a simplified form of the bias eliminating least squares method for errors in variables identification this note considers the bias eliminating least squares bels method for identifying the errors in variables systems with white input noise and colored output noise a simplified form of the bels algorithm is proposed that is proved to be equivalent to the existing one some expositions of this simplified bels expression are also given the new relation is a form of linear iv equations which will not only reduce the computational load but also simplify the analysis of the properties of the bels estimates

high speed vlsi multiplication algorithm with a redundant binary addition tree a high speed vlsi multiplication algorithm internally using redundant binary representation is proposed in n bit binary integer multiplication n partial products are first generated and then added up pairwise by means of a binary tree of redundant binary adders since parallel addition of two n digit redundant binary numbers can be performed in a constant time independent of n without carry propagation n bit multiplication can be performed in a time proportional to log2 n the computation time is almost the same as that by a multiplier with a wallace tree in which three partial products will be converted into two in contrast to our two to one conversion and is much shorter than that by an array multiplier for longer operands the number of computation elements of an n bit multiplier based on the algorithm is proportional to n2 it is almost the same as those of conventional ones furthermore since the multiplier has a regular cellular array structure similar to an array multiplier it is suitable for vlsi implementation thus the multiplier is excellent in both computation speed and regularity in layout it can be implemented on a vlsi chip with an area proportional to n2 log2 n the algorithm can be directly applied to both unsigned and 2 s complement binary integer multiplication

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

a bias correction method for indirect identification of closed loop systems a novel least squares like method is developed to deal with the bias problem in indirect identification of closed loop systems with coloured disturbances it is shown that combined with a bias correction procedure this method can give rise to consistent parameter estimates by fully and efficiently using the given information about the regulator simulation results are also included for illustration

some optimal designs for repeated measurements with autoregressive errors summary a number of individuals are observed at equally spaced time points different individuals behave independently but the observations on the same individual have the autocorrelation structure of a first order autoregressive process we are concerned with the optimal allocation of treatments assuming that at each time point a new selection must be made conditions for optimality are given for models without nuisance parameters and also with covariates and with block effects

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

logistic regression for dependent binary observations summary the likelihood of a set of binary dependent outcomes with or without explanatory variables is expressed as a product of conditional probabilities each of which is assumed to be logistic the models are called regressive logistic models they provide a simple but relatively unknown parametrization of the multivariate distribution they have the theoretical and practical advantage that they can be analyzed and fitted as in logistic regression for independent outcomes and with the same computer programs the paper is largely expository and is intended to motivate the development and usage of the regressive logistic models the discussion includes serially dependent outcomes equally predictive outcomes more specialized patterns of dependence multidimensional tables and three examples this paper seeks to promote the development and usage of a simple but relatively unknown approach to the specification of models for dependent binary outcomes that are useful in situations where it is apt to describe the dependence in terms of conditional probabilities the joint probability is decomposed into a product of successive conditional probabilities each of which is assumed to be univariate logistic since the probability of an observation is conditioned on all preceding observations the models will be referred to as regressive logistic models two broad situations are distinguished in this paper the first concerning sequences of binary outcomes possibly with measures on associated explanatory variables can usually be supported by simple patterns of dependence these will be discussed in sections 2 5 the second broad situation concerns dependent binary outcomes crossclassified into multidimensional tables that admit a fuller parametrization this is discussed in section 6 for all the regressive logistic models discussed here the parametrization is such that jointly dependent binary observations with or without explanatory variables can be fitted with existing computer programs for the standard logistic regression for independent observations some of the possibilities of the approach are illustrated with real data in section 8

distribution theory of runs a markov chain approach abstract the statistics of the number of success runs in a sequence of bernoulli trials have been used in many statistical areas for almost a century even in the simplest case of independent and identically distributed bernoulli trials the exact distributions of many run statistics still remain unknown departing from the traditional combinatorial approach in this article we present a simple unified approach for the distribution theory of runs based on a finite markov chain imbedding technique our results cover not only the identical bernoulli trials but also the nonidentical bernoulli trials as a byproduct our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run

analysis of repeated measures designs with changing covariates in clinical trials summary a multivariate model is proposed for analysing repeated measures designs with chang ing or within subject covariates under the assumption of multivariate normality the likelihood ratio tests are derived for testing certain linear hypotheses some special designs are discussed and a numerical example is given to illustrate the method for analysing a two period crossover design during a long term clinical trial environmental factors can affect a disease condition in different ways air pollution is likely to influence the frequency of asthma attacks in patients with chronic bronchial asthma the effectiveness of a therapeutic drug in the treatment of atherosclerosis is probably influenced by factors such as diet exercise and smoking response measurements obtained periodically during a trial are affected jointly by the treatment being received and by certain environmental factors if the influencing factors are quantified over the periods between successive clinic visits a repeated measures model can be constructed to accommodate such information in a between patient i e parallel group design each patient receives the assigned treatment throughout the trial in a within patient design each patient receives some or all of the treatments in an assigned order crossover and incomplete block designs are examples of a within patient design a fixed or between patient covariate remains unchanged during the trial a changing or within patient covariate varies from one visit to the next for the same patient the covariates associated with environmental factors fall into this category in a within patient design the baseline obtained just before the start of each treatment period also falls into this category a similar situation occurs in a between patient design when the responses at successive visits are evaluated relative to the corresponding baseline performances for example in a parallel group study designed to evaluate once a day short acting therapies in the treatment of chronic stable angina treadmill walking time is recorded just before the administration of a dose and then at some post dose time at each clinic visit the effectiveness of the visit doses is evaluated relative to the corresponding baseline walking times however there must be a strong evidence prior to study initiation that the baseline values are independent of the assigned treatments whenever baseline is to be used as a changing covariate the situations described above are special cases of the multiple design multivariate linear model studied by roy srivastava 1963 and srivastava 1967 this model in

instrumental variable methods for closed loop system identification in this paper several instrumental variable iv and instrumental variable related methods for closed loop system identification are considered and set in an extended iv framework extended iv methods require the appropriate choice of particular design variables as the number and type of instrumental signals data prefiltering and the choice of an appropriate norm of the extended iv criterion the optimal iv estimator achieves minimum variance but requires the exact knowledge of the noise model for the closed loop situation several iv methods are put in an extended iv framework and characterized by different choices of design variables their variance properties are considered and illustrated with a simulation example

identification of closed loop systems with low order controllers a bias correction method without noise modelling was recently proposed for indirect identification of closed loop systems a key assumption used in deriving this method required that the order of the controller is not less than that of the open loop plant a significant feature of the results presented in this paper is the removal of this assumption to enable the method to be applicable to unbiased identification of closed loop systems with low order controllers

on runlength codes several results on binary d k codes are given first a novel derivation for the capacity of these codes based on information theoretic principles is given based on this result the spectrum of a d k code is computed finally the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the d k constraint is considered lower bounds on the capacity of such a channel are derived

an output error recursive algorithm for unbiased identification in closed loop the problem of unbiased recursive identification of a plant model in closed loop operation is considered a particular form of an output error predictor for the closed loop is introduced this allows one to derive a parameter estimation algorithm for the plant model that is globally asymptotically stable and asymptotically unbiased in the presence of noise the paper presents a stability analysis in a deterministic environment and a convergence analysis in the stochastic environment both require a mild sufficient passivity condition to be satisfied simulations and real time experiments on a flexible transmission illustrate the performances of the proposed algorithm

nonlinear component of variance models summary general aspects of nonlinearity in the context of component of variance models are discussed and two special topics are examined in detail firstly simple procedures both formal and informal are proposed for describing departures from normal theory linear models transformation models are shown to be a special case of a more general formulation and data on blood pressure are analyzed in illustration secondly an approximate likelihood is proposed and its accurate performance is examined numerically using examples of exponential regression and the analysis of several related 2 x 2 tables in the latter example the approximate score test has improved power over the mantelhaenszel test

estimation and hypothesis testing for collections of autoregressive time series summary the analysis of a number of independent first order autoregressive time series is considered in a normal theory context a model is studied which allows for nonstationary and nonidentical distribution of the series caused by both fixed effect and random effect components

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

comments on on a least squares based algorithm for identification of stochastic linear systems the bias eliminated least squares estimator proposed in the paper by zheng see ibid vol 46 p 1631 8 1998 is shown to be identical to a simple instrumental variable estimator using delayed input values as instruments

worst case identification of errors in variables models in closed loop a worst case identification method in frequency domain is proposed to cope with the identification of errors in variables models eivms in closed loop with a priori bound for the disturbing noises of an eivm in closed loop a frequency domain normalized coprime factor model ncfm with perturbation is derived and thus the identification of the eivm becomes that of the ncfm by employing the v gap metric as an optimization criterion the worst case error for an identified nominal ncfm is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities lmis during the parameter optimization the derivative of the nominal ncfm is constrained to some degree to reduce the effect of overfitting phenomenon different from other eivm identification methods we use v gap metric to characterize the disturbing noises and quantify the worst case error for the nominal ncfm as a result the identification result is not a deterministic model but a model set moreover this model set can be perfectly combined with the robust controller design finally a numerical simulation is presented to verify the proposed method

orthogonality and transformations in variance components models summary we consider variance components and other models for repeated measures in which a general transformation is applied to the response variable using cox reid s 1987 concept of parameter orthogonality and some approximations to the information matrix we show that the intraclass correlation coefficient in the one way model is robust to the choice of transformation this robustness result generalises to a vector of parameters determining the correlation structure to more complex variance components models to multivariate normal models to some longitudinal models and models involving linear regression functions for which we show that ratios of regression parameters are robustly estimated the results suggest that a natural way to parameterise the covariance structure in repeated measures models may be in terms of the variance and the correlation determined by separate sets of parameters

bayesian and frequentist predictive inference for the patterns of care studies abstract the patterns of care studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy in this article we propose and evaluate models which if acceptable permit bayesian and frequentist model based predictive inference for the desired finite population parameters using both hierarchical bayesian and frequentist mixed linear models we describe methodology for making the desired inferences emphasizing the use of transformed random variables finally we compare the frequentist bayes and empirical bayes approaches using data from one of the surveys all three methods produce essentially the same value for the finite population mean the standard empirical bayes and frequentist measures of variability are very much smaller than those derived from the bayesian approach the latter reflecting uncertainty about the values of the scale parameters in the model

transformations for components of variance and covariance summary variance component models make various independence assumptions and typically assume effects are normally distributed here we assume that the data possibly after suitable transformation satisfy such a model an analysis of transformations for balanced variance component models is presented components of covariance being incorporated in the multivariate case an analysis of some blood pressure data is discussed transformations of data are often applied in the analysis of variance of linear models with fixed effects little or no investigation has been done on transformations for component of variance models the formal analysis for finding a transformation which maximizes the log likelihood for fixed effects models box cox 1964 requires modification for components of variance models in 2 we consider the simplest nontrivial case namely the balanced one way classification we note extensions to more complex univariate balanced models in 3 we deal only with cases where all the variance components are appreciable and the possibility that the maximum likelihood estimates occur on the boundary of the parameter space can be disregarded we examine in 4 an analysis of transformations for the multivariate balanced one way classification components of covariance thus being incorporated in the model in 5 we describe an analysis of some bivariate blood pressure data components of covariance are an important contribution to the analysis

a bias correction method for closed loop identification of linear parameter varying systems abstract due to safety constraints and unstable open loop dynamics system identification of many real world processes often requiresgathering data from closed loop experiments in this paper we present a bias correction scheme for closed loop identification of linear parameter varying input output lpv io models which aims at correcting the bias caused by the correlation between the input signal exciting the process and output noise the proposed identification algorithm provides a consistent estimate of the open loop model parameters when both the output signal and the scheduling variable are corrupted by measurement noise the effectiveness of the proposed methodology is tested in two simulation case studies

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above

on a least squares based algorithm for identification of stochastic linear systems a new form of bias eliminated least squares bels algorithm is developed to identify transfer function parameters of a linear time invariant system irrespective of noise dynamics unlike the bels estimator previously presented the main feature with the developed algorithm is that the transfer function parameters are consistently estimated in such a direct way that there is no need to prefilter observed data or to deal with a high order augmented system this greatly simplifies implementation of the bels based algorithms and reduces numerical efforts whereas a desirable estimation accuracy can still be achieved two simulation examples are presented that clearly illustrate the good performances of the developed algorithm including its superiority over one type of simple instrumental variable method

on the mean and extreme distances between failures in markovian binary sequences this paper is concerned with the mean minimum and maximum distances between two successive failures in a binary sequence consisting of markov dependent elements these random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented

brief on the relation between a bias eliminated least squares bels and an iv estimator in closed loop identification a bias correction method for closed loop identification introduced in the literature as the bias eliminated least squares bels method zheng feng automatica 31 1995 1019 is shown to be equivalent to a basic instrumental variable estimator applied to a predictor for the closed loop system this predictor is a function of the plant parameters and the known controller corresponding to the related method using a least squares criterion the method is referred to as the tailor made iv method for closed loop identification the indicated equivalence greatly facilitates the understanding and the analysis of the bels method

indirect closed loop identification by optimal instrumental variable method recently a new bias compensating least squares bcls method was proposed for the identification of a closed loop system with high order controller the major feature of this method is that it can achieve consistent parameter estimation without modelling the coloured noises acting on the system this paper studies the connection between the bcls method and the instrumental variable iv family it is shown that the bcls method is a kind of weighted instrumental variable wiv method whose results do not depend upon the order of the controller

genotype by environment variance heterogeneity in a two stage analysis the analysis of a series of crop variety trials often proceeds using a mixed model in which the data are the combined means from individual trials the residual variation for this model consists of genotype by environment g e interactions and within trial error variation the latter is regarded as known from the analyses of individual trials and any associated heterogeneity can be accounted for in the overall mixed model by the use of weights the g e interactions may also have nonconstant variance and since the variances themselves are often of interest we propose that heterogeneity arising from these sources be accommodated by modelling the g e variances as a log linear function of explanatory variables we present a residual maximum likelihood estimation method and develop a diagnostic technique for detecting dependence the approach is demonstrated using a large unbalanced set of crop variety testing data the methodology is easily generalized to residual variance modelling in any mixed model application