regulatory assessment of drug dissolution profiles comparability via maximum deviation in drug development comparability of dissolution profiles of 2 different formulations is usually assessed using the similarity factor f2 in practice the drug dissolution profiles are deemed similar if the f2 exceeds 50 which occurs when a 10 maximum difference in the mean percentage of the dissolved drug at each time point between test and reference formulation is obtained according to the guideline on the investigation of bioequivalence cpmp ewp qwp 1401 98 rev 1 corr use of the f2 is however restricted by a set of validity conditions if some of these conditions are not satisfied the f2 is not considered suitable and alternative statistical methods are needed in this article we propose an inferential framework based on the maximum deviation between curves to test the comparability of drug dissolution profiles the new methodology is applicable regardless whether the validity criteria of the f2 are met or not contrary to the f2 this approach also integrates the variability of the measurements over time and not only their average to benchmark our method we performed simulations informed by 3 real case studies provided by the european medicines agency and extracted from dossiers submitted to the centralised procedure for marketing authorisation application in the scenarios of the simulation study the new method controlled its type i error rate when the maximum deviation was greater than the similarity acceptance limit of 10 the power exceeded 80 for small values of the maximum deviation while the test was more conservative for intermediate ones our results were also very robust to sampling variations based on these positive findings we encourage applicants to consider the new maximum deviation based method as a valid alternative to the f2 especially when the validity criteria of the latter are not met

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

on residual generation by observer and parity space approaches a unifying framework for observer design by eigenstructure assignment is described a new technique for structured residual generation based on this framework is proposed one of the main features of this technique is that the equivalence between residual generation by means of observers or parity space devices are made conspicuous more precisely from a computational point of view the equations to solve in both cases are shown to be similar and for implementation both devices are shown to be identical a necessary and sufficient condition for the existence of structured residuals is given finally the sensitivity of structured residuals to nondecoupled failures is studied and a procedure for maximizing this sensitivity is described

random calibration with many measurements an application of stein estimation in the problem considered a vector of many imprecise measurements e g spectroscopic is used to linearly predict a quantity whose precise measurement is difficult or expensive the regression vector is estimated from a calibration experiment having both types of measurements for a random sample most previous approaches to this problem adjust for approximate multicollinearity which often results from the correlations among the imprecise measurements by inverting an approximation e g factor analytic to their covariance matrix in the approach here it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix it is then estimated by applying a stein contraction of the least squares estimator to the principal components regression estimator examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation

brief a minimal polynomial basis solution to residual generation for fault diagnosis in linear systems a fundamental part of a fault diagnosis system is the residual generator here a new method the minimal polynomial basis approach for design of residual generators for linear systems is presented the residual generation problem is transformed into a problem of finding polynomial bases for null spaces of polynomial matrices this is a standard problem in established linear systems theory which means that numerically efficient computational tools are generally available it is shown that the minimal polynomial basis approach can find all possible residual generators and explicitly those of minimal order

a universal chow willsky scheme and detectability criteria an important issue in diagnosis research is design methods for residual generation one method is the chow willsky scheme here the chow willsky scheme is extended as it becomes universal in the sense that for both discrete and continuous linear systems it is shown to be able to generate all possible parity functions this result means it can also be used to design all possible residual generators it is shown that previous extensions to the chow willsky scheme are not universal which is the case when dynamics controllable from faults exist but not from the inputs or disturbances also included here are two conditions on the process for fault detectability and strong fault detectability

equivalence of regression curves sharing common parameters in clinical trials the comparison of two different populations is a common problem nonlinear parametric regression models are commonly used to describe the relationship between covariates such as concentration or dose and a response variable in the two groups in some situations it is reasonable to assume some model parameters to be the same for instance the placebo effect or the maximum treatment effect in this paper we develop a parametric bootstrap test to establish the similarity of two regression curves sharing some common parameters we show by theoretical arguments and by means of a simulation study that the new test controls its significance level and achieves a reasonable power moreover it is demonstrated that under the assumption of common parameters a considerably more powerful test can be constructed compared with the test that does not use this assumption finally we illustrate the potential applications of the new methodology by a clinical trial example

generalized g convergence for quasilinear elliptic differential operators generalized g convergence for a quasilinear elliptic differential equation is defined and studied the equation describes heat conduction in the cores of large electric transformers the coefficients of the equation depend on temperature and the corresponding differential operator is neither potential nor monotone a theory which generalizes the classical g convergence is proposed the theory is applied to the homogenization of the quasilinear elliptic differential equation with periodic coefficients

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

equivalence of regression curves this article investigates the problem whether the difference between two parametric models m1 m2 describing the relation between a response variable and several covariates in two different groups

detection filter design spectral theory and algorithms a new formulation of the detection filter problem is generated by assignment of the closed loop eigenstructure under certain constraints detection filters which are actually a specific class of observers fix the output error direction of the system so that it can be associated with a particular failure mode and its known design failure direction the derivation of detection filters from an eigensystem assignment approach permits a very transparent theory the detection filter gains and closed loop eigenvectors are obtained from a set of simultaneous equations necessary and sufficient conditions for the solution of these algebraic equations are determined which produce a complete theory for detection filters

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

range image segmentation using surface selection criterion in this paper we address the problem of recovering the true underlying model of a surface while performing the segmentation first and in order to solve the model selection problem we introduce a novel criterion which is based on minimising strain energy of fitted surfaces we then evaluate its performance and compare it with many other existing model selection techniques using this criterion we then present a robust range data segmentation algorithm capable of segmenting complex objects with planar and curved surfaces the presented algorithm simultaneously identifies the type order and geometric shape of each surface and separates all the points that are part of that surface this paper includes the segmentation results of a large collection of range images obtained from objects with planar and curved surfaces the resulting segmentation algorithm successfully segments various possible types of curved objects more importantly the new technique is capable of detecting the association between separated parts of a surface which has the same cartesian equation while segmenting a scene this aspect is very useful in some industrial applications of range data analysis

analytical redundancy relations for fault detection and isolation in algebraic dynamic systems this paper extends the analytical redundancy techniques well developed for linear systems to fdi in non linear dynamic systems modeled by polynomial differential algebraic equations the residual evaluation form is developed for sensor actuator and process component faults fault detectability and isolability conditions are given and the design of robust structured residuals is addressed

brief paper robust fault detection based on observers for bilinear systems the design of a residual generator for robust fault detection in bilinear systems is considered two methods are presented the first one is based on a linear time invariant observer up to output injection while the second one relies on a so called kalman like observer it is shown via examples that the approach based on a kalman like observer allows one to handle a larger class of bilinear systems than the other observer based methods presented in the literature

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

on continuous time parameter identification by using observers this paper describes a continuous time parameter estimation technique this technique consists of designing two observers and comparing the observation bias due to parameter uncertainties the comparison of both biases is used to estimate the parameter values it comes out that under some conditions the system of equations to solve reduces to a division of output signals of the observers optimization of the design to reject disturbances is also discussed

fault detection and isolation by a continuous parity space method the well known parity space method for fault detection and isolation is generalized to a continuous time case as in the discrete time case it is shown that the parity space equations can be implemented using a number of time delays and are equivalent to a continuous deadbeat observer algorithms for isolation of sensor and actuator faults are derived and illustrated by a numerical example

reliable solution of a quasilinear nonpotential elliptic problem of a nonmonotone type with respect to the uncertainty in coefficients abstract a quasilinear elliptic equation with mixed nonlinear boundary conditions is considered where the admissible coefficients are given in a certain interval we are looking for maximal values of the solution with respect to the set of admissible coefficients the existence of a maximal solution is proven both in the continuous and in a discretized formulation some convergence analysis is also presented

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

optimally robust redundancy relations for failure detection in uncertain systems all failure detection methods are based either explicitly or implicitly on the use of redundancy i e on possibly dynamic relations among the measured variables the robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations which in turn is affected by the inevitable presence of model uncertainties in this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection a procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations ordered in terms of their level of robustness this procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors

piecewise polynomial estimation of a regression function we deal with the problem of choosing a piecewise polynomial estimator of a regression function s mapping 0 1 p into r in a first part of this paper we consider some collection of piecewise polynomial models each model is defined by a partition m of 0 1 p and a series of degrees d d j j m nm we propose a penalized least squares criterion which selects a model whose associated piecewise polynomial estimator performs approximately as well as the best one in the sense that its quadratic risk is close to the infimum of the risks the risk bound we provide is nonasymptotic in a second part we apply this result to tree structured collections of partitions which look like the one constructed in the first step of the cart algorithm and we propose an extension of the cart algorithm to build a piecewise polynomial estimator of a regression function

why bandwidth selectors tend to choose smaller bandwidths and a remedy summary this note is concerned with the problem of automatic data driven bandwidth selectors for nonparametric regression though some selectors were shown to be consistent and asymptotically unbiased by rice 1984 and hardle hall marron 1988 it is often observed in simulation studies that most selectors are biased toward undersmoothing an explanation for this is given the source of the large sample variation in the bandwidth estimates is also pointed out this leads to the consideration of a new procedure which is a simple modification of a classical selector a simulation study suggests that the proposed selector is much more consistent than the classical one

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

a new structural framework for parity equation based failure detection and isolation abstract the paper describes a new framework for developing parity equations that prevent incorrect isolation decisions under marginal size failures in a decision process that tests each residual independently test thresholds that take the noise conditions into account are set high to reduce the occurrence of false alarms while maintaining the algorithm s ability to detect and isolate larger failures the method is applicable to additive failures on the measured input and output variables and to additive plant disturbances a transformation algorithm provides a multitude of models that satisfy the isolability requirements a search procedure utilizing this model redundancy integrates model robustness considerations into the design

on galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type abstract we prove the convergence of galerkin approximations for a second order quasilinear elliptic problem of a divergence form with nonlinear mixed boundary conditions the existence and uniqueness of a weak and approximate solution is studied as well

bandwidth selection for indirect density estimation based on corrupted histogram data abstract motivated by a number of practical applications we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts due to variability in the process of correction the histogram cannot be modeled in terms of simple scaled poisson statistics this departure necessitates the development of a new methodology for bandwidth selection a variant of the method of unbiased risk estimation is proposed the methodology is studied using numerical simulations and asymptotic analysis tools in the context of a class of idealized density deconvolution problems the methodology is adapted for application to the practical reconstruction problem of positron emission tomography pet realistic numerical simulations and physical phantom data are presented to validate the approach in this setting some illustrations with cerebral glucose utilization and myocardial blood flow studies from some actual patient data sets

nonparametric variable selection the earth algorithm we consider regression experiments involving a response variable y and a large number of predictor variables x1 xd many of which may be irrelevant for the prediction of y and thus must be removed before y can be predicted from the x s we consider two procedures that select variables by using importance scores that measure the strength of the relationship between predictor variables and a response and keep those variables whose importance scores exceed a threshold in the first of these procedures scores are obtained by randomly drawing subregions tubes of the predictor space that constrain all but one predictor and in each subregion computing a signal to noise ratio efficacy based on a nonparametric univariate regression of y on the unconstrained variable the subregions are adapted to boost weak variables iteratively by searching hunting for the subregions in which the efficacy is maximized the efficacy can be viewed as an approximation to a one to one function of the probability of identif

information criteria for residual generation and fault detection and isolation using an information point of view we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation fdi in linear time invariant lti state space systems in both types of approaches to off line fdi residual generation can be viewed as the design of a linear transformation of a gaussian vector the finite window input adjusted observations several statistical isolation methods are revisited using both a linear transform formulation and the information content of the corresponding residuals we formally state several multiple fault cases with or without causality assumptions and discuss an optimality criterion for the most general one new information criteria are proposed for investigating the residual optimization problem

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

criterions for detectability and strong detectability of faults in linear systems a fault is strongly detectable if it is possible to construct a residual generator that is sensitive to the constant fault while decoupling all disturbances existing fault detectability criterions are reviewed and in two cases improved versions are derived for strong fault detectability three new criterions are presented to prove all criterions a framework of polynomial bases is utilized with these new and improved criterions there exists now a criterion for models given both on transfer function form and state space form and for both fault detectability and strong fault detectability investigations recommendations are given on what criterion to use in different situations

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

comparison of drug dissolution profiles a proposal based on tolerance limits meaningful comparison of the dissolution profiles between the reference and test formulations of a drug is critical for assessing similarity between the two formulations and for quality control purposes such a dissolution profile comparison is required by regulatory authorities and the criteria used for this include the widely used difference factor f1 and a similarity factor f2 recommended by the food and drug administration in spite of their extensive use in practice the two factors have been heavily criticized on various grounds the criticisms include ignoring sampling variability and ignoring the correlations across time points while using the criteria in practice the goal of this article is to put f1 and f2 on a firm statistical footing by developing tolerance limits for the distributions of f1 and f2 so that both the sampling variability and the correlations over time points are taken into account because f1 and f2 are defined in terms of sample mean dissolution profiles they are not appropriate for comparing individual dissolution profiles for the latter we have considered similar criteria and have derived tolerance limits both parametric and nonparametric approaches are explored and a bootstrap calibration is used to improve accuracy of the tolerance limits simulated coverage probabilities show that the method leads to accurate tolerance limits two examples are used to illustrate the methodology copyright 2016 john wiley sons ltd

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature