on finite sample properties of alternative estimators of coefficients in a structural equation with many instruments abstract we compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables as the classical methods we consider the limited information maximum likelihood liml estimator and the two stage least squares tsls estimator and as the semi parametric estimation methods we consider the maximum empirical likelihood mel estimator and the generalized method of moments gmm or the estimating equation estimator tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most linear models of interest and we include some heteroscedastic cases and nonlinear cases we have found that the liml estimator has good performance in terms of the bounded loss functions and probabilities when the number of instruments is large that is the micro econometric models with many instruments in the terminology of recent econometric literature

dynamic analysis of continuous plane trusses with equidistant supports the natural and forced vibrations of a continuous warren truss resting on equidistant roller supports are studied in the analyses the longitudinal inertial forces are neglected in the equation of motion and the mass of the truss is replaced by two sets of lumped masses at the nodes in the forced vibration case the truss is subjected to transverse harmonic loads acting at the nodes the truss can be considered as an equivalent system with cyclic bi periodicity periodicities due to the repetitive units of the truss and the supports respectively therefore the governing equation for such a system can be uncoupled by applying u transformation twice to form a set of single degree of freedom equations such equations can be used to solve for the natural frequencies of the trusses or their responses due to external excitations typical warren trusses are taken as examples to demonstrate the advantages of the proposed method and the accuracy that can be achieved the response of a truss with six substructures and four supports with a harmonic load acting at the centre node is investigated

gmm with many moment conditions this paper provides a first order asymptotic theory for generalized method of moments gmm estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak examples in which these asymptotics are relevant include instrumental variable iv estimation with many possibly weak or uninformed instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments under certain regularity conditions the gmm estimators are shown to converge in probability but not necessarily to the true parameter and conditions for consistent gmm estimation are given a general framework for the gmm limit distribution theory is developed based on epiconvergence methods some illustrations are provided including consistent gmm estimation of a panel model with time varying individual effects consistent limited information maximum likelihood estimation as a continuously updated gmm estimator and consistent iv structural estimation using large numbers of weak or irrelevant instruments some simulations are reported

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

secret key and private key constructions for simple multiterminal source models we propose an approach for constructing secret and private keys based on the long known slepian wolf code due to wyner for correlated sources connected by a virtual additive noise channel our work is motivated by results of csiszar and narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and slepian wolf near lossless data compression explicit procedures for such constructions and their substantiation are provided the performance of low density parity check channel codes in devising a new class of secret keys is examined

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

uniform random number generation from markov chains non asymptotic and asymptotic analyses in this paper we derive non asymptotic achievability and converse bounds on the random number generation with without side information our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length we also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds which implies that our bounds are asymptotically tight in those regimes we also show the second order rates of those problems and derive single letter forms of the variances characterizing the second order rates furthermore we address the relative entropy rate and the modified mutual information rate for these problems

the optimal choice of moments in dynamic panel data models this paper derives an approximation of the mean square error mse of the gmm estimator in dynamic panel data models the approximation is based on higher order asymptotic theory under double asymptotics while first order theory under double asymptotics provides information about the bias it does not provide enough information about the variance of the estimator higher order theory enables us to obtain information about the variance from this result a procedure for choosing the number of instruments is proposed the simulations confirm that the proposed procedure improves the precision of the estimator

instrumental variable estimation in functional linear models in an increasing number of empirical studies the dimensionality measured e g as the size of the parameter space of interest can be very large two instances of large dimensional models are the linear regression with a large number of covariates and the estimation of a regression function with many instrumental variables an appropriate setting to analyze high dimensional problems is provided by a functional linear model in which the covariates belong to hilbert spaces this paper considers the case where covariates are endogenous and assumes the existence of instrumental variables that are functional as well the paper shows that estimating the regression function is a linear ill posed inverse problem with a known but data dependent operator the first contribution is to analyze the rate of convergence of the penalized least squares estimator based on the result we discuss the notion of instrument strength in the high dimensional setting we also discuss a generalized version of the estimator when the problem is premultiplied by an instrument dependent operator this extends the technology of generalized method of moments to high dimensional functional data a central limit theorem is also established on the inner product of the estimator the studied estimators are easy and fast to implement and the finite sample performance is discussed through simulations and an application to the impact of age specific fertility rate curves on yearly economic growth in the united kingdom

bootstrap inference for instrumental variable models with many weak instruments this study s main contribution is to theoretically analyze the application of bootstrap methods to instrumental variable models when the available instruments may be weak and the number of instruments goes to infinity with the sample size we demonstrate that a standard residual based bootstrap procedure cannot consistently estimate the distribution of the limited information maximum likelihood estimator or fuller 1977 estimator under many many weak instrument sequence the primary reason is that the standard procedure fails to capture the instrument strength in the sample adequately in addition we consider the restricted efficient re bootstrap of davidson and mackinnon 2008 2010 2014 that generates bootstrap data under the null restricted and uses an efficient estimator of the coefficient of the reduced form equation efficient we find that the re bootstrap is also invalid however it effectively mimics more key features in the limiting distributions of interest and thus is less distorted in finite samples than the standard bootstrap procedure finally we propose modified bootstrap procedures that provide a valid distributional approximation for the two estimators with many many weak instruments a monte carlo experiment shows that hypothesis testing based on the asymptotic normal approximation can have severe size distortions in finite samples instead our modified bootstrap procedures greatly reduce these distortions

communication with imperfectly shared randomness communication complexity investigates the amount of communication needed for two or more players to determine some joint function of their private inputs for many interesting functions the communication complexity can be much smaller than basic information theoretic measures associated with the players inputs such as the input length the entropy or even the conditional entropy communication complexity of many functions reduces further when the players share randomness classical works studied the communication complexity of functions when the interacting players share randomness perfectly i e they get identical copies of randomness from a common source this paper considers the variant of this question when the players share randomness imperfectly i e when they get noisy copies of the randomness produced by some common source our main result shows that any function that can be computed by a k bit protocol in the perfect sharing model has a 2 k bit protocol in the setting of imperfectly shared randomness and such an exponential growth is necessary our upper bound relies on ideas from locality sensitive hashing while lower bounds rely on hypercontractivity and a new invariance principle tailored for communication protocols

security analysis of varepsilon almost dual universal 2 hash functions smoothing of min entropy versus smoothing of renyi entropy of order 2 recently varepsilon almost dual universal2 hash functions have been proposed as a new and wider class of hash functions using this class of hash functions several efficient hash functions were proposed this paper evaluates the security performance when we apply this kind of hash functions we evaluate the security in several kinds of setting based on the l 1 distinguishability criterion and the modified mutual information criterion the obtained evaluation is based on smoothing of renyi entropy of order 2 and or min entropy we clarify the difference between these two methods

hypothesis testing in linear regression when k n is large abstract this paper derives the asymptotic distribution of the f test for the significance of linear regression coefficients as both the number of regressors k and the number of observations n increase together so that their ratio remains positive in the limit the conventional critical values for this test statistic are too small and the standard version of the f test is invalid under this asymptotic theory this paper provides a correction to the f statistic that gives correctly sized tests both under this paper s limit theory and also under conventional asymptotic theory that keeps k finite this paper also presents simulations that indicate the new statistic can perform better in small samples than the conventional test the statistic is then used to reexamine olivei and tenreyro s results from olivei g tenreyro s 2007 the timing of monetary policy shocks the american economic review 97 636 663 and sala i martin s results from sala i martin x x 1997 i just ran two million regressions the american economic review 87 2 178 183

minimum distance approach to inference with many instruments abstract i analyze a linear instrumental variables model with a single endogenous regressor and many instruments i use invariance arguments to construct a new minimum distance objective function with respect to a particular weight matrix the minimum distance estimator is equivalent to the random effects estimator of chamberlain and imbens 2004 and the estimator of the coefficient on the endogenous regressor coincides with the limited information maximum likelihood estimator this weight matrix is inefficient unless the errors are normal and i construct a new more efficient estimator based on the optimal weight matrix finally i show that when the minimum distance objective function does not impose a proportionality restriction on the reduced form coefficients the resulting estimator corresponds to a version of the bias corrected two stage least squares estimator i use the objective function to construct confidence intervals that remain valid when the proportionality restriction is violated

large deviation analysis for quantum security via smoothing of renyi entropy of order 2 it is known that the security evaluation can be done by smoothing of renyi entropy of order 2 in the classical and quantum settings when we apply universal 2 hash functions using the smoothing of renyi entropy of order 2 we derive security bounds for l 1 distinguishability and modified mutual information criterion under the classical and quantum setting and have derived these exponential decreasing rates these results are extended to the case when we apply e almost dual universal 2 hash functions furthermore we apply this analysis to the secret key generation with error correction

alternative approximations to the distributions of instrumental variable estimators the paper considers the ols the iv and two method of moments estimators mm and mmk of the coefficients of a single equation where the explanatory variables are correlated with the disturbance term the mm and mmk estimators are generalizations of the liml and limlk estimators respectively multivariate first order approximations to the distributions are derived under normality using a parameter sequence where the number of instruments increases as the number of observations increases numerical results show these approximations are more accurate compared to large sample approximations even if the number of instruments is small the moments of the multivariate limit distributions of the mm and mmk estimators can be consistently estimated under a variety of parameter sequences including the large sample sequence the new approximate confidence regions perform well in terms of exact levels compared to traditional ones the iv estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator which is dominated in practical cases by the mm and mmk estimators in terms of nearness to the true value in the sense of pitman

applications of ldpc codes to the wiretap channel with the advent of quantum key distribution qkd systems perfect i e information theoretic security can now be achieved for distribution of a cryptographic key qkd systems and similar protocols use classical error correcting codes for both error correction for the honest parties to correct errors and privacy amplification to make an eavesdropper fully ignorant from a coding perspective a good model that corresponds to such a setting is the wire tap channel introduced by wyner in 1975 in this correspondence we study fundamental limits and coding methods for wire tap channels we provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel we also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes in some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity for the special case of a noiseless main channel and binary erasure channel we consider encoder and decoder design for codes achieving secrecy on the wiretap channel we show that it is possible to construct linear time decodable secrecy codes based on low density parity check ldpc codes that achieve secrecy

on secret sharing systems a secret sharing system permits a secret to be shared among n trustees in such a way that any k of them can recover the secret but any k 1 have complete uncertainty about it a linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by shamir and can also be viewed as a deterministic version of blakley s probabilistic method bounds on the maximum value of n for a given k and secret size are derived for any system linear or nonlinear the proposed scheme achieves the lower bound which for practical purposes differs insignificantly from the upper bound the scheme may be extended to protect several secrets methods to protect against deliberate tampering by any of the trustees are also presented

asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system abstract in this paper asymptotic expansions are derived for the density functions of the tsls and liml estimates of coefficients in a simultaneous equation system when the sample size increases and the effect of the exogenous variables increases along the sample size these approximations are used to compare the asymptotic moments of the tsls and liml estimates and the concentration of probability around the true value of the estimates

secret key agreement by public discussion from common information the problem of generating a shared secret key s by two parties knowing dependent random variables x and y respectively but not sharing a secret key initially is considered an enemy who knows the random variable z jointly distributed with x and y according to some probability distribution p sub xyz can also receive all messages exchanged by the two parties over a public channel the goal of a protocol is that the enemy obtains at most a negligible amount of information about s upper bounds on h s as a function of p sub xyz are presented lower bounds on the rate h s n as n to infinity are derived for the case in which x x sub 1 x sub n y y sub 1 y sub n and z z sub 1 z sub n result from n independent executions of a random experiment generating x sub i y sub i and z sub i for i 1 n it is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels even when the enemy s channel is superior to the other two channels

feedback based collaborative secrecy encoding over binary symmetric channels in this paper we propose a feedback scheme for transmitting secret messages between two legitimate parties over an eavesdropped communication link relative to wyner s traditional encoding scheme our feedback based encoding often yields larger rate equivocation regions and achievable secrecy rates more importantly by exploiting the channel randomness inherent in the feedback channels our scheme achieves a strictly positive secrecy rate even when the eavesdropper s channel is less noisy than the legitimate receiver s channel all channels are modeled as binary and symmetric we demonstrate the versatility of our feedback based encoding method by using it in three different configurations the stand alone configuration the mixed configuration when it combines with wyner s scheme and the reversed configuration depending on the channel conditions significant improvements over wyner s secrecy capacity can be observed in all configurations

testing overidentifying restrictions with many instruments and heteroskedasticity this paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity it is based on a jackknife version of the overidentifying test statistic correct asymptotic critical values are derived for this statistic when the number of instruments grows large at a rate up to the sample size it is also shown that the test is valid when the number of instruments is fixed and there is homoskedasticity this test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix this paper finds in monte carlo studies that the test is more accurate and less sensitive to the number of instruments than the hausman sargan or gmm tests of overidentifying restrictions

the time series and cross section asymptotics of dynamic panel data estimators in this paper we derive the asymptotic properties of within groups wg gmm and liml estimators for an autoregressive model with random effects when both t and n tend to infinity gmm and liml are consistent and asymptotically equivalent to the wg estimator when t n 0 the fixed t results for gmm and liml remain valid but wg although consistent has an asymptotic bias in its asymptotic distribution when t n tends to a positive constant the wg gmm and liml estimators exhibit negative asymptotic biases of order 1 t 1 n and 1 2n t respectively in addition the crude gmm estimator that neglects the autocorrelation in first differenced errors is inconsistent as t n c 0 despite being consistent for fixed t finally we discuss the properties of a random effects pseudo mle with unrestricted initial conditions when both t and n tend to infinity

properties of the cue estimator and a modification with moments abstract in this paper we analyze properties of the continuous updating estimator cue proposed by hansen et al 1996 which has been suggested as a solution to the finite sample bias problems of the two step gmm estimator we show that the estimator should be expected to perform poorly in finite samples under weak identification in particular the estimator is not guaranteed to have finite moments of any order we propose the regularized cue rcue as a solution to this problem the rcue solves a modification of the first order conditions for the cue estimator and is shown to be asymptotically equivalent to cue under many weak moment asymptotics our theoretical findings are confirmed by extensive monte carlo studies

information theoretic key agreement of multiple terminals part i we study the problem of information theoretically secure secret key agreement under the well known source model and channel model in both of these models multiple terminals wish to create a shared secret key that is secure from a passive eavesdropper the terminals have access to a noiseless public communication channel and an additional resource that depends on the model in the source model the resource is an external source that repeatedly beams correlated randomness to the terminals whereas in the channel model the resource is a secure but noisy discrete memoryless broadcast channel we derive new lower and upper bounds on the secret key capacity under both the source model and the channel model the technique used for deriving our bound for the source model is to find certain properties of functions of joint probability distributions which applied to the joint distribution of the source will imply that they dominate the secret key capacity and then prove the bound by a verification argument a similar technique is used for the channel model finally we also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement this generalizes an earlier result of csiszar and narayan

a lossy source coding interpretation of wyner s common information wyner s common information was originally defined for a pair of dependent discrete random variables its significance is largely reflected in and also confined to several existing interpretations in various source coding problems this paper attempts to expand its practical significance by providing a new operational interpretation in the context of the gray wyner network it is established that wyner s common information has a new lossy source coding interpretation specifically it is established that under suitable conditions wyner s common information equals to the smallest common message rate when the total rate is arbitrarily close to the rate distortion function with joint decoding for the gray wyner network a surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are within some distortion region the new lossy source coding interpretation provides the first meaningful justification for defining wyner s common information for continuous random variables and the result can also be extended to that of multiple variables examples are given for characterizing the rate distortion region for the gray wyner lossy source coding problem and for identifying conditions under which wyner s common information equals that of the smallest common rate as a by product the explicit expression for the common information between a pair of gaussian random variables is obtained

secrecy capacity analysis over kappa mu fading channels theory and applications in this paper we consider the transmission of confidential information over a kappa mu fading channel in the presence of an eavesdropper who also experiences kappa mu fading in particular we obtain novel analytical solutions for the probability of strictly positive secrecy capacity spsc and a lower bound of secure outage probability sop l for independent and non identically distributed channel coefficients without parameter constraints we also provide a closed form expression for the probability of spsc when the mu parameter is assumed to take positive integer values monte carlo simulations are performed to verify the derived results the versatility of the kappa mu fading model means that the results presented in this paper can be used to determine the probability of spsc and sop l for a large number of other fading scenarios such as rayleigh rice nakagami n nakagami m one sided gaussian and mixtures of these common fading models in addition due to the duality of the analysis of secrecy capacity and co channel interference cci the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by cci and background noise bn to demonstrate the efficacy of the novel formulations proposed here we use the derived equations to provide a useful insight into the probability of spsc and sop l for a range of emerging wireless applications such as cellular device to device peer to peer vehicle to vehicle and body centric communications using data obtained from real channel measurements

exact solution for vibration analysis of rectangular cable networks with periodically distributed supports abstract rectangular cable networks supported by periodically distributed posts can be regarded as a structure with bi periodicity in two orthogonal directions by considering an equivalent system with cyclic bi periodicity and applying the double u transformation technique twice the harmonic vibration equation can be uncoupled into a set of single variable equations and that leads to the exact solutions as an example a square cable network with a 6 6 mesh and 2 2 internal supports is considered the solutions of natural and forced vibrations are worked out by using the formulas obtained in the present study

computational complexity of continuous variable quantum key distribution the continuous variable quantum key distribution has been considered to have the potential to provide high secret key rate however in present experimental demonstrations the secret key can be distilled only under very small loss rates here by calculating explicitly the computational complexity with the channel transmission we show that under high loss rate it is hard to distill the secret key in present continuous variable scheme and one of its advantages the potential of providing high secret key rate may therefore be limited

change of multivariate mutual information from local to global we study the change of multivariate mutual information among a set of random variables when some common randomness is added to or removed from a subset of the random variables this is formulated more precisely as two new multiterminal secret key agreement problems that respectively ask how one can increase the secrecy capacity efficiently by adding common randomness to a small subset of users and how one can simplify the source model by removing redundant common randomness that does not contribute to the secrecy capacity characterizations and strongly polynomial time computations are derived for the rates of change maximum usable increment and redundancy these results can be applied to study the communication complexity for secret key agreement

simultaneous selection and weighting of moments in gmm using a trapezoidal kernel abstract this paper proposes a novel procedure to estimate linear models when the number of instruments is large at the heart of such models is the need to balance the trade off between attaining asymptotic efficiency which requires more instruments and minimizing bias which is adversely affected by the addition of instruments two questions are of central concern 1 what is the optimal number of instruments to use 2 should the instruments receive different weights this paper contains the following contributions toward resolving these issues first i propose a kernel weighted generalized method of moments gmm estimator that uses a trapezoidal kernel this kernel turns out to be attractive to select and weight the number of moments second i derive the higher order mean squared error of the kernel weighted gmm estimator and show that the trapezoidal kernel generates a lower asymptotic variance than regular kernels finally monte carlo simulations show that in finite samples the kernel weighted gmm estimator performs on par with other estimators that choose optimal instruments and improves upon a gmm estimator that uses all instruments

common randomness and distributed control a counterexample when agents collaborate to perform a control task it is of interest to characterize the set of joint probability distributions they can achieve on their joint action space when they are passively provided with external common randomness we give a simple counterexample to a natural conjecture about this class of joint distributions

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

perfect omniscience perfect secrecy and steiner tree packing we consider perfect secret key generation for a pairwise independent network model in which every pair of terminals share a random binary string with the strings shared by distinct terminal pairs being mutually independent the terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity all the terminals as well as an eavesdropper observe this communication the objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible and concealed from the eavesdropper first we show how the notion of perfect omniscience plays a central role in characterizing perfect secret key capacity second a multigraph representation of the underlying secrecy model leads us to an efficient algorithm for perfect secret key generation based on maximal steiner tree packing this algorithm attains capacity when all the terminals seek to share a key and in general attains at least half the capacity third when a single helper terminal assists the remaining user terminals in generating a perfect secret key we give necessary and sufficient conditions for the optimality of the algorithm also a weak helper is shown to be sufficient for optimality

exact analysis of localized modes in two dimensional bi periodic mass spring systems with a single disorder abstract the frequency equation and localized modes in two dimensional bi periodic mass spring systems with one disordered subsystem are exactly analyzed by means of double u transformation at first a plane distributed mass spring system with 2 n 1 2 n 2 subsystems and cyclic periodicity in x and y directions is considered then by adopting a limiting process with n 1 n 2 approaching to infinity the limiting solution is applicable for the plane distributed bi periodic mass spring systems with boundary at infinity the explicit frequency equation and localized modes are derived some specific systems are taken as examples to demonstrate how to apply the formulas and equations obtained in the present paper in order to find the localized modes and corresponding frequencies

instrumental variable estimation in the presence of many moment conditions abstract this paper develops shrinkage methods for addressing the many instruments problem in the context of instrumental variable estimation it has been observed that instrumental variable estimators may behave poorly if the number of instruments is large this problem can be addressed by shrinking the influence of a subset of instrumental variables the procedure can be understood as a two step process of shrinking some of the ols coefficient estimates from the regression of the endogenous variables on the instruments then using the predicted values of the endogenous variables based on the shrunk coefficient estimates as the instruments the shrinkage parameter is chosen to minimize the asymptotic mean square error the optimal shrinkage parameter has a closed form which makes it easy to implement a monte carlo study shows that the shrinkage method works well and performs better in many situations than do existing instrument selection procedures

communication efficient secret sharing a secret sharing scheme is a method to store information securely and reliably particularly in a threshold secret sharing scheme a secret is encoded into n shares such that any set of at least t 1 shares suffice to decode the secret and any set of at most t 2 shares reveal no information about the secret assuming that each party holds a share and a user wishes to decode the secret by receiving information from a set of parties the question we study is how to minimize the amount of communication between the user and the parties we show that the necessary amount of communication termed decoding bandwidth decreases as the number of parties that participate in decoding increases we prove a tight lower bound on the decoding bandwidth and construct secret sharing schemes achieving the bound particularly we design a scheme that achieves the optimal decoding bandwidth when d parties participate in decoding universally for all t 1 le d le n the scheme is based on a generalization of shamir s secret sharing scheme and preserves its simplicity and efficiency in addition we consider the setting of secure distributed storage where the proposed communication efficient secret sharing schemes not only improve decoding bandwidth but further improve disk access complexity during decoding

modified three stage least squares estimator which is third order efficient abstract a modified three stage least squares 3sls estimator is proposed which shares the same asymptotic expansion of the distribution as the fiml estimator to terms of order o 1 t therefore this modified 3sls estimator is third order efficient this estimator includes a modified 2sls estimator and a modified sur estimator as specific cases

the commitment capacity of the gaussian channel is infinite we prove that the commitment capacity of the power constrained gaussian channel i e the optimal rate at which this channel can be used for implementing commitment schemes is infinite

tight exponential analysis of universally composable privacy amplification and its applications motivated by the desirability of universal composability we analyze in terms of l1 distinguishability the task of secret key generation from a joint random variable under this secrecy criterion using the renyi entropy of order 1 s for s 0 1 we derive a new upper bound of eve s distinguishability under the application of the universal2 hash functions it is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions the result is applied to the wiretap channel model and to secret key generation distillation by public discussion

high dimensional stochastic regression with latent factors endogeneity and nonlinearity abstract we consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms a linear regression of some observed regressors a linear combination of some latent and serially correlated factors and a vector white noise we investigate the inference without imposing stationary conditions on the target multivariate time series the regressors and the underlying factors furthermore we deal with the endogeneity that there exist correlations between the observed regressors and the unobserved factors we also consider the model with nonlinear regression term which can be approximated by a linear regression function with a large number of regressors the convergence rates for the estimators of regression coefficients the number of factors factor loading space and factors are established under the settings when the dimension of time series and the number of regressors may both tend to infinity together with the sample size the proposed method is illustrated with both simulated and real data examples

jackknife instrumental variable estimation with heteroskedasticity we present a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity it weighs observations such that many instruments consistency is guaranteed while the signal component in the data is maintained we show that this results in a smaller signal component in the many instruments asymptotic variance when compared to estimators that neglect a part of the signal to achieve consistency both many strong instruments and many weak instruments asymptotic distributions are derived using high level assumptions that allow for instruments with identifying power that varies between explanatory variables standard errors are formulated compactly we review briefly known estimators and show in particular that our symmetric jackknife estimator performs well when compared to the hlim and hful estimators of hausman et al in monte carlo experiments

secret key generation for correlated gaussian sources secret key generation by multiple terminals is considered based on their observations of jointly distributed gaussian signals followed by public communication among themselves exploiting an inherent connection between secrecy generation and lossy data compression two main contributions are made the first is a characterization of strong secret key capacity and entails a converse proof technique that is valid for real valued and not necessarily gaussian as well as finite valued signals the capacity formula acquires a simple form when the terminals observe symmetrically correlated jointly gaussian signals for the latter setup with two terminals considering schemes that involve quantization at one terminal the best rate of an achievable secret key is characterized as a function of quantization rate secret key capacity is attained as the quantization rate tends to infinity structured codes are shown to attain the optimum tradeoff between secret key rate and quantization rate constituting our second main contribution

dynamic response of infinite continuous beams subjected to a moving force an exact method this paper describes an exact method for investigating the dynamic response of an infinite uniform beam resting on periodic rolle supports and subjected to a moving force at first an exact solution for a rotationally periodic continous beam subjected to a moving force is obtained by the u transformation and mode method then by a limiting process with the number of spans approaching infinity the result is generalized to give a solution for an infinite continuous beam subjected to a moving force this method will be applicable to the forced vibration analysis of an infinite continuous beam under arbitrary excitation

transverse vibration analysis of plane trusses by analytical method abstract the type of plane truss considered in this paper is the warren truss which is built up with basic units consisting of four sets of bars pin jointed at the nodes and subjected to transverse nodal loads the natural vibration and dynamic response are studied for the simply supported truss with lumped masses at the nodes closed form solutions are deduced by using the u transformation technique which leads to the uncoupling of the governing equations in order to explain the procedure of the present method the response functions for the nodal displacements of a truss subjected to the action of a suddenly applied load at a node are derived it is obvious that the present method is also applicable to the forced vibration analysis of trusses subjected to arbitrary transverse loads applied at the nodes

hahn hausman test as a specification test abstract this paper develops a modified version of the sargan sargan j d 1958 the estimation of economic relationships using instrumental variables econometrica 26 3 393 415 restrictions and shows that it is numerically equivalent to the test statistic of hahn and hausman hahn j hausman j 2002 a new specification test for the validity of instrumental variables econometrica 70 1 163 189 up to a sign the modified sargan test is constructed such that its asymptotic distribution under the null hypothesis of correct specification is standard normal when the number of instruments increases with the sample size the equivalence result is useful in understanding what the hahn hausman test detects and its power properties

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

dynamics of bi periodic structures abstract many structures considered for space applications are bi periodic in their construction bi periodicity means that two types of structural subassemblies alternating in one or more directions make up the structure to gain insight into the dynamics of bi periodic space structures a variety of one and two dimensional bi periodic structures are considered results indicate that bands in which natural frequencies lie for periodic structures are further subdivided as a consequence of the bi periodicity analytical solutions for the modes and frequencies of finite length one dimensional bi periodic structures are obtained for general boundary conditions a transmission method is developed to simplify the application of boundary conditions it is found that some modes occur at frequencies which are outside the frequency bands predicted for bi periodic structures two dimensional bi periodic crossed beam grillage and truss structures are considered in this study for cases where a separation of variables solution is possible the two dimensional structures exhibit similar properties to the one dimensional bi periodic structures analytical solutions for the one and two dimensional bi periodic structures considered above lead to a compact solution form similar to that of periodic structures analysis

a maximum likelihood method for the incidental parameter problem this paper uses the invariance principle to solve the incidental parameter problem of 35 we seek group actions that pre serve the structural parameter and yield a maximal invariant in the parameter space with flxed dimension m estimation from the likeli hood of the maximal invariant statistic yields the maximum invariant likelihood estimator mile consistency of mile for cases in which the likelihood of the maximal invariant is the product of marginal likelihoods is straightforward we illustrate this result with a sta tionary autoregressive model with flxed efiects and an agent speciflc monotonic transformation model asymptotic properties of mile when the likelihood of the maxi mal invariant does not factorize remain an open question we are able to provide consistency asymptotic normality and e ciency results of mile when invariance yields wishart distributions two examples are an instrumental variable iv model and a dynamic panel data model with flxed efiects

secure multiplex coding attaining channel capacity in wiretap channels it is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so called secrecy capacity cs which is usually smaller than the channel capacity c in order to remove the loss c cs we propose a multiplex coding scheme with plural independent messages in this paper it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information spectral methods by extending hayashi s proof in which the coding of the channel resolvability is applied to wiretap channels furthermore the exact region for deterministic coding is determined for stationary memoryless full rank wiretap channels

alternative approximations of the bias and mse of the iv estimator under weak identification with an application to bias correction abstract we provide analytical formulae for the asymptotic bias abias and mean squared error amse of the iv estimator and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage f statistic to converge to a finite possibly small positive limit as the number of instruments approaches infinity our analytical formulae can be viewed as generalizing the bias and mse results of richardson and wu 1971 a note on the comparison of ordinary and two stage least squares estimators econometrica 39 973 982 to the case with nonnormal errors and stochastic instruments our approximations are shown to compare favorably with approximations due to morimune 1983 approximate distributions of k class estimators when the degree of overidentifiability is large compared with the sample size econometrica 51 821 841 and donald and newey 2001 choosing the number of instruments econometrica 69 1161 1191 particularly when the instruments are weak we also construct consistent estimators for the abias and amse and we use these to further construct a number of bias corrected ols and iv estimators the properties of which are examined both analytically and via a series of monte carlo experiments

moment restriction based econometric methods an overview the 2011 special issue of the journal of econometrics discusses papers based on moment restriction based econometric methods in the first paper peter robinson of london school of economics considers asymptotic theory for nonparametric regression with spatial data specifically nonparametric regression with spatial or spatio temporal data the author discusses application of the established conditions to spatial autoregressive models and models defined on a regular lattice liqun wang and cheng hsiao consider method of moments estimation and identifiability of semiparametric nonlinear errors in variables models their paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric shih hsun hsu and chung ming kuan examine estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

testing with many weak instruments abstract this paper establishes the asymptotic distributions of the likelihood ratio lr anderson rubin ar and lagrange multiplier lm test statistics under many weak iv asymptotics these asymptotics are relevant when the number of ivs is large and the coefficients on the ivs are relatively small the asymptotic results hold under the null and under suitable alternatives hence power comparisons can be made provided k 3 n 0 as n where n is the sample size and k is the number of instruments these tests have correct asymptotic size this holds no matter how weak the instruments are hence the tests are robust to the strength of the instruments the asymptotic power results show that the conditional lr test is more powerful asymptotically than the ar and lm tests under many weak iv asymptotics

robust estimation with many instruments abstract linear instrumental variables models are widely used in empirical work but often associated with low estimator precision this paper proposes an estimator that is robust to outliers and shows that the estimator is minimax optimal in a class of estimators that includes the limited maximum likelihood estimator liml intuitively this optimal robust estimator combines liml with winsorization of the structural residuals and the winsorization leads to improved precision under thick tailed error distributions consistency and asymptotic normality of the estimator are established under many instruments asymptotics and a consistent variance estimator which allows for asymptotically valid inference is provided

exact random coding secrecy exponents for the wiretap channel we analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in wyner s wiretap channel setting using wiretap channel codes constructed from both i i d and constant composition random codes our analysis for those sampled from i i d random coding ensemble shows that the previously known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble furthermore our analysis on wiretap channel codes constructed from the ensemble of constant composition random codes leads to an exponent which in addition to being the exact exponent for an average code is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i i d random coding ensemble we show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant composition codes is larger than that of those constructed from i i d random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i i d random codes is larger than that of those constructed from constant composition random codes we hence conclude that unlike the error correction problem there is no general ordering between the two random coding ensembles in terms of their secrecy exponent

communication in key distribution schemes a g b key distribution scheme allows conferences of g users to generate secret keys such that disjoint coalitions of b users cannot gain any information on the generated key in the information theoretic sense we study the relationships between communication and space efficiency of key distribution schemes we prove that communication does not help in the context of unrestricted schemes on the other hand we show that for restricted schemes which are secure only when used by a limited number of conferences communication can substantially improve the space efficiency we also present lower bounds on the space efficiency of restricted schemes

key generation algorithms for pairwise independent networks based on graphical models we consider two secret key generation problems under a pairwise independent network model and propose low complexity key generation schemes in a framework that connects our problems to network flow problems in graphs our schemes have two components 1 local key generation and 2 global key propagation in the local key generation we use point to point source coding with side information to establish pairwise keys from which we construct a graph with the capacity of each edge being the key rate of the corresponding point to point local key in the global key propagation depending on the particular problem secret keys are delivered to users in the network using various network flow algorithms in particular in the first problem in which one is required to generate a group key for a group of users in the network we propose a network coding based global key propagation approach this approach has a low complexity and has a better performance than the existing approach in the second problem in which one is required to generate multiple keys simultaneously for different pairs of users we propose a multicommodity flow based global key propagation approach we show that the proposed approach is optimal for the case of generating two keys for the general case of generating more than two keys we show that the sum rate of the proposed scheme is larger than an upper bound characterized in this paper divided by a constant

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

consistent estimation with a large number of weak instruments this paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables iv regression when the available instruments are weak and the number of instruments k n goes to infinity with the sample size we show that consistent estimation depends importantly on the strength of the instruments as measured by r the rate of growth of the so called concentration parameter and also on k n in particular when k n the concentration parameter can grow even if each individual instrument is only weakly correlated with the endogenous explanatory variables and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature hence the use of many weak instruments may actually improve the performance of certain point estimators more specifically we find that the limited information maximum likelihood liml estimator and the bias corrected two stage least squares b2sls estimator are consistent when k n r n 0 while the two stage least squares 2sls estimator is consistent only if k n r n 0 as n these consistency results suggest that liml and b2sls are more robust to instrument weakness than 2sls

coding theorems for a 2 2 threshold scheme with detectability of impersonation attacks coding theorems on a 2 2 threshold scheme with an opponent are discussed in an asymptotic setup where the opponent tries to impersonate one of the two participants a situation is considered where n secrets s n from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to s n with permitting negligible decoding error we introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a 2 2 threshold scheme that is secure against the impersonation attack by the opponent it is shown that if the correlation level between the two shares equals to ell geq 0 the minimum attainable rates coincide with h s ell where h s denotes the entropy of the source and the maximum attainable exponent of the success probability of the impersonation attack equals to ell it is also shown that a simple scheme using an ordinary 2 2 threshold scheme attains all the bounds as well

reconciliation of a quantum distributed gaussian key two parties alice and bob wish to distill a binary secret key out of a list of correlated variables that they share after running a quantum key distribution qkd protocol based on continuous spectrum quantum carriers we present a novel construction that allows the legitimate parties to get equal bit strings out of correlated variables by using a classical channel with as little leaked information as possible this opens the way to securely correcting nonbinary key elements in particular the construction is refined to the case of gaussian variables as it applies directly to recent continuous variable protocols for qkd

secret sharing with public reconstruction all known constructions of information theoretic t out of n secret sharing schemes require secure private communication channels among the parties for the reconstruction of the secret we investigate the cost of performing the reconstruction over public communication channels a naive implementation of this task distributes 2n 2 one times pads to each party this results in shares whose size is 2n 1 times the secret size we present three implementations of such schemes that are substantially more efficient a scheme enabling multiple reconstructions of the secret by different subsets of parties with factor o n t increase in the shares size a one time scheme enabling a single reconstruction of the secret with o log n t increase in the shares size a one time scheme enabling a single reconstruction by a set of size exactly t with factor o 1 increase in the shares size we prove that the first implementation is optimal up to constant factors by showing a tight spl omega n t lower bound for the increase in the shares size

on the asymptotic optimality of the liml estimator with possibly many instruments we consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables we derive some asymptotic properties of the limited information maximum likelihood liml estimator when the number of instruments is large some of these results are new as well as old and we relate them to results in some recent studies we have found that the variance of the limiting distribution of the liml estimator and its modifications often attain the asymptotic lower bound when the number of instruments is large and the disturbance terms are not necessarily normally distributed that is for the micro econometric models of some cases recently called many instruments and many weak instruments