustering via l1 fusion penalization summary we study the large sample behaviour of a convex clustering framework which minimizes the sample within cluster sum of squares under an l1 fusion constraint on the cluster centroids this recently proposed approach has been gaining in popularity however its asymptotic properties have remained mostly unknown our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems we use this representation to provide a simple and intuitive formulation for the population clustering procedure we then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence the proof conducts a careful simultaneous analysis of a collection of m estimation problems whose cardinality grows together with the sample size on the basis of the new perspectives gained from the asymptotic investigation we propose a key post processing modification of the original clustering framework we show both theoretically and empirically that the resulting approach can be successfully used to estimate the number of clusters in the population using simulated data we compare the proposed method with existing number of clusters and modality assessment approaches and obtain encouraging results we also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single cell virology study

qudit basis universal quantum computation using χ 2 interactions we prove that universal quantum computation can be realized using only linear optics and 2 three wave mixing interactions in any n 1 dimensional qudit basis of the n pump photon subspace first we exhibit a strictly universal gate set for the qubit basis in the one pump photon subspace next we demonstrate qutrit basis universality by proving that 2 hamiltonians and photon number operators generate the full u 3 lie algebra in the two pump photon subspace and showing how the qutrit controlled z gate can be implemented with only linear optics and 2 interactions we then use proof by induction to obtain our general qudit result our induction proof relies on coherent photon injection or subtraction a technique enabled by 2 interaction between the encoding modes and ancillary modes finally we show that coherent photon injection is more than a conceptual tool in that it offers a route to preparing high photon number fock states from single photon fock states

quantum gates on hybrid qudits we introduce quantum hybrid gates that act on qudits of different dimensions in particular we develop two representative two qudit hybrid gates sum and swap and many qudit hybrid toffoli and fredkin gates we apply the hybrid sum gate to generating entanglement and find that operator entanglement of the sum gate is equal to the entanglement generated by it for certain initial states we also show that the hybrid sum gate acts as an automorphism on the pauli group for two qudits of different dimensions under certain conditions finally we describe a physical realization of these hybrid gates for spin systems

asymptotic properties for a class of partially identified models we propose inference procedures for partially identified population features for which the population identification region can be written as a transformation of the aumann expectation of a properly defined set valued random variable svrv an svrv is a mapping that associates a set rather than a real number with each element of the sample space examples of population features in this class include interval identified scalar parameters best linear predictors with interval outcome data and parameters of semiparametric binary models with interval regressor data we extend the analogy principle to svrvs and show that the sample analog estimator of the population identification region is given by a transformation of a minkowski average of svrvs using the results of the mathematics literature on svrvs we show that this estimator converges in probability to the population identification region with respect to the hausdorff distance we then show that the hausdorff distance and the directed hausdorff distance between the population identification region and the estimator when properly normalized by n converge in distribution to functions of a gaussian process whose covariance kernel depends on parameters of the population identification region we provide consistent bootstrap procedures to approximate these limiting distributions using similar arguments as those applied for vector valued random variables we develop a methodology to test assumptions about the true identification region and its subsets we show that these results can be used to construct a confidence collection and a directed confidence collection those are respectively collection of sets that when specified as a null hypothesis for the true value a subset of values of the population identification region cannot be rejected by our tests

analytic controllability of time dependent quantum control systems the question of controllability is investigated for a quantum control system in which the hamiltonian operator components carry explicit time dependence which is not under the control of an external agent we consider the general situation in which the state moves in an infinite dimensional hilbert space a drift term is present and the operators driving the state evolution may be unbounded however considerations are restricted by the assumption that there exists an analytic domain dense in the state space on which solutions of the controlled schrodinger equation may be expressed globally in exponential form the issue of controllability then naturally focuses on the ability to steer the quantum state on a finite dimensional submanifold of the unit sphere in hilbert space and thus on analytic controllability a relatively straightforward strategy allows the extension of lie algebraic conditions for strong analytic controllability derived earlier for the simpler time independent system in which the d

more on confidence intervals for partially identified parameters this paper extends imbens and manski s 2004 analysis of confidence intervals for interval identified parameters the extension is motivated by the discovery that for their final result imbens and manski implicitly assumed locally superefficient estimation of a nuisance parameter i reanalyze the problem both with assumptions that merely weaken this superefficiency condition and with assumptions that remove it altogether imbens and manski s confidence region is valid under weaker assumptions than theirs yet superefficiency is required i also provide a confidence interval that is valid under superefficiency but can be adapted to the general case a methodological contribution is to observe that the difficulty of inference comes from a preestimation problem regarding a nuisance parameter clarifying the connection to other work on partial identification

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

inference for parameters defined by moment inequalities using generalized moment selection the topic of this paper is inference in models in which parameters are defined by moment inequalities and or equalities the parameters may or may not be identified this paper introduces a new class of confidence sets and tests based on generalized moment selection gms gms procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative the power of gms tests is compared to that of subsampling m out of n bootstrap and plug in asymptotic pa tests the latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size in a uniform sense for the moment inequality equality model gms tests are shown to have asymptotic power that dominates that of subsampling m out of n bootstrap and pa tests subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of pa tests

intersection bounds estimation and inference we develop a practical and novel method for inference on intersection bounds namely bounds defined by either the infimum or supremum of a parametric or nonparametric function or equivalently the value of a linear programming problem with a potentially infinite constraint set we show that many bounds characterizations in econometrics for instance bounds on parameters under conditional moment inequalities can be formulated as intersection bounds our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters and also applies to models with inequalities that are nonseparable in parameters since analog estimators for intersection bounds can be severely biased in finite samples routinely underestimating the size of the identified set we also offer a median bias corrected estimator of such bounds as a by product of our inferential procedures we develop theory for large sample inference based on the strong approximation of a sequence of series or kernel based empirical processes by a sequence of penultimate gaussian processes these penultimate processes are generally not weakly convergent and thus are non donsker our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes our construction also provides new adaptive inequality moment selection methods we provide conditions for the use of nonparametric kernel and series estimators including a novel result that establishes strong approximation for any general series estimator admitting linearization which may be of independent interest

quantum computer with mixed states and four valued logic in this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations not necessarily unitary a mixed state operator of density matrix of n twolevel quantum systems is considered as an element of 4 n dimensional operator hilbert space liouville space it allows us to use a quantum computer model with four valued logic the gates of this model are general superoperators which act on n ququat state ququat is a quantum state in a four dimensional operator hilbert space unitary two valued logic gates and quantum operations for an n qubit open system are considered as four valued logic gates acting on n ququats we discuss properties of quantum four valued logic gates in the paper we study universality for quantum four valued logic gates

adaptive fem based nonrigid image registration using truncated hierarchical b splines we present an efficient approach of finite element method fem based nonrigid image registration in which the spatial transformation is constructed using truncated hierarchical b splines thb splines the image registration framework minimizes an energy functional using an fem based method and thus involves solving a large system of linear equations this framework is carried out on a set of successively refined grids however due to the increased number of control points during subdivision large linear systems are generated which are generally demanding to solve instead of using uniform subdivision an adaptive local refinement scheme is carried out only refining the areas of large change in deformation of the image by incorporating the key advantages of thb spline basis functions such as linear independence partition of unity and reduced overlap into the fem based framework we improve the matrix sparsity and computational efficiency the performance of the proposed method is demonstrated on 2d synthetic and medical images

universality in quantum computation we show that in quantum computation almost every gate that operates on two or more bits is a universal gate we discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

parametric rate inference for one sided differentiable parameters suppose one has a collection of parameters indexed by a possibly infinite dimensional set given data generated from some distribution the objective is to estimate the maximal parameter in this

nonparametric inference for counterfactual means bias correction confidence sets and weak iv abstract this paper supplements manski 1990 and manski and pepper 2000 and contributes to the literature by introducing the concept of weak iv for the partially identified mean counterfactual outcomes when an instrumental variable iv or a monotone instrumental variable miv is available iv or miv assumption respectively developing asymptotically uniformly valid confidence sets for the counterfactual mean outcomes and average treatment effects under the assumptions correcting biases of estimates of bounds on the counterfactual mean outcomes under the assumptions we apply the confidence sets to further examining the effect of family intactness on a child s high school graduation originally studied in manski et al 1992

a novel dynamic multilevel technique for image registration we present a novel dynamic multilevel technique for solving image registration problems the development is carried out to construct a spatial transformation based on cubic b spline basis functions and determine the control points dynamically unlike fem based image registration methods we do not have the difficulty of solving a complicated matrix system in addition the presented method is enhanced by a multilevel technique which makes it more efficient and flexible the numerical results and several comparison studies on real bio medical images show our technique is stable accurate and fast especially for large deformation registration problems

new dependence coefficients examples and applications to statistics to measure the dependence between a real valued random variable x and a algebra we consider four distances between the conditional distribution function of x given and the distribution function of x the coefficients obtained are weaker than the corresponding mixing coefficients and may be computed in many situations in particular we show that they are well adapted to functions of mixing sequences iterated random functions and dynamical systems starting from a new covariance inequality we study the mean integrated square error for estimating the unknown marginal density of a stationary sequence we obtain optimal rates for kernel estimators as well as projection estimators on a well localized basis under a minimal condition on the coefficients using recent results we show that our coefficients may be also used to obtain various exponential inequalities a concentration inequality for lipschitz functions and a berry esseen type inequality

inference based on conditional moment inequalities in this paper we propose an instrumental variable approach to constructing confidence sets cs s for the true parameter in models defined by conditional moment inequalities equalities we show that by properly choosing instrument functions one can transform conditional moment inequalities equalities into unconditional ones without losing identification power based on the unconditional moment inequalities equalities we construct cs s by inverting cramer von mises type or kolmogorov smirnov type tests critical values are obtained using generalized moment selection gms procedures we show that the proposed cs s have correct uniform asymptotic coverage probabilities new methods are required to establish these results because an infinite dimensional nuisance parameter affects the asymptotic distributions we show that the tests considered are consistent against all fixed alternatives and typically have power against n 1 2 local alternatives to some but not all sequences of distributions in the null hypothesis monte carlo simulations for five different models show that the methods perform well in finite samples

confidence sets for partially identified parameters that satisfy a finite number of moment inequalities this paper proposes a computationally simple way to construct confidence sets for a parameter of interest in models comprised of moment inequalities building on results from the literature on multivariate one sided tests i show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities the associated test statistic has an asymptotic chi bar square distribution and can be inverted to construct an asymptotic confidence set for the parameter of interest even if that parameter is only partially identified critical values for the test are easily computed and a monte carlo study demonstrates implementation and finite sample performance

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

decidable and undecidable problems about quantum automata we study the following decision problem is the language recognized by a quantum finite automaton empty or nonempty we prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds this result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and nonstrict thresholds both lead to undecidable problems

el inference for partially identified models large deviations optimality and bootstrap validity this paper addresses the issue of optimal inference for parameters that are partially identied in models with moment inequalities there currently exists a variety of inferential methods for use in this setting however the question of choosing optimally among contending procedures is unresolved in this paper i rst consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal this nding is a direct analog to that in kitamura 2001 for moment equality models second i introduce a new empirical likelihood bootstrap that provides a valid resampling method for moment inequality models and overcomes the implementation challenges that arise as a result of non pivotal limit distributions lastly i analyze the nite sample properties of the proposed framework using monte carlo simulations the

an improved bootstrap test of stochastic dominance we propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling the method admits prospects involving infinite as well as finite dimensional unknown parameters so that the variables are allowed to be residuals from nonparametric and semiparametric models the proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions this paper also characterizes the set of probabilities so that the asymptotic size is exactly equal to the nominal level uniformly as our simulation results show these characteristics of our tests lead to an improved power property in general the improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test s limiting distribution

criteria for reachability of quantum states we address the question of which quantum states can be inter converted under the action of a time dependent hamiltonian in particular we consider the problem as applied to mixed states and investigate the difference between pure and mixed state controllabilities introduced in previous work we provide a complete characterization of the eigenvalue spectrum for which the state is controllable under the action of the symplectic group we also address the problem of which states can be prepared if the dynamical lie group is not sufficiently large to allow the system to be controllable

confidence intervals for partially identified parameters recently a growing body of research has studied inference in settings where parameters of interest are partially identified in many cases the parameter is real valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data for this case confidence intervals cis have been proposed that cover the entire identification region with fixed probability here we introduce a conceptually different type of confidence interval rather than cover the entire identification region with fixed probability we propose cis that asymptotically cover the true value of the parameter with this probability however the exact coverage probabilities of the simplest version of our new cis do not converge to their nominal values uniformly across different values for the width of the identification region to avoid the problems associated with this we modify the proposed ci to ensure that its exact coverage probabilities do converge uniformly to their nominal values we motivate this modified ci through exact results for the gaussian case

a universal two bit gate for quantum computation we prove the existence of a class of two input two output gates any one of which is universal for quantum computation this is done by explicitly constructing the three bit gate introduced by deutsch proc r soc lond a 425 73 1989 as a network consisting of replicas of a single two bit gate

rapid solution of problems by quantum computation a class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method the quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation

efficient shrinkage in parametric models this paper introduces shrinkage for general parametric models we show how to shrink maximum likelihood estimators towards parameter subspaces de ned by general nonlinear restrictions we derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework we show that if the shrinkage dimension exceeds two the asymptotic risk of the shrinkage estimator is strictly less than that of the mle this reduction holds globally in the parameter space we show that the reduction in asymptotic risk is substantial even for moderately large values of the parameters the formula simplify in a very convenient way in the context of high dimensional models we derive a simple bound for the asymptotic risk we also provide a new large sample minimax e ciency bound we use the concept of local asymptotic minimax bounds a generalization of the conventional asymptotic minimax bounds the

likelihood ratio tests for monotone functions we study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function the likelihood ratio test for this hypothesis is derived in the particular case of interval censoring or current status data and its limiting distribution is obtained the limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving brownian motion t 2 and greatest convex minorants thereof inversion of the family of tests yields pointwise confidence intervals for the unknown distribution function we also study the behavior of the statistic under local and fixed alternatives 1 introduction we shall consider likelihood ratio tests and the corresponding confidence intervals in a class of problems involving nonparametric estimation of a monotone function the problem in each case involves testing the null hypothesis h 0 that the monotone function has a particular value at afixed point t 0 in the domain of the function of course with each testing problem there is a related problem of finding confidence intervals here are some examples of the problems we have in mind

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

manifold algorithmic errors in quantum computers with static internal imperfections the inevitable existence of static internal imperfections and residual interactions in some quantum computer architectures results in internal decoherence dissipation and destructive unitary shifts of active algorithms by exact numerical simulations we determine the relative importance and origin of these errors for a josephson charge qubit quantum computer in particular we determine that the dynamics of a cnot gate interacting with its idle neighboring qubits via native residual coupling behaves much like a perturbed kicked top in the exponential decay regime where fidelity decay is only weakly dependent on perturbation strength this means that retroactive removal of gate errors whether unitary or non unitary may not be possible and that effective error correction schemes must operate concurrently with the implementation of subcomponents of the gate

rates of convergence for the gaussian mixture sieve gaussian mixtures provide a convenient method of densityestimation that lies somewhere between parametric models and kernel densityestimators when the number of components of the mixture is allowed to increase as sample size increases the model is called a mixture sieve we establish a bound on the rate of convergence in hellinger distance for densityestimation using the gaussian mixture sieve assuming that the true density is itself a mixture of gaussians the underlying mixing measure of the true densityis not necessarilyassumed to have finite support computing the rate involves some delicate calculations since the size of the sieve as measured bybracketing entropy and the saturation rate cannot be found using standard methods when the mixing measure has compact support using kn n 2 3 log n 1 3 components in the mixture yields a rate of order log n 1 6 n1 6 for every 0 the rates depend heavilyon the tail behavior of the true density the sensitivity to the tail behavior is diminished byusing a robust sieve which includes a long tailed component in the

quantum implicit computational complexity we introduce a quantum lambda calculus inspired by lafont s soft linear logic and capturing the polynomial quantum complexity classes eqp bqp and zqp the calculus is based on the classical control and quantum data paradigm this is the first example of a formal system capturing quantum complexity classes in the spirit of implicit computational complexity it is machine free and no explicit bound e g polynomials appears in its syntax