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

diagnostics for nonlinearity and heteroscedasticity in errors in variables regression we suggest new plotting methods for residual analysis in errors in variables regression the standard residuals analyses are based on the methods of miller and fuller and are appropriate when the errors in the regression and the measurement error are symmetrically distributed by appropriate we mean that in large samples the plots will not falsely identify a nonexistent pattern of heteroscedasticity or nonlinearity the standard methods are not appropriate in this sense for skewed error distributions our methods require replication of the error prone predictors but they are appropriate for both symmetric and skewed error distributions besides residual plots we also construct hypothesis tests for heteroscedasticity in terms of power for detecting heteroscedasticity we show that the standard plot is more efficient when the residuals are normally distributed although it does not achieve its nominal level for skewed error distributions simulations are used to illustrate the results we also conside

exact nonparametric inference when doses are measured with random errors studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose if the doses are measured with error then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response if one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0 that is the dose errors are pure errors and not say systematic underreporting of exposure then the presence of zero dose controls is all that is needed to obtain exact distribution free confidence intervals and tests and consistent point estimates the method is simpler for matched pairs than for matched sets with two or more matched subjects and it is illustrated using two studies one of each kind with matched pairs as in this first example the method uses wilcoxon s signed rank test as the basis for inference when there are several zero dos

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

gauge fields in a dsd and connections of its symmetry algebra the generalized connections of the de sitter algebra so d 1 and anti de sitter algebra so d 1 2 which are differential forms of arbitrary degree with values in any irreducible spin tensor representation of the anti de sitter algebra are studied it is shown that an arbitrary spin gauge field in anti de sitter space massless or partially massless can be described by a single connection a one to one correspondence between the connections of the anti de sitter algebra and the gauge fields is established the gauge symmetry is manifest and auxiliary fields are automatically included in the formalism

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

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

estimating the reliability of an exposure variable in the presence of confounders in this paper we discuss estimation of the reliability of an exposure variable in the presence of confounders measured without error we give an explicit formula that shows how the exposure becomes less reliable as the degree of correlation between the exposure and confounders increases we also discuss biases in the corresponding logistic regression estimates and methods for correction data from a matched case control study of hormone levels and risk of breast cancer are used to illustrate the methods

term structure models and the zero bound an empirical investigation of japanese yields abstract when japanese short term bond yields were near their zero bound yields on long term bonds showed substantial fluctuation and there was a strong positive relationship between the level of interest rates and yield volatilities risk premiums we explore whether several families of dynamic term structure models that enforce a zero lower bound on short rates imply conditional distributions of japanese bond yields consistent with these patterns multi factor shadow rate and quadratic gaussian models evaluated at their maximum likelihood estimates capture many features of the data furthermore model implied risk premiums track realized excess returns during extended periods of near zero short rates in contrast the conditional distributions implied by non negative affine models do not match their sample counterparts and standard gaussian affine models generate implausibly large negative risk premiums

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

covariate adjusted regression mue11er wa1d ucdavis edu summary we introduce covariate adjusted regression for situations where both predictors and response in a regression model are not directly observable but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate we demonstrate how the regression coefficients can be estimated by establishing a connection to varying coefficient regression the proposed covariate adjustment method is illustrated with an analysis of the regression of plasma fibrinogen concentration as response on serum transferrin level as predictor for 69 haemodialysis patients in this example both response and predictor are thought to be influenced in a multiplicative fashion by body mass index a bootstrap hypothesis test enables us to test the significance of the regression parameters we establish consistency and convergence rates of the parameter estimators for this new covariate adjusted regression model simulation studies demonstrate the efficacy of the proposed method

a quadratic kalman filter abstract we propose a new filtering and smoothing technique for non linear state space models observed variables are quadratic functions of latent factors following a gaussian var stacking the vector of factors with its vectorized outer product we form an augmented state vector whose first two conditional moments are known in closed form we also provide analytical formulae for the unconditional moments of this augmented vector our new quadratic kalman filter qkf exploits these properties to formulate fast and simple filtering and smoothing algorithms a simulation study first emphasizes that the qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70 rmses improvement of filtered values second it provides evidence that qkf based maximum likelihood estimates of model parameters always possess lower bias or lower rmses than the alternative estimators

proportional hazards model with covariates subject to measurement error when covariates of a proportional hazards model are subject to measurement error the maximum likelihood estimates of regression coefficients based on the partial likelihood are asymptotically biased prentice 1982 biometrika 69 331 342 presents an example of such bias and suggests a modified partial likelihood this paper applies the corrected score function method nakamura 1990 biometrika 77 127 137 to the proportional hazards model when measurement errors are additive and normally distributed the result allows a simple correction to the ordinary partial likelihood that yields asymptotically unbiased estimates the validity of the correction is confirmed via a limited simulation study

comparing the effects of continuous and discrete covariate mismeasurement with emphasis on the dichotomization of mismeasured predictors it is well known that imprecision in the measurement of predictor variables typically leads to bias in estimated regression coefficients we compare the bias induced by measurement error in a continuous predictor with that induced by misclassification of a binary predictor in the contexts of linear and logistic regression to make the comparison fair we consider misclassification probabilities for a binary predictor that correspond to dichotomizing an imprecise continuous predictor in lieu of its precise counterpart on this basis nondifferential binary misclassification is seen to yield more bias than nondifferential continuous measurement error however it is known that differential misclassification results if a binary predictor is actually formed by dichotomizing a continuous predictor subject to nondifferential measurement error when the postulated model linking the response and precise continuous predictor is correct this differential misclassification is found to yield less bias than continuous measurement error in contrast with nondifferential misclassification i e dichotomization reduces the bias due to mismeasurement this finding however is sensitive to the form of the underlying relationship between the response and the continuous predictor in particular we give a scenario where dichotomization involves a trade off between model fit and misclassification bias we also examine how the bias depends on the choice of threshold in the dichotomization process and on the correlation between the imprecise predictor and a second precise predictor

the use of maximin efficiency robust tests in combining contingency tables and survival analysis abstract a test is the maximin efficiency robust test for a family of possible models underlying the data if no other test has higher minimum efficiency relative to the asymptotically optimum test for each model methods used to examine the efficiency robustness of rank tests for the two sample problem are adapted to obtain maximin efficiency robust procedures for testing the equality of proportions across several 2 2 tables for combining the results of tests for trend in several 2 x j tables in which the dose response function is one of a set of possible monotone functions and to analyze censored survival data when either the wilcoxon or log rank may be appropriate in the survival setting the robust test has maximin efficiency 93 3 relative to the wilcoxon or long rank when each is optimum in contrast to the 75 relative efficiency each statistic has when the other is optimum

group detection for synchronous gaussian code division multiple access channels the concept of group detection is introduced to address the design of suboptimum multiuser detectors for code division multiple access cdma channels a group detection scheme consists of a bank of p group detectors one each for detecting the information symbols of users in each group of a p group partition of the k simultaneously transmitting users in a parallel group detection scheme these group detectors operate independently whereas in a sequential scheme each group detector uses the decisions of the previous group detectors to successively cancel the interference from those users group detectors based on the generalized likelihood ratio test glrt are obtained for the synchronous gaussian cdma channel the complexity of these detectors is exponential in the group size whereas that of the optimum detector is exponential in k since the partition of users is a design parameter group sizes can be chosen to satisfy a wide range of complexity constraints a key performance result is that the glrt group detectors are optimally group near far resistant furthermore upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived these bounds reveal that the sequential group detectors can under certain conditions perform as well as glrt group detectors of much larger group sizes group detection provides a unifying approach to multiuser detection when the users are partitioned into k single user groups the glrt a modified form of glrt and the sequential group detectors reduce to previously proposed suboptimal detectors namely the decorrelator the two stage detector and the decorrelating decision feedback detector respectively for the other nontrivial partitions the group detectors are new and have a performance that is commensurate with their complexity

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

flexible regression models with cubic splines we describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates this simple method can help prevent the problems that result from inappropriate linearity assumptions we compare restricted cubic spline regression to non parametric procedures for characterizing the relationship between age and survival in the stanford heart transplant data we also provide an illustrative example in cancer therapeutics

inflation of the type i error rate when a continuous confounding variable is categorized in logistic regression analyses this paper demonstrates an inflation of the type i error rate that occurs when testing the statistical significance of a continuous risk factor after adjusting for a correlated continuous confounding variable that has been divided into a categorical variable we used monte carlo simulation methods to assess the inflation of the type i error rate when testing the statistical significance of a risk factor after adjusting for a continuous confounding variable that has been divided into categories we found that the inflation of the type i error rate increases with increasing sample size as the correlation between the risk factor and the confounding variable increases and with a decrease in the number of categories into which the confounder is divided even when the confounder is divided in a five level categorical variable the inflation of the type i error rate remained high when both the sample size and the correlation between the risk factor and the confounder were high

power and sample size calculations for generalized regression models with covariate measurement error covariate measurement error is often a feature of scientific data used for regression modelling the consequences of such errors include a loss of power of tests of significance for the regression parameters corresponding to the true covariates power and sample size calculations that ignore covariate measurement error tend to overestimate power and underestimate the actual sample size required to achieve a desired power in this paper we derive a novel measurement error corrected power function for generalized linear models using a generalized score test based on quasi likelihood methods our power function is flexible in that it is adaptable to designs with a discrete or continuous scalar covariate exposure that can be measured with or without error allows for additional confounding variables and applies to a broad class of generalized regression and measurement error models a program is described that provides sample size or power for a continuous exposure with a normal measurement error model and a single normal confounder variable in logistic regression we demonstrate the improved properties of our power calculations with simulations and numerical studies an example is given from an ongoing study of cancer and exposure to arsenic as measured by toenail concentrations and tap water samples

corrected score function for errors in variables models methodology and application to generalized linear models summary statistical models whose independent variables are subject to measurement errors are often referred to as errors in variables models to correct for the effects of measurement error on parameter estimation this paper considers a correction for score functions a corrected score function is one whose expectation with respect to the measurement error distribution coincides with the usual score function based on the unknown true independent variables this approach makes it possible to do inference as well as estimation of model parameters without additional assumptions the corrected score functions of some generalized linear models are obtained

the nonexistence of 100 1 alpha confidence sets of finite expected diameter in errors in variables and related models on montre que pour certains modeles il est impossible de construire des intervalles de confiance pour les parametres cles qui aient a la fois une confiance positive et une longueur esperee finie

some relations between extended and unscented kalman filters the unscented kalman filter ukf has become a popular alternative to the extended kalman filter ekf during the last decade ukf propagates the so called sigma points by function evaluations using the unscented transformation ut and this is at first glance very different from the standard ekf algorithm which is based on a linearized model the claimed advantages with ukf are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model we point out several less known links between ekf and ukf in terms of two conceptually different implementations of the kalman filter the standard one based on the discrete riccati equation and one based on a formula on conditional expectations that does not involve an explicit riccati equation first it is shown that the sigma point function evaluations can be used in the classical ekf rather than an explicitly linearized model second a less cited version of the ekf based on a second order taylor expansion is shown to be quite closely related to ukf the different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications

estimation for the nonlinear functional relationship on etudie les proprietes asymptotiques de l estimateur du maximum de vraisemblance pour le modele fonctionnel implicite

multiuser detection for overloaded cdma systems multiuser detection for overloaded code division multiple access cdma systems in which the number of users is larger than the dimension of the signal space is of particular interest when bandwidth is at a premium in this paper certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and or interfering signal subspaces are of reduced rank and or have a nontrivial intersection in the process two new suboptimum detectors are proposed that are especially well suited to overloaded systems namely the group pseudo decorrelator and the group minimum mean squared error mmse detector the former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form in the low noise regime of the group mmse detector pseudo decorrelation is also used as a feedforward filter in a new decision feedback scheme for the particular case of real valued modulation it is shown that the proposals of the so called improved linear also known as linear conjugate or widely linear detectors were more simply derived earlier using the idea of minimal sufficiency which we also apply to the new detectors of this paper

a detailed evaluation of adjustment methods for multiplicative measurement error in linear regression with applications in occupational epidemiology it is often appropriately assumed based on both theoretical and empirical considerations that airborne exposures in the workplace are lognormally distributed and that a worker s mean exposure over a reference time period is a key predictor of subsequent adverse health effects for that worker unfortunately it is generally impossible to accurately measure a worker s true mean exposure we begin by introducing a familiar model for exposure that views this true mean as well as logical surrogates for it as lognormal random variables in a more general context we then consider the linear regression of a continuous health outcome on a lognormal predictor measured with multiplicative error we discuss several candidate methods of adjusting for the measurement error to obtain consistent estimators of the true regression parameters these methods include a simple correction of the ordinary least squares estimator based on the surrogate regression the regression of the outcome on the covariates and on the conditional expectation of the true predictor given the observed surrogate and a quasi likelihood approach by means of a simulation study we compare the various methods for practical sample sizes and discuss important issues relevant to both estimation and inference finally we illustrate promising adjustment strategies using actual lung function and dust exposure data on workers in the dutch animal feed industry

conformal self dual fields conformal self dual fields in flat spacetime of even dimension greater than or equal to 4 are studied ordinary derivative formulation of such fields is developed gauge invariant lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained gauge symmetries are realized by involving the stueckelberg fields the realization of global conformal symmetries is obtained the light cone gauge lagrangian is found also we demonstrate the use of the light cone gauge for counting the on shell degrees of freedom of the conformal self dual fields

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

testing hypotheses with binary data subject to misclassification errors analysis and experimental design summary consider a binary random variable having outcomes subject to misclassification errors where the probabilities of misclassification errors depend on outcome the asymptotic relative efficiencies are derived for comparing two binomial populations comparing stratified binomial populations and for paired comparisons the probabilities of misclassification can vary with strata or be different for each pair the criterion for optimum experimental designs is shown to be the ratio of the asymptotic relative efficiency to expected cost per observation this criterion implies that mixtures of different experiments can never be optimal a number of experimental strategies is discussed

stacked ostbc error performance and rate analysis it is well known that the alamouti scheme is the only space time code from orthogonal designs achieving the capacity of a multiple input multiple output mimo wireless communication system with nt 2 transmit antennas and nr 1 receive antenna in this paper we propose the n times stacked alamouti scheme for nt 2n transmit antennas and show that this scheme achieves the capacity in the case of nr 1 receive antenna this result may regarded as an extension of the alamouti case for the more general case of more than one receive antenna we show that if the number of transmit antennas is higher than the number of receive antennas we achieve a high portion of the capacity with this scheme further we show that the mimo capacity is at most twice the rate achieved with the proposed scheme for all signal to noise ratio snr we derive lower and upper bounds for the rate achieved with this scheme and compare it with upper and lower bounds for the capacity in addition to the capacity analysis based on the assumption of a coherent channel we analyze the error rate performance of the stacked orthogonal space time block code ostbc with the optimal maximum likelihood ml detector and with the suboptimal lattice reduction lr aided zero forcing detector we compare the error rate performance of the stacked ostbc with spatial multiplexing sm and full diversity achieving schemes finally we illustrate the theoretical results by numerical simulations

recursive nonparametric testing for dose response relaflonships subject to downturns at high doses summary a general recursive strategy is introduced to test nonparametrically for an increasing dose response relationship when a downturn in response at high doses is possible a specific implementation involving a test of jonckheere 1954 and terpstra 1952 is considered and its size and power properties are investigated via monte carlo methods data from mutation research illustrate the phenomenon of concern

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

a fast recursive algorithm for g stbc this paper proposes a fast recursive algorithm for group wise space time block code g stbc which takes full advantage of the alamouti structure in the equivalent channel matrix to reduce the computational complexity with respect to the existing efficient algorithms for g stbc the proposed algorithm achieves better performance and usually requires less computational complexity

two stage instrumental variables estimators for the nonlinear errors in variables model abstract estimation for the nonlinear functional errors in variables model is considered under the assumption that instrumental variables are available the approximate bias in the ordinary instrumental variable estimator due to the nonlinearity of the relationship is derived utilizing the nonlinearity of the relationship an estimator of the error covariance matrix is introduced using the error covariance matrix estimator two types of two stage instrumental variable estimators are proposed the two two stage estimators do not have the asymptotic bias due to the nonlinearity a monte carlo experiment also shows the superiority of the two stage estimators over the ordinary estimator

on the polynomial functional relationship summary a method for obtaining consistent estimators of the coefficients in a polynomial functional relationship model with normal errors is proposed when the error covariance matrix is either completely known or known up to a proportionality factor for quadratic functional relationships with possibly non normal errors we present a consistent estimator when the error covariance matrix is known a large sample test of the quadratic against the linear functional relationship is also suggested in this case

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

performance analysis of zf and mmse equalizers for mimo systems an in depth study of the high snr regime this paper presents an in depth analysis of the zero forcing zf and minimum mean squared error mmse equalizers applied to wireless multiinput multioutput mimo systems with no fewer receive than transmit antennas in spite of much prior work on this subject we reveal several new and surprising analytical results in terms of output signal to noise ratio snr uncoded error and outage probabilities diversity multiplexing d m gain tradeoff and coding gain contrary to the common perception that zf and mmse are asymptotically equivalent at high snr we show that the output snr of the mmse equalizer conditioned on the channel realization is mmse zf ssrsnr where zf is the output snr of the zf equalizer and that the gap ssrsnr is statistically independent of zf and is a nondecreasing function of input snr furthermore as ssr snr ura ssrsnr converges with probability one to a scaled f random variable it is also shown that at the output of the mmse equalizer the interference to noise ratio inr is tightly upper bounded by ssrsnr zf using the decomposition of the output snr of mmse we can approximate its uncoded error as well as outage probabilities through a numerical integral which accurately reflects the respective snr gains of the mmse equalizer relative to its zf counterpart the e outage capacities of the two equalizers however coincide in the asymptotically high snr regime we also provide the solution to a long standing open problem applying optimal detection ordering does not improve the d m tradeoff of the vertical bell labs layered space time v blast architecture it is shown that optimal ordering yields a snr gain of 10log10n db in the zf v blast architecture where n is the number of transmit antennas whereas for the mmse v blast architecture the snr gain due to ordered detection is even better and significantly so

an analysis of the mimo sdma channel with space time orthogonal and quasi orthogonal user transmissions and efficient successive cancellation decoders we consider space time transceiver architectures for space division multiple access sdma fading channels with simultaneous transmissions from multiple users each user has up to four transmit antennas and employs a space time orthogonal or a quasi orthogonal design as an inner code at the multiple antenna receiver efficient successive group interference cancellation strategies based on zero forcing or minimum mean square error mmse filtering are employed in some fixed or channel dependent order these strategies are efficient in the sense that they exploit the special structure of the inner codes to yield much higher diversity orders than would be otherwise possible while at the same time preserving what we call the decoupling property of the constituent inner codes which enables the use of low complexity outer encoders decoders for each user motivated by the special structure of the effective channel matrix induced by the inner codes we obtain several new distribution results on the qr and eigenvalue decompositions of certain structured random matrices these results are the key to a comprehensive performance analysis of the proposed multiuser transceiver architectures including the characterization of diversity multiplexing tradeoff dmt curves and exact per user bit error rates bers without making simplifying assumptions about error propagation

staying at zero with affine processes an application to term structure modelling we build an affine term structure model that provides non negative yields at any maturity and that is able to accommodate a short term rate that stays at the zero lower bound zlb for extended periods of time while longer term rates feature high volatilities we introduce these features through a new univariate non negative affine process called arg zero and its multivariate affine counterpart varg entailing conditional distributions with zero point masses the affine property of this new class of processes implies both explicit bond pricing and quasi explicit lift off probability formulas we provide an empirical application to japanese government bond jgb yields observed weekly from june 1995 to may 2014 with maturities from six months to ten years our four factor specification is able to closely match yield levels and to capture conditional yield variances

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

measuring information loss due to inconsistencies in duration data from longitudinal surveys abstract in this paper we take a functional errors in variables approach to modeling longitudinal duration data containing observed inconsistencies this approach separates the problem into two parts an errors in variables problem and an estimation problem this approach also enables us to develop measures of the effect of the data inconsistencies on the parameter estimates from a duration model one measure is the loss in precision in the parameter estimates that results from the inconsistencies we refer to the proportion of parameter variances that is due to the inconsistencies in the data as information loss the second is a distance measure which is used to provide information about how close we are to a consistent estimator an example is provided using a four month panel of current population survey data

the asymptotic relative efficiency of score tests in a generalized linear model with surrogate covariates summary in many epidemiological studies the exposure variable of interest cannot be measured directly the classical approaches to errors in variables in regression do not extend easily to the nonlinear models commonly used in epidemiologic al research furthermore the traditional additive measurement error model cannot adequately represent many surrogate relationships by considering the effect of using surrogate independent variables on the efficient score statistic some of the difficulties inherent in the estimation problem may be avoided for the null hypothesis of no association a simple and flexible procedure can be used to calculate the optimal score test the asymptotic relative efficiency of this test to the test based upon the true exposures is derived the optimal test is also compared to the naive procedure of substituting the surrogate into the score test for the true exposure

reprojecting partially observed systems with application to interest rate diffusions abstract we introduce reprojection as a general purpose technique for characterizing the dynamic response of a partially observed nonlinear system to its observable history reprojection is the third step of a procedure wherein first data are summarized by projection onto a hermite series representation of the unconstrained transition density for observables second system parameters are estimated by minimum chi squared where the chi squared criterion is a quadratic form in the expected score of the projection and third the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of the estimated system onto a hermite series representation of the constrained transition density for observables the constrained transition density can be used to study the response of the system to its observable history we utilize the technique to assess the dynamics of several diffusion models for the short term interest rate that have been proposed and to compare them to a ne

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

polynomial regression with errors in the variables a polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients assuming hypothetically the latent true regressor variable to be known and then adjusting for the errors if normality of the error variables can be assumed the estimator can be simplified considerably only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known if the variance of the errors in the dependent variable is also known another estimator can be constructed

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

polynomial regression and estimating functions in the presence of multiplicative measurement error we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor two general methods are considered with the methods differing in their assumptions about the distributions of the predictor and the measurement errors consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory diagnostics are presented for distinguishing additive and multiplicative measurement error data from a nutrition study are analysed by using the methods the results from a simulation study are presented and the performances of the methods are compared

estimation of the quadratic errors in variables model summary an estimator is presented for the coefficients of the quadratic functional relationship the estimator is shown to be asymptotically normally distributed as the sample size increases in deriving this result it is not assumed that replication occurs a monte carlo study is presented agreeing well with the asymptotic results an example from the earth sciences is analysed

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

the loss in efficiency from misspecifying covariates in proportional hazards regression models summary this note considers partial likelihood score tests for association between a covariate process and survival time based on a proportional hazards regression model we derive the asymptotic efficiency of the test based on a misspecified form of the covariate process relative to the test based on the correct form the results can be used to assess the consequences of various types of misspecification

testing for gene environment interaction under exposure misspecification complex interplay between genetic and environmental factors characterizes the etiology of many diseases modeling gene environment gxe interactions is often challenged by the unknown functional form of the environment term in the true data generating mechanism we study the impact of misspecification of the environmental exposure effect on inference for the gxe interaction term in linear and logistic regression models we first examine the asymptotic bias of the gxe interaction regression coefficient allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects for linear regression we show that under gene environment independence and some confounder dependent conditions when the environment effect is misspecified the regression coefficient of the gxe interaction can be unbiased however inference on the gxe interaction is still often incorrect in logistic regression we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly further we show that the standard robust sandwich variance estimator for the gxe interaction does not perform well in practical gxe studies and we provide an alternative testing procedure that has better finite sample properties

loss in efficiency caused by omitting covariates and misspecifying exposure in logistic regression models we examine the effects of omitting covariates and misspecifying the explanatory variable of interest on tests of association between the explanatory variable and response based on logistic regression models we assume throughout that the covariates are statistically independent of the explanatory variable as under simple randomization a general expression for the asymptotic loss in efficiency from omitting covariates and misspecifying the explanatory variable is derived the expression for the asymptotic efficiency of the misspecified test statistic relative to the correctly specified test can be factored into two parts each of which is less than or equal to 1 the first part reflects the consequences of misspecifying exposure whereas the other part captures the effect of omitting needed covariates this result permits numerical evaluation of the approximate loss in efficiency and can be useful in developing guidelines for study design and model fitting procedures we discuss applications of the resul

tensor gauge fields in arbitrary representations of gl d ℝ duality and poincare lemma using a mathematical framework which provides a generalization of the de rham complex well designed for p form gauge fields we have studied the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of gl d we have proven a generalization of the poincare lemma which enables us to solve the above mentioned problems in a systematic and unified way

tensor gauge fields in arbitrary representations of gl d mathbb r ii quadratic actions quadratic second order non local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in d dimensional minkowski space are explicitly written in a compact form by making use of levi civita tensors the field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non lagrangian local field equations proposed previously moreover these actions allow a frame like reformulation a la macdowell mansouri without any trace constraint in the tangent indices

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

consistent estimation for some nonlinear errors in variables models abstract the issues of identification and estimation of nonlinear errors in variables models are explored the deficiencies of the conventional definition of identification are discussed and an alternative definition in terms of observed samples is suggested the consistency and asymptotic normality of minimum distance estimators are studied to simplify the computation a two step estimation procedure is also suggested in which a consistent estimate of a subset of parameters is first obtained and treated as if they were known in the second step estimation of the rest of the parameters conditions for the consistency of this two step estimator and its asymptotic variance covariance matrix are also derived

analysis of decision feedback detection for mimo rayleigh fading channels and the optimization of power and rate allocations for an uncoded k transmit n receive antenna coherent narrow band communication system employing a decorrelating decision feedback detector d dfd the exact average over channel realizations joint error probability jep as well as the average per symbol error probabilities seps are derived without making any simplifying assumptions on error propagation it is proved that the diversity orders of the jep and the sep of every symbol is limited by error propagation to n k 1 based on our exact error probability analysis however we suggest an optimization of jep over nonnegative quadrature amplitude modulation qam constellation sizes rates and average powers across transmitters which yield significant improvements over the usual equal power and equal rate assignment in fact the jep of such an optimized design has the much improved diversity order of n which is also the diversity order obtained through the optimum maximum likelihood ml detector moreover it is seen that these simple optimized designs can achieve a significant fraction of the spl epsi outage capacity even without outer codes it is also known but only through simulations that when the symbols are detected in certain channel realization dependent orders it is possible to improve substantially over fixed order detection in the case of the equal rate and equal power assignment we provide an analysis for a recently proposed channel dependent ordering rule and show that it does not provide an improvement of the diversity order of the jep beyond n k 1 another ordering rule that was proposed earlier to maximize the worst case post detection signal to noise ratio snr under the perfect feedback assumption is shown to be optimal under a more compelling criterion that does not involve that simplifying assumption while efficiently computable this ordering rule is seen to perform almost as well as the optimal channel dependent ordering rule that minimizes the conditional jep and hence the jep nevertheless a multiple input multiple output mimo system with an optimized rate and power allocation and a fixed order of detection is not only less complex but also has a significantly lower jep than that of the equal power equal rate system where transmitters are detected in a channel dependent order optimal or otherwise

identification and estimation of polynomial errors in variables models abstract methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a true regressor which is measured with error two sources of additional information concerning the unobservable regressor are considered either an additional indicator of the regressor itself measured with error or instrumental variables which characterize the systematic variation in the true regressor in both cases estimators are constructed by relating moments involving the unobserved variables to moments of observables these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters e g moments of the measurement error consistency and asymptotic normality of the estimated coefficients is demonstrated and consistent estimators of the asymptotic covariant matrices are provided

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

regression dilution in the proportional hazards model the problem of regression dilution arising from covariate measurement error is investigated for survival data using the proportional hazards model the naive approach to parameter estimation is considered whereby observed covariate values are used inappropriately in the usual analysis instead of the underlying covariate values a relationship between the estimated parameter in large samples and the true parameter is obtained showing that the bias does not depend on the form of the baseline hazard function when the errors are normally distributed with high censorship adjustment of the naive estimate by the factor 1 lambda where lambda is the ratio of within person variability about an underlying mean level to the variability of these levels in the population sampled removes the bias as censorship increases the adjustment required increases and when there is no censorship is markedly higher than 1 lambda and depends also on the true risk relationship