conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

adaptive estimation of the dynamics of a discrete time stochastic volatility model abstract this paper is concerned with the discrete time stochastic volatility model y i exp x i 2 i x i 1 b x i x i i 1 where only y i is observed the model is rewritten as a particular hidden model z i x i e i x i 1 b x i x i i 1 where i and e i are independent sequences of i i d noise moreover the sequences x i and e i are independent and the distribution of e is known then our aim is to estimate the functions b and 2 when only observations z 1 z n are available we propose to estimate b f and b 2 2 f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces by ratio strategy estimators of b and 2 are then deduced the mean square risk of the resulting estimators are studied and their rates are discussed lastly simulation experiments are provided constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples

performance analysis of optical synchronous cdma communication systems with ppm signaling direct detection optical synchronous code division multiple access cdma systems with m ary pulse position modulation ppm signaling are investigated optical orthogonal codes are used as the signature sequences of our system a union upper bound on the bit error rate is derived taking into account the effect of the background noise multiple user interference and receiver shot noise the performance characteristics are then discussed for a variety of system parameters another upper bound on the probability of error is also obtained based on chernoff inequality this bound is utilized to derive achievable expressions for both the maximum number of users that can communicate simultaneously with asymptotically zero error rate and the channel capacity our results show that under average power and bit error rate constraints there always exists a pulse position multiplicity that permit all the subscribers to communicate simultaneously

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

efficient estimation in the errors in variables model we consider efficient estimation of the slope in the errors in variables model with normal error when either the ratio of error variances is known and the distribution of the independent is arbitrary and unknown or the distribution of the independent variable is not gaussian or degenerate we calculate information bounds and exhibit estimates achieving these bounds using an initial minimum distance estimate and suitable estimates of the efficient score function

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

nonparametric regression in the presence of measurement error summary in many regression applications the independent variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the distribution of the unobserved error prone predictor for this approach we derive an asymptotic theory for kernel regression which has some surprising implications penalised regression splines are also considered for fixed number of known knots the second approach assumes that the error prone predictor has a distribution of a mixture of normals with an unknown number of components and uses regression splines simulations illustrate the results

performance analysis of direct detection optical cdma communication systems with avalanche photodiodes direct detection optical code division multiple access cdma communication systems with avalanche photodiode apd photodetectors are investigated a chernoff upper bound modified chernoff upper bound and gaussian approximation on the probability of bit error are presented for general apds and arbitrary

cramer rao lower bounds for a damped sinusoidal process the cramer rao lower bounds crlbs for the parameter estimators of a damped sinusoidal process are derived in this paper succinct matrix expressions for crlb s of frequency damping factor amplitude and initial phase are given for both scalar and vector processes the relationships between the crlbs of the characteristic parameters are established in the general multimode case in particular explicit closed form expressions for the single mode scalar vector damped undamped cases are provided

nonparametric regression estimation in the heteroscedastic errors in variables problem in the classical errors in variables problem the goal is to estimate a regression curve from data in which the explanatory variable is measured with error in this context nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed although there are many situations in which this assumption is too restrictive nonparametric estimators in the more realistic setting of heteroscedastic errors have not been studied in the literature we propose an estimator of the regression function in such a setting and show that it is optimal we give estimators in cases in which the error distributions are unknown and replicated observations are available practical methods including an adaptive bandwidth selector for the errors in variables regression problem are suggested and their finite sample performance is illustrated through simulated and real data examples

a semiparametric method for estimating nonlinear autoregressive model with dependent errors abstract the first order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate regression function in the presented model dependent errors are defined as first order autoregressive ar 1 the conditional least squares method is used for parametric estimation and the nonparametric kernel approach is applied to estimate regression adjustment in this case some asymptotic behaviors and simulated results for the semiparametric method are presented furthermore the method is applied for the financial data in iran s tejarat bank

semi parametric estimation in the nonlinear structural errors in variables model in the nonlinear structural errors in variables model we propose a consistent estimator of the unknown parameter using a modified least squares criterion we give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n 1 2 nevertheless the rate is of order n 1 2 for some particular analytic regression functions for instance when the regression function is either a polynomial function or an exponential function we prove that our estimator achieves the parametric rate of convergence

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

a semiclassical analysis of optical code division multiple access a model noncoherent optical asynchronous cdma system is described the error rate for a single user matched filter receiver that is valid for arbitrary photomultipliers and signature sequence sets adheres to the semiclassical model of light and does not depend on approximations for large user groups strong received optical fields or chip synchronism is analyzed the exact minimum probability of error and optimal threshold are compared to those obtained with user synchronism and multiple access interference mai distribution approximations for the special case of unity gain photodetectors and prime sequences it is shown that the approximation of chip synchronism yields a weak upper bound on the exact error rate it is demonstrated that the approximations of perfect optical to electrical conversion and gaussian distributed mai yield a poor approximation to the minimum error rate and an underestimate of the optimal threshold arbitrarily tight bounds are developed on the error rate for unequal energies per bit in the case when the signal energies coincide these bounding expressions are considerably easier to compute than the exact error rate

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

orthogonal polynomials random matrices and the numerical inversion of the laplace transform of positive functions a method for the numerical inversion of the laplace transform of a continuous positive function f t is proposed random matrices distributed according to a gibbs law whose energy v x is a function of f t are considered as well as random polynomials orthogonal with respect to w x e v x the equation relating w x to the reproducing kernel and to the condensed density of the roots of the random orthogonal polynomials is exploited basic results from the theories of orthogonal polynomials random matrices and random polynomials are revisited in order to provide a unified and almost self contained context the qualitative behavior of the solutions provided by the proposed method is illustrated by numerical examples and discussed by using logarithmic potentials with external fields that give insight into the asymptotic behavior of the condensed density when the number of data points goes to infinity

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

a new estimation method in modal analysis in this paper the modal analysis model which is made up of a linear combination of complex exponential functions is considered the problem of estimating the number of modes as well as the frequencies decays amplitudes and phases and their variability is afforded by means of the condensed distribution of the poles of pade approximants to the z transform of the data this provides a unified framework in which all of these problems can be solved in an almost automatic way it is experimentally proved that the results favorably compare with that provided by well established methods

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

total least squares approach for frequency estimation using linear prediction the resolution of the estimated closely spaced frequencies of the multiple sinusoids degrades as the signal to noise ratio snr of the received signal becomes low this resolution can be improved by using the total least squares tls method in solving the linear prediction lp equation this approach makes use of the singular value decomposition svd of the augmented matrix for low rank approximation to reduce the noise effect from both the observation vector and the lp data matrix simultaneously comparison is made to the principle eigenvector pe method of tufts and kumaresan both on theoretical and experimental grounds the tls algorithm exhibits superior performance over the pe method where low rank approximation is applied to the data matrix only

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

minimum distance regression model checking with berkson measurement errors lack of fit testing of a regression model with berkson measurement error has not been discussed in the literature to date to fill this void we propose a class of tests based on minimized integrated square distances between a nonparametric regression function estimator and the parametric model being fitted we prove asymptotic normality of these test statistics under the null hypothesis and that of the corresponding minimum distance estimators under minimal conditions on the model being fitted we also prove consistency of the proposed tests against a class of fixed alternatives and obtain their asymptotic power against a class of local alternatives orthogonal to the null hypothesis these latter results are new even when there is no measurement error a simulation that is included shows very desirable finite sample behavior of the proposed inference procedures

accelerated convergence for nonparametric regression with coarsened predictors we consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened that is less precise or contaminated predictors specifically while one has available a sample w 1 y 1 w n y n of independent and identically distributed data representing observations with precisely measured predictors where e y i w i g w i instead ofthe smooth regression function g the target of interest is another smooth regression function m that pertains to predictors x i that are noisy versions of the w i our target is then the regression function m x e y x x where x is a contaminated version of w that is x w it is assumed that either the density of the errors is known or replicated data are available resembling but not necessarily the same as the variables x in either case and under suitable conditions we obtain n rates of convergence of the proposed estimator and its derivatives and establish a functional limit theorem weak convergence to a gaussian limit process implies pointwise and uniform confidence intervals and n consistent estimators of extrema and zeros of m it is shown that these results are preserved under more general models in which x is determined by an explanatory variable finite sample performance is investigated in simulations and illustrated by a real data example

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

on the optimal rates of convergence for nonparametric deconvolution problems deconvolution problems arise in a variety of situations in statistics an interesting problem is to estimate the density f of a random variable x based on n i i d observations from y x varepsilon where varepsilon is a measurement error with a known distribution in this paper the effect of errors in variables of nonparametric deconvolution is examined insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions the smoother the harder in fact there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth it is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

some properties of the asymptotic location of poles of pade approximants to noisy rational functions relevant for modal analysis the modal analysis model made up by a linear combination of complex exponential functions is considered pade approximants to the z transform of a noisy sample are then considered and the asymptotic locus of their poles is studied it turns out that this locus is strongly related to the complex exponentials of the model by exploiting these properties powerful methods for estimating the model parameters can be devised which have both denoising and super resolution capabilities

limits to the encoding and bounds on the performance of coherent ultrashort light pulse code division multiple access the authors obtain lower and upper bounds on the peak intensity of a spectrally phase encoded ultrashort light pulse as a function of the length of spectral phase encoding it is shown that using random phase codes for spectral encoding of ultrashort light pulses in a coherent ultrashort light pulse code division multiple access cdma system is almost optimal furthermore simple upper bounds and an asymptotic approximation on the bit error rate ber for a wide class of ultrashort light pulse cdma systems are obtained it is shown that in spite of being simple these upper bounds can be used to evaluate the performance of a coherent ultrashort light pulse cdma system

recursive identification of errors in variables wiener systems this paper considers the recursive identification of errors in variables eiv wiener systems composed of a linear dynamic system followed by a static nonlinearity both the system input and output are observed with additive noises being arma processes with unknown coefficients by a stochastic approximation incorporated with the deconvolution kernel functions the recursive algorithms are proposed for estimating the coefficients of the linear subsystem and for the values of the nonlinear function all the estimates are proved to converge to the true values with probability one a simulation example is given to verify the theoretical analysis