on the efficient use of the informational content of estimating equations implied probabilities and euclidean empirical likelihood abstract a number of information theoretic alternatives to gmm have recently been proposed in the literature for practical use and general interpretation the main drawback of these alternatives particularly in the case of conditional moment restrictions is that they give up the computational and interpretational simplicity of quadratic optimization the main contribution of this paper is to analyze the informational content of estimating equations within the unified framework of chi square distance improved inference by control variables closed form formulae for implied probabilities and information theoretic interpretations of continuously updated gmm are discussed in the two cases of unconditional and conditional moment restrictions

point estimation with exponentially tilted empirical likelihood parameters defined via general estimating equations gee can be estimated by maximizing the empirical likelihood el newey and smith econometrica 72 2004 219 255 have recently shown that this el estimator exhibits desirable higher order asymptotic properties namely that its o n 1 bias is small and that bias corrected el is higher order efficient although el possesses these properties when the model is correctly specified this paper shows that in the presence of model misspecification el may cease to be root n convergent when the functions defining the moment conditions are unbounded even when their expectations are bounded in contrast the related exponential tilting et estimator avoids this problem this paper shows that the et and el estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood etel exhibiting the same o n 1 bias and the same o n 2 variance as el while maintaining root n convergence under model misspecification

a simple resampling method by perturbing the minimand suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a u process structure the covariance matrix of the estimator is generally a function of the underlying density function which may be difficult to estimate well by conventional methods in this paper we present a simple resampling method by perturbing the objective function repeatedly inferences of the parameters can then be made based on a large collection of the resulting optimisers we illustrate our proposal by three examples with a heteroscedastic regression model

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

consistent estimation of models defined by conditional moment restrictions in econometrics models stated as conditional moment restrictions are typically estimated by means of the generalized method of moments gmm the gmm estimation procedure can render inconsistent estimates since the number of arbitrarily chosen instruments is finite in fact consistency of the gmm estimators relies on additional assumptions that imply unclear restrictions on the data generating process this article introduces a new simple and consistent estimation procedure for these models that is directly based on the definition of the conditional moments the main feature of our procedure is its simplicity since its implementation does not require the selection of any user chosen number and statistical inference is straightforward since the proposed estimator is asymptotically normal in addition we suggest an asymptotically efficient estimator constructed by carrying out one newton raphson step in the direction of the efficient gmm estimator

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

the eigenstructure of finite field trigonometric transforms in this paper we discuss the eigenstructure of finite field trigonometric transforms fftt this transform family includes different types of cosine and sine transforms that correspond in the finite field case to the well known discrete cosine and sine transforms defined over the real numbers more specifically we determine the eigenvalues of the fftt matrices and study their multiplicities we propose procedures for constructing the associated eigenvectors applications of the developed theory to multiuser communication systems and error correcting codes are also suggested

extending the scope of empirical likelihood this article extends the scope of empirical likelihood methodology ill three directions to allow for plug in estimates of nuisance parameters in estimating equations slower than root n rates of convergence and settings in which there are a relatively large number of estimating equations compared to the sample size calibrating empirical likelihood confidence regions with plug in is sometimes intractable due to the complexity of the asymptotics so we introduce a bootstrap approximation that call be used in such situations we provide a range of examples from survival analysis and nonparametric statistics to illustrate the main results

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

eigenvalues and eigenvectors of generalized dft generalized dht dct iv and dst iv matrices in this paper the eigenvalues and eigenvectors of the generalized discrete fourier transform gdft the generalized discrete hartley transform gdht the type iv discrete cosine transform dct iv and the type iv discrete sine transform dst iv matrices are investigated in a unified framework first the eigenvalues and their multiplicities of the gdft matrix are determined and the theory of commuting matrices is applied to find the real symmetric orthogonal eigenvectors set that constitutes the discrete counterpart of hermite gaussian function then the results of the gdft matrix and the relationships among these four unitary transforms are used to find the eigenproperties of the gdht dct iv and dst iv matrices finally the fractional versions of these four transforms are defined and an image watermarking scheme is proposed to demonstrate the effectiveness of fractional transforms

the discrete fractional cosine and sine transforms this paper is concerned with the definitions of the discrete fractional cosine transform dfrct and the discrete fractional sine transform dfrst the definitions of dfrct and dfrst are based on the eigen decomposition of dct and dst kernels this is the same idea as that of the discrete fractional fourier transform dfrft the eigenvalue and eigenvector relationships between the dfrct dfrst and dfrft can be established the computations of dfrft for even or odd signals can be planted into the half size dfrct and dfrst calculations this will reduce the computational load of the dfrft by about one half

efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals this paper considers semiparametric efficient estimation ofconditional moment models with possibly nonsmooth residuals in unknown parametric components and unknown functions h of endogenous variables we show that 1 the penalized sieve minimum distance psmd estima tor can simultaneously achieve root n asymptotic normality ofand nonparametric optimal convergence rate of allowing for noncompact function parameter spaces 2 a simple weighted bootstrap procedure consistently estimates the limiting distribution of the psmd 3 the semi parametric efficiency bound formula of ai and chen 2003 remains valid for conditional models with nonsmooth residuals and the optimally weighted psmd estimator achieves the bound 4 the centered profiled optimally weighted psmd criterion is asymptotically chi square distributed we illustrate our theories using a partially linear quantile instrumental variables iv regression a monte carlo study and an empirical estimation of the shape invariant quantile iv engel curves

smooth minimum distance estimation and testing with conditional estimating equations uniform in bandwidth theory abstract to study the influence of a bandwidth parameter in inference with conditional moments we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth which can vary within a wide range including bandwidths independent of the sample size we study its behavior under misspecification we also propose an efficient version of our estimator we develop a procedure based on a distance metric statistic for testing restrictions on parameters as well as a bootstrap technique to account for the bandwidth s influence our new methods are simple to implement apply to non smooth problems and perform well in our simulations

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

a block cipher cryptosystem using wavelet transforms over finite fields we present a new private key cryptosystem based on the finite field wavelet the encryption and decryption are performed by the synthesis and analysis banks of the nonlinear finite field wavelet transform whose filter coefficients are determined by the keys of the users we exploit the polyphase representation of the wavelets to introduce a shared key mechanism for the wavelet cryptosystem we propose to use wavelets that operate over gf 256 and a nonlinear device that performs a mapping on the field elements to their inverse in the field the introduced cryptographic system can operate in either stream cipher or block cipher modes depending on whether the filterbanks perform linear or circular convolution the block cipher system has a key length of 16 symbols 128 bits and an input block size of 30 symbols 240 bits to evaluate the efficiency of the developed two round wavelet cryptographic scheme we compare it with des and aes our results suggest that the wavelet cryptosystem has comparable computational complexity to aes and approximately half the complexity of des the security is tied to the length of the wavelet basis function and to the nonlinearity within the wavelet transform we study the security of the block cipher wavelet cryptosystem in response to classical attacks and those specific to this algorithm particularly those which use variations of the divide and conquer interpolation attack and discrete fourier transform techniques we show that chosen ciphertext attacks of the wavelet encryption system can reduce to the problem of solving a set of nonlinear equations over finite fields by considering existing classical and structure specific attacks we conclude that the lowest complexity of any of these attacks is greater than an exhaustive key search

efficient information theoretic inference for conditional moment restrictions abstract the generalised method of moments estimator may be substantially biased in finite samples especially so when there are large numbers of unconditional moment conditions this paper develops a class of first order equivalent semi parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel weighted version of the cressie read power divergence family of discrepancies this approach is similar in spirit to the empirical likelihood methods of kitamura et al 2004 empirical likelihood based inference in conditional moment restrictions models econometrica 72 1667 1714 and tripathi and kitamura 2003 testing conditional moment restrictions annals of statistics 31 2059 2095 these efficient local methods avoid the necessity of explicit estimation of the conditional jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations

maximal inequalities for degenerate u processes with applications to optimization estimators maximal inequalities for degenerate u processes of order k k geq 1 are established the results rest on a moment inequality due to bonami for k th order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes rates of uniform convergence are obtained the maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having u process structure as an application a semiparametric regression estimator that maximizes a u process of order 3 is shown to be sqrt n consistent and asymptotically normally distributed

conditional moment models under semi strong identification we consider conditional moment models under semi strong identification identification strength is directly defined through the conditional moments that flatten as the sample size increases our new minimum distance estimator is consistent asymptotically normal robust to semi strong identification and does not rely on the choice of a user chosen parameter such as the number of instruments or some smoothing parameter heteroskedasticity robust inference is possible through wald testing without prior knowledge of the identification pattern simulations show that our estimator is competitive with alternative estimators based on many instruments being well centered with better coverage rates for confidence intervals

conditional empirical likelihood estimation and inference for quantile regression models abstract this paper considers two empirical likelihood based estimation inference and specification testing methods for quantile regression models first we apply the method of conditional empirical likelihood cel by kitamura et al 2004 empirical likelihood based inference in conditional moment restriction models econometrica 72 1667 1714 and zhang and gijbels 2003 sieve empirical likelihood and extensions of the generalized least squares scandinavian journal of statistics 30 1 24 to quantile regression models second to avoid practical problems of the cel method induced by the discontinuity in parameters of cel we propose a smoothed counterpart of cel called smoothed conditional empirical likelihood scel we derive asymptotic properties of the cel and scel estimators parameter hypothesis tests and model specification tests important features are i the cel and scel estimators are asymptotically efficient and do not require preliminary weight estimation ii by inverting the cel and scel ratio parameter hypothesis tests asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators and iii in contrast to cel the scel method can be implemented by some standard newton type optimization simulation results demonstrate that the scel method in particular compares favorably with existing alternatives

the fractional discrete cosine transform the extension of the fourier transform operator to a fractional power has received much attention in signal theory and is finding attractive applications the paper introduces and develops the fractional discrete cosine transform dct on the same lines discussing multiplicity and computational aspects similarities and differences with respect to the fractional fourier transform are pointed out

eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design the n n trigonometric matrix p whose entries are p i j 1 i j 2 cos i j appears in connection with the design of finite impulse response fir digital filters with real coefficients we prove several results about its eigenvalues in particular assuming n 4 we prove that p has one positive and one negative eigenvalue when is an integer while it has two positive and two negative eigenvalues when is not an integer we also show that for not being an integer and a sufficiently large n the two positive eigenvalues converge to n 2 and the two negative eigenvalues to n 2 where 1 2 p 3 8 furthermore an equivalent transformation diagonalizing p is described

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

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

symmetric convolution and the discrete sine and cosine transforms this paper discusses the use of symmetric convolution and the discrete sine and cosine transforms dsts and dcts for general digital signal processing the operation of symmetric convolution is a formalized approach to convolving symmetrically extended sequences the result is the same as that obtained by taking an inverse discrete trigonometric transform dtt of the product of the forward dtts of those two sequences there are 16 members in the family of dtts each provides a representation for a corresponding distinct type of symmetric periodic sequence the author defines symmetric convolution relates the dsts and dcts to symmetric periodic sequences and then use these principles to develop simple but powerful convolution multiplication properties for the entire family of dsts and dcts symmetric convolution can be used for discrete linear filtering when the filter is symmetric or antisymmetric the filtering will be efficient because fast algorithms exist for all versions of the dtts conventional linear convolution is possible if one first zero pad the input data symmetric convolution and its fast implementation using dtts are now an alternative to circular convolution and the dft

bootstrap confidence sets under model misspecification a multiplier bootstrap procedure for construction of likelihood based confidence sets is considered for finite samples and a possible model misspecification theoretical results justify the bootstrap consistency for a small or moderate sample size and allow to control the impact of the parameter dimension p the bootstrap approximation works if p n is small the main result about bootstrap consistency continues to apply even if the underlying parametric model is misspecified under the so called small modeling bias condition in the case when the true model deviates significantly from the considered parametric family the bootstrap procedure is still applicable but it becomes a bit conservative the size of the constructed confidence sets is increased by the modeling bias we illustrate the results with numerical examples for misspecified constant and logistic regressions jel classification codes c13 c15

fractional cosine and sine transforms over finite fields abstract in this paper we introduce fractional cosine and sine transforms over finite fields the basis for the definition of such transforms which are respectively referred by the acronyms gfrct and gfrst is the recently proposed fractional fourier transform over finite fields gfrft 1 more specifically we use the eigenvectors of the finite field fourier transform to construct eigenvectors of the finite field cosine and sine transforms such eigenvectors are then used in spectral expansions that allow to compute fractional powers of the finite field cosine and sine transform matrices

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

uniform in bandwidth consistency of kernel type function estimators we introduce a general method to prove uniform in bandwidth consistency of kernel type function estimators examples include the kernel density estimator the nadaraya watson regression estimator and the conditional empirical process our results may be useful to establish uniform consistency of data driven bandwidth kernel type function estimators

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

block error correcting codes using finite field wavelet transforms this paper extends the popular wavelet framework for signal representation to error control coding the primary goal of the paper is to use cyclic finite field wavelets and filter banks to study arbitrary rate l circulant codes it is shown that the wavelet representation leads to an efficient implementation of the block code encoder and the syndrome generator a formulation is then given for constructing maximum distance separable mds wavelet codes using frequency domain constraints this paper also studies the possibility of finding a wavelet code whose tail biting trellis is efficient for soft decision decoding the wavelet method may provide an easy way to look for such codes

the modified number theoretic transform over the direct sum of finite fields to compute the linear convolution the modified number theoretic transform mntt over the direct sum of finite fields is constructed the mntt application to computing linear convolution lc is discussed the main advantage of the mntt is the possibility of reducing computational complexity of an lc in terms of numbers of arithmetical operations or computation time however using the mntt decreases the dynamic range of the lc input

a class of linear regression parameter estimators constructed by nonparametric estimation on demontre la consistance forte et la normalite asymptotique des estimateurs obtenus sous des conditions moins restrictives que celles donnees par faraldo roca et gonzalez manteiga 1985