adapting for heteroscedasticity in linear models in a heteroscedastic linear model it is known that if the variances are a parametric function of the design then one can construct an estimate of the regression parameter which is asymptotically equivalent to the weighted least squares estimate with known variances we show that the same is true when the only thing known about the variances is that they are determined by an unknown but smooth function of the design or the mean response

a note on nonregular likelihood functions in heteroscedastic regression models summary the existence of maximum likelihood estimates for a class of heteroscedastic regression models is considered for a given dispersion function we show that under a weak condition the likelihood is singular at points corresponding to nonreplicated observations causing unrestricted maximum likelihood estimation to break down whilst for an alternative class of dispersion functions we obtain a much stronger linear independence condition for the likelihood to be unbounded

a comparison between maximum likelihood and generalized least squares in a heteroscedastic linear model abstract we consider a linear model with normally distributed but heteroscedastic errors when the error variances are functionally related to the regression parameter one can use either maximum likelihood or generalized least squares to estimate the regression parameter we show that likelihood is more sensitive to small misspecifications in the functional relationship between the error variances and the regression parameter

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

the predictive ability of several models of exchange rate volatility abstract we compare the out of sample forecasting performance of univariate homoskedastic garch autoregressive and nonparametric models for conditional variances using five bilateral weekly exchange rates for the dollar 1973 1989 for a one week horizon garch models tend to make slightly more accurate forecasts for longer horizons it is difficult to find grounds for choosing between the various models none of the models perform well in a conventional test of forecast efficiency

modeling of hormone secretion generating mechanisms with splines a pseudo likelihood approach a flexible and robust approach is proposed for the investigation of underlying hormone secretion generating mechanisms characterizing hormone time series is a difficult task as most hormones are secreted in a pulsatile manner and pulses are often masked by slow decay we model hormone concentration as a filtered counting process where the intensity function of the counting process is modeled nonparametrically using periodic splines the intensity function and parameters are estimated using a combination of weighted least squares and pseudo likelihood based on the first two moments our method uses concentration measurements directly which avoids the difficult task of estimating pulse numbers and locations both simulations and applications suggest that our method performs well for estimating the intensity function of the pulse generating counting processes

some new estimation methods for weighted regression where there are possible outliers the problem considered is the robust estimation of the variance parameter in a heteroscedastic linear model we treat the situation in which the variance is a function of the explanatory variables to estimate robustly the variance in this case it is necessary to guard against the influence of outliers in the design as well as outliers in the response by analogy with the homoscedastic regression case we propose two estimators that do this their performances are evaluated on a number of data sets we had considerable success with estimators that bound the self influence that is the influence an observation has on its own fitted value we conjecture that in other situations e g homoscedastic regression bounding the selfinfluence will lead to estimators with good robustness properties

semiparametric quasilikelihood and variance function estimation in measurement error models abstract we consider a quasilikelihood variance function model when a predictor x is measured with error and a surrogate w is observed when in addition to a primary data set containing y w a validation data set exists for which x w is observed we can i estimate the first and second moments of the response y given w by kernel regression ii use quasilikelihood and variance function techniques to estimate the regression parameters as well as variance structure parameters the estimators are shown to be asymptotically normally distributed with asymptotic variance depending on the size of the validation data set and not on the bandwith used in the kernel estimates a more refined analysis of the asymptotic covariance shows that the optimal bandwidth converges to zero at the rate n 1 3

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

variance functions and the minimum detectable concentration in assays abstract assay data are often fit by a nonlinear regression model incorporating heterogeneity of variance as ion radioimmunoassay for example typically the standard deviation of the response is taken to be proportional to a power theta of the mean there is considerable empirical evidence suggesting that for assays of a reseasonable size how one estimates the parameter theta does not greatly affect how well one estimates the the mean regression function an additional component of assay analysis is the estimation of auxillary constructs such as the minimum detectable concentration for which many definitions exist we focus on one such definition the minimum detectable concentration depends both on theta and the mean regression function we compare three standard method of estimating the parameter theta due to rodbard 1978 raab 1981a and carroll and ruppert 1982b when duplicate counts are taken at each concentration the first method is only 20 efficient asymptotically in comparison to the third and the resulting estimate of the minimum detectable concentration is asymptotically 3 3 times more variable for first than the third less dramatic results obtain for the second estimator compared to the third this estimator is still not efficient however simulation results and an example are supportive of the asymptotic theory keywords least squares method

direct regression models for longitudinal rates of change comparing rates of growth or rates of change across covariate defined subgroups is a primary objective for many longitudinal studies in the special case of a linear trend over time the interaction between a covariate and time will characterize differences in longitudinal rates of change however in the presence of a non linear longitudinal trajectory the standard mean regression approach does not permit parsimonious description or inference regarding differences in rates of change therefore we propose regression methodology for longitudinal data that allows a direct structured comparison of rates across subgroups even in the presence of a non linear trend over time our basic longitudinal rate regression method assumes a proportional difference across covariate groups in the rate of change across time but this assumption can be relaxed rates are compared relative to a generally specified time trend for which we discuss both parametric and non parametric estimating approaches we develop mixed model longitudinal methodology that explicitly characterizes subject to subject variation in rates as well as a marginal estimating equation based method in addition we detail a score test to detect violations of the proportionality assumption and we allow time varying rate effects as a natural generalization simulation results demonstrate potential gains in power for the longitudinal rate regression model relative to a linear mixed effects model in the presence of a non linear trend in time we apply our method to a study of growth among infants born to hiv infected mothers and conclude with a discussion of possible extensions for our methods

the impact of unidentified location effects on dispersion effects identification from unreplicated factorial designs there have been several publications on identifying dispersion effects from an unreplicated fractional or full factorial experiment some of these methods implicitly assume that unknown location effects are first identified correctly from the data in practice however an empirical location effects identification procedure may leave some small to moderate location effects undetected it is shown in this study that such unidentified location effects can cumulatively impair subsequent dispersione effects identification numerical evidence based on a welding experiment and results from a simulation study are provided a mathematical explanation of the impact of unidentified location effects on dispersion effects identification is given the dispersion effects identification methods initially proposed for unreplicated data can be naturally extended to replicated experiments with the impact of unidentified location effects eliminated a fluorescent lamp experiment is analyzed to illustrate these methods

a comparison of the variance estimation methods for heteroscedastic nonlinear models heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice we discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters the simulation study suggests that when the true variance is a function of the mean model the power of the mean variance function estimation method and the transform both sides method are the best choices for estimating the standard errors of the estimated model parameters in general the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias especially when the heterogeneity is nonsystematic across values of the covariate furthermore we note that the two modified sandwich estimators are appealing choices in practice considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform both sides approach copyright 2016 john wiley sons ltd

confidence bounds for nonlinear dose response relationships an important aim of drug trials is to characterize the dose response relationship of a new compound such a relationship can often be described by a parametric nonlinear function that is monotone in dose if such a model is fitted it is useful to know the uncertainty of the fitted curve it is well known that wald confidence intervals are based on linear approximations and are often unsatisfactory in nonlinear models apart from incorrect coverage rates they can be unreasonable in the sense that the lower confidence limit of the difference to placebo can be negative even when an overall test shows a significant positive effect bootstrap confidence intervals solve many of the problems of the wald confidence intervals but are computationally intensive and prone to undercoverage for small sample sizes in this work we propose a profile likelihood approach to compute confidence intervals for the dose response curve these confidence bounds have better coverage than wald intervals and are more precise and generally faster than bootstrap methods moreover if monotonicity is assumed the profile likelihood approach takes this automatically into account the approach is illustrated using a public dataset and simulations based on the emax and sigmoid emax models

a new test for the parametric form of the variance function in non parametric regression in the common non parametric regression model the problem of testing for the parametric form of the conditional variance is considered a stochastic process based on the difference between the empirical processes that are obtained from the standardized non parametric residuals under the null hypothesis of a specific parametric form of the variance function and the alternative is introduced and its weak convergence established this result is used for the construction of a kolmogorov smimov and a cramer von mises type of statistic for testing the parametric form of the conditional variance the consistency of a bootstrap approximation is established and the finite sample properties of this approximation are investigated by means of a simulation study in particular the new procedure is compared with some of the currently available methods for this problem

a semiparametric model for the analysis of recurrent event panel data summary in many longitudinal studies interest focuses on the occurrence rate of some phenomenon for the subjects in the study when the phenomenon is nonterminating and possibly recurring the result is a recurrent event data set examples include epileptic seizures and recurrent cancers when the recurring event is detectable only by an expensive or invasive examination only the number of events occurring between follow up times may be available this article presents a semiparametric model for such data based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function a random subject specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data estimators are determined from quasi likelihood estimating functions because only first and second moment assumptions are required for quasi likelihood the method is more robust than those based on the specification of a full parametric likelihood consistency of the estimators depends only on the assumption of the proportional intensity model the semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators as with semiparametric methods in survival analysis the method provides useful diagnostics for specific parametric models including a quasi score statistic for testing specific baseline intensity functions the techniques are used to analyze cancer recurrences and a pheromone based mating disruption experiment in moths a simulation study confirms that for many practical situations the estimators possess appropriate small sample characteristics

double exponential families and their use in generalized linear regression abstract in one parameter exponential families such as the binomial and poisson the variance is a function of the mean double exponential families allow the introduction of a second parameter that controls variance independently of the mean double families are used as constituent distributions in generalized linear regressions in which both means and variances are allowed to depend on observed covariates the theory is applied to two examples a logistic regression and a large two way contingency table in such cases the binomial model of variance is often untrustworthy for example because genuine random sampling was infeasible the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes clumped sampling is just one of many possible causes of overdispersion a habitual source of concern to users of binomial and poisson models this article concerns a class of regression families that allow the statistician to model overdispersion while carrying

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

statistical inference of a time to failure distribution derived from linear degradation in the study of semiconductor degradation records of transconductance loss or threshold voltage shift over time are useful in constructing the cumulative distribution function cdf of the time until the degradation reaches a specified level in this article we propose a model with random regression coefficients and a standard deviation function for analyzing linear degradation data both analytical and empirical motivations of the model are provided we estimate the model parameters the cdf and its quantiles by the maximum likelihood ml method and construct confidence intervals from the bootstrap from the asymptotic normal approximation and from inverting likelihood ratio tests simulations are conducted to examine the properties of the ml estimates and the confidence intervals analysis of an engineering dataset illustrates the proposed procedures

bootstrap adjusted calibration confidence intervals for immunoassay abstract in immunoassay a nonlinear heteroscedastic regression model is used to characterize assay concentration response and the model fitted to data from standard samples is used to calibrate unknown test samples usual large sample methods to construct individual confidence intervals for calibrated concentrations have been observed in empirical studies to be seriously inaccurate in terms of achieving the nominal level of coverage we show theoretically that this inaccuracy is due largely to estimation of parameters characterizing assay response variance by exploiting the theory we propose a bootstrap procedure to adjust the usual intervals to achieve a higher degree of accuracy we provide both theoretical results and simulation evidence to show that the proposed method attains the nominal level a practical advantage of the procedure is that it may be implemented reliably using far fewer bootstrap samples than are needed in other resampling schemes

a regularization corrected score method for nonlinear regression models with covariate error present here a new general method for adjusting for covariate error our method consists of an approximate version of the stefanski nakamura corrected score approach using the method of regularization to obtain an approximate solution of the relevant integral equation we develop the theory in the setting of classical likelihood models this setting covers for example linear regression nonlinear regression logistic regression and poisson regression the method is extremely general in terms of the types of measurement error models covered and is a functional method in the sense of not involving assumptions on the distribution of the true covariate we discuss the theoretical properties of the method and present simulation results in the logistic regression setting univariate and multivariate for illustration we apply the method to data from the harvard nurses health study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

some simple methods for estimating intraindividual variability in nonlinear mixed effects models methods are proposed to improve both population and individual inference within the nonlinear random coefficient regression framework by incorporating possible heterogeneity in the intraindividual variance structure these methods extend existing variance function estimation techniques by pooling information across individuals the methods are appropriate when it is reasonable to assume that there exists a common intraindividual variance structure

a note on extended quasi likelihood abstract we study the method of extended quasi likelihood estimation and inference of a variance function recently proposed by nelder pregibon 1987 the estimates are inconsistent in general and the test levels can be biased but in many cases such as the exponential family the inconsistency and bias will not be a major concern extended quasi likelihood is compared with carroll ruppert s 1982 pseudo likelihood method which gives consistent estimates and when slightly modified asymptotically unbiased tests we quantify the showing in this instance that the two estimates are closely related and may be asymptotically equivalent in many important cases however in some cases outside the exponential family an asymptotic bias can persist heteroscedastic regression model

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

likelihood quasi likelihood and pseudolikelihood some comparisons summary there is considerable interest in the fitting of models jointly to the mean and dispersion of a response for the mean parameter the wedderburn estimating equations are widely accepted however there is some controversy about estimating the dispersion parameters finite sampling properties of several dispersion estimators are investigated for three models by simulation we compare the maximum extended quasi likelihood estimator the maximum pseudolikelihood estimator and the maximum likelihood estimator if it exists of these estimators the maximum extended quasi likelihood estimator is usually superior in minimizing the mean squared error

variance function partially linear single index models we consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model we do not insist that the variance function depend only upon the mean function as happens in the classical generalized partially linear single index model we develop efficient and practical estimation methods for the variance function and for the mean function asymptotic theory for the parametric and nonparametric parts of the model is developed simulations illustrate the results an empirical example involving ozone levels is used to further illustrate the results and is shown to be a case where the variance function does not depend upon the mean function

dispersion effects from 7 unreplicated designs in the 2 k p series quality improvement requires reduction of undesired variation design of experiments haa become a useful tool for discovering such minimum variance conditions but most existing techniques require a large experimental effort involving replicated experiments in this article we develop a method for significance testing of dispersion effects from unreplicated two level fractional factorial experiments using principles close to those for identifying location effects the method provides an f distributed test statistic and appears to be useful for identification of dispersion effects as early as the screening stage when fractionated unreplicated experiments are frequently employed

linear mixed models with heterogeneous within cluster variances this paper describes an extension of linear mixed models to allow for heterogeneous within cluster variances in the analysis of clustered data unbiased estimating equations based on quasilikelihood pseudolikelihood and method of moments are introduced and are shown to give consistent estimators of the regression coefficients variance components and heterogeneity parameter under regularity conditions cluster specific random effects and variances are predicted by the posterior modes the method is illustrated through an analysis of menstrual diary data and its properties are evaluated in a simulation study

estimation of parameters in heteroscedastic linear models this paper deals with linear regression models with non homogeneous error variances the common situation where the error variance is a smooth function of the values of the regressor variables is considred the error variance function is represented by a function of known form but its expression involves the vector of unknown regression coeffcients and an additional vector parameter estimation of by iterative weighted least squares iwls therefore also requires updating the estimate of at each iteration when the error variance function is misspecified different methods of updating would yield iwls estimators of varying degrees of efficiency under such situations a method of updating is proposed resulting in an iterative procedure for estimating that is asymptotically optimal in the class of iwls estimators

a bayesian analysis of the linear calibration problem as part of a bayesian analysis of the linear calibration problem a posterior distribution is derived that is mathematically identical to the structural distribution obtained by kalotay 1971 but different from the bayesian distribution obtained by hoadley 1970 useful approximations are given although this posterior distribution has infinite variance no practical problems arise in using it the controversy concerning infinite variances and the use of inverse regression is discussed

distributed non fragile filtering in sensor networks with energy constraints this paper investigates the distributed filtering problem for sensor networks with energy constraint and filter gain variation firstly two strategies are proposed to reduce energy consumption i e the measurement size and the transmission rate reduction strategies to reduce the measurement size a useful measurement selection policy is introduced to choose which element of local measurements is transmitted the selected measurement which has a smaller size than the original one is then stochastically transmitted in order to reflect the imprecision in filter implementation the additive filter gain variation problem is considered based on the switched system approach and some stochastic system analysis methods a sufficient condition is obtained such that the filtering error system is exponentially stable in the mean square sense and a prescribed h performance level is guaranteed filter gains are shown to be determined by solving a set of linear matrix inequalities lmis finally a simulation example is given to demonstrate the effectiveness of the proposed design

partial interference alignment for k user mimo interference channels in this paper we consider a partial interference alignment and interference detection piaid design for k user quasi static mimo interference channels with discrete constellation inputs each transmitter has m antennas and transmits l independent data streams to the desired receiver with n receive antennas we focus on the case where not all k 1 interfering transmitters can be aligned at every receiver as a result there will be residual interference at each receiver that cannot be aligned each receiver detects and cancels the residual interference based on the constellation map however there is a window of unfavorable interference profile at the receiver for interference detection id in this paper we propose a low complexity partial interference alignment scheme in which we dynamically select the user set for ia so as to create a favorable interference profile for id at each receiver we first derive the average symbol error rate ser by taking into account of the non guassian residual interference due to discrete constellation using graph theory we then devise a low complexity user set selection algorithm for the piaid scheme which minimizes the asymptotically tight bound for the average end to end ser performance moreover we substantially simplify interference detection at the receiver using semi definite relaxation sdr techniques it is shown that the ser performance of the proposed piaid scheme has significant gain compared with various conventional baseline solutions

further studies in the variability of pock counts the problem of estimating viral activity from pock counts that exhibit a substantial degree of overdispersion is revisited from the viewpoint of quasilikelihood with unknown parameters in the variance function score statistics are developed for tests and interval estimates of both mean and variance parameters these yield somewhat different conclusions than do methods based exclusively on point estimates and standard errors especially for the variance parameters a monte carlo study confirms that in the absence of strong prior information about the shape of the error distribution inferences on variances are highly unstable in small to moderate samples

efficiency lost by analyzing counts rather than event times in poisson and overdispersed poisson regression models abstract inference for point processes is most efficient if the event times for each individual are available sometimes the study design is such that only aggregated data are collected consisting of the number of events or recurrences for each individual over the observation period this article discusses the loss in efficiency of an analysis of the aggregated counts versus an analysis of the actual event times one particular case is exemplified that in which the purpose of the experiment or trial is to compare the effects of treatments and the loss in efficiency in the estimator of the treatment effect is computed the specific point process considered here is the nonhomogeneous poisson process with a proportional intensity model for the treatment effects random effects models are also considered with estimation via a quasi likelihood approach the quasi likelihood analysis proposed here is an extension of such techniques for the homogeneous poisson process the resulting estimating equations for

on a semiparametric variance function model and a test for heteroscedasticity we propose a general semiparametric variance function model in a fixed design regression setting in this model the regression function is assumed to be smooth and is modelled nonparametrically whereas the relation between the variance and the mean regression function is assumed to follow a generalized linear model almost all variance function models that were considered in the literature emerge as special cases least squares type estimates for the parameters of this model and the simultaneous estimation of the unknown regression and variance functions by means of nonparametric kernel estimates are combined to infer the parametric and nonparametric components of the proposed model the asymptotic distribution of the parameter estimates is derived and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model this result is applied to obtain a data based test for heteroscedasticity under minimal assumptions on the shape of the regression function

variable selection and model averaging in semiparametric overdispersed generalized linear models we express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use bayesian variable selection to determine which predictors enter the model and whether they enter linearly or flexibly when the variance term is null we obtain a generalized additive model which becomes a generalized linear model if the predictors enter the mean linearly the model is estimated using markov chain monte carlo simulation and the methodology is illustrated using real and simulated data sets

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

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

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

on modelling metabolism based biomarkers of exposure a comparative analysis of nonlinear models with few repeated measurements establishing and characterizing exposure biomarker relationships is an important problem in molecular epidemiology the problem is difficult due to several complicating features namely the biomarker response is a nonlinear function of exposure and unknown parameters variation in exposure and biomarker levels occurs both within and between subjects and errors tend to be heteroscedastic to overcome some of the statistical challenges in analysing such data it is common for the investigator to make several assumptions about the data structure for example it is common to assume that the natural logarithm of right skewed biomarker measurements lead to homoscedasicity and normality so the effect of outliers is minimized and gauss markov theory is applicable in this paper we compare a lognormal maximum likelihood estimator mle to generalized estimating equations gee for drawing statistical inference in a nonlinear model of a benzene biomarker benzene oxide albumin adducts as a function of benzene exposure we explore the characteristic properties of the lognormal mle under a certain type of model misspecification and compare its small sample performance to the estimating equation approach in simulation studies we show that the multiplicative lognormal model can lead to severe biases for modest deviations from the true outcome biomarker distribution furthermore the lognormal mle can exhibit very poor small sample properties even under the true model all methods are applied in a novel data analysis from a study of benzene exposed workers in china

a generalized linear modeling approach to robust design this article presents an extension of the response surface approach to taguchi s parameter design by accommodating generalized linear modeling the approach of myers khuri and vining is taken as a starting point treating noise variables as fixed effects it is however assumed that process variability is caused not only by the presence of noise factors but also by residual variation therefore in addition to a model with a linear link function that relates the process mean to design and noise factors a second model with a log link function is proposed that relates the variance to a linear predictor in the design factors the conditional response model with noise factors taken as fixed is fitted by iteratively reweighted least squares unconditionally response surfaces for the process mean and process variance are produced through the use of a mean and variance operator on the conditional response model as an illustration data from an injection molding experiment are reanalyzed and residual disp

the effect of estimating weights in weighted least squares abstract in weighted least squares it is typical that the weights are unknown and must be estimated most packages provide standard errors assuming that the weights are known this is fine for sufficiently large sample sizes but what about for small to moderate sample sizes the investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice that one has a parametric model for the variance function in this context generalized least squares consists of a an initial estimate of the regression parameter b a method for estimating the variance function and c the number of iterations in reweighted least squares by means of expansions for the covariance it is shown that each of a c can matter in problems of small to moderate size a few conclusions may be of practical interest first estimated standard errors assuming that the weights are known can be too small in practice the investigation indicates that a simple bootstrap operation resul