radon nikodym derivatives of quantum instruments a convenient representation for radon nikodym derivatives of completely positive c p instruments on b h with respect to a scalar measure is suggested similar to the stinespring kraus representation for c p maps but involving possibly nonclosable unbounded operators the structure of covariant c p instruments is studied in detail in particular an exhaustive description is given to instruments covariant with respect to shifts or rotations corresponding to position or angle measurements

quantum probabilities for time extended alternatives we study the probability assignment for the outcomes of time extended measurements we construct the class operator that incorporates the information about a generic time smeared quantity these class operators are employed for the construction of positive operator valued measures for the time averaged quantities the scheme highlights the distinction between velocity and momentum in quantum theory propositions about velocity and momentum are represented by different class operators hence they define different probability measures we provide some examples we study the classical limit and we construct probabilities for generalized time extended phase space variables

bootstrapping a regression equation some empirical results abstract the bootstrap like the jackknife is a technique for estimating standard errors the idea is to use monte carlo simulation based on a nonparametric estimate of the underlying error distribution the main object of this article is to present the bootstrap in the context of an econometric equation describing the demand for energy by industry as it turns out the conventional asymptotic formulas for estimating standard errors are too optimistic by factors of nearly three when applied to a particular finite sample problem in a simpler context this finding can be given a mathematical proof

a new conjugate gradient method based on quasi newton equation for unconstrained optimization abstract the spectral conjugate gradient method is an effective method for large scale unconstrained optimization problems in this paper based on quasi newton direction and quasi newton equation a new spectral conjugate gradient method is proposed this method is motivated by the three term modified polak ribiyre polyak prp method and spectral parameters the global convergence of algorithm is proved for general functions under a strong wolfe line search numerical results show that the new algorithm is superior to the three term modified prp method

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

a decomposition method for large scale box constrained optimization a decomposition method for solving large scale box constrained optimization is proposed the algorithm is motivated by the successful use of the decomposition method presented by joachims for training support vector machines in particular a new technique based on the new definition kkt violating index is introduced for working set identification finally the numerical experiments and implementation details show that this method is practical for large scale problems

a globally convergent version of the polak ribiere conjugate gradient method in this paper we propose a new line search algorithm that ensures global convergence of the polak ribiere conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions in particular we show that with this line search every limit point produced by the polak ribiere iteration is a stationary point of the objective function moreover we define adaptive rules for the choice of the parameters in a way that the first stationary point along a search direction can be eventually accepted when the algorithm is converging to a minimum point with positive definite hessian matrix under strong convexity assumptions the known global convergence results can be reobtained as a special case from a computational point of view we may expect that an algorithm incorporating the step size acceptance rules proposed here will retain the same good features of the polak ribiere method while avoiding pathological situations

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

error in unsaturated stochastic models parameterized with field data 1 we use monte carlo error analysis to illustrate the impact of measurement errors in field estimated hydraulic properties on predictions made with 1d and 3d unconditional stochastic models of unsaturated flow and transport monte carlo simulations are conducted across a series of simplified artificial realities completely described by the gardner russo parametric model the mean values of properties are varied between simulations to elucidate the relationship between true properties and prediction errors hydraulic properties are reestimated by simulating tension infiltrometer measurements in the presence of small simple errors two types of observation error are considered along with one inversion model error resulting from poor contact between the instrument and the medium errors in the spatial statistics of hydraulic properties cause critical stochastic model assumptions to be violated limiting the usable parameter space for model predictions even where critical assumptions are valid stochastic model predictions show significant error and the magnitude and pattern of error changes with the true property means the flow conditions and the type of measurement error mean velocities may show errors up to an order of magnitude the velocity variance is overestimated by up to three orders of magnitude during 3d flow and eight orders of magnitude during 1d flow the 1d velocity integral scale is underestimated by as much as five orders of magnitude the estimates for 1d longitudinal macrodispersivity are surprisingly robust and show relatively small error across most of the parameter space

quantum stochastic processes as models for state vector reduction an elementary introduction of quantum state valued markovian stochastic processes qsp for n state quantum systems is given it is pointed out that a so called master constraint must be fulfilled for a given master equation a continuous and as a new alternative possibility a discontinuous qsp are derived both are discussed as possible models for state reduction during measurement

weighted least squares finite elements based on particle imaging velocimetry data the solution of the navier stokes equations requires that data about the solution is available along the boundary in some situations such as particle imaging velocimetry there is additional data available along a single plane within the domain and there is a desire to also incorporate this data into the approximate solution of the navier stokes equation the question that we seek to answer in this paper is whether two dimensional velocity data containing noise can be incorporated into a full three dimensional solution of the navier stokes equations in an appropriate and meaningful way for addressing this problem we examine the potential of least squares finite element methods lsfem because of their flexibility in the enforcement of various boundary conditions further by weighting the boundary conditions in a manner that properly reflects the accuracy with which the boundary values are known we develop the weighted lsfem the potential of weighted lsfem is explored for three different test problems the first uses randomly generated gaussian noise to create artificial experimental data in a controlled manner and the second and third use particle imaging velocimetry data in all test problems weighted lsfem produces accurate results even for cases where there is significant noise in the experimental data

a new conjugate gradient method with guaranteed descent and an efficient line search a new nonlinear conjugate gradient method and an associated implementation based on an inexact line search are proposed and analyzed with exact line search our method reduces to a nonlinear version of the hestenes stiefel conjugate gradient scheme for any inexact line search our scheme satisfies the descent condition bf g k sf t bf d k le frac 7 8 bf g k 2 moreover a global convergence result is established when the line search fulfills the wolfe conditions a new line search scheme is developed that is efficient and highly accurate efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer high accuracy is achieved by using a convergence criterion which we call the approximate wolfe conditions obtained by replacing the sufficient decrease criterion in the wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion numerical comparisons are given with both l bfgs and conjugate gradient methods using the unconstrained optimization problems in the cute library

time orthogonal unitary dilations and noncommutative feynman kac formulae an analysis of feynman kac formulae reveals that typically the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group of translations and reflections of the line we consider generalisations of the classical commutative formalism in which the probabilistic properties are described in terms of non commutative probability theory based on von neumann algebras examples of this type are generated by means of second quantisation from a unitary dilation of a given self adjoint contraction semigroup called the time orthogonal unitary dilation whose key feature is that the dilation operators corresponding to disjoint time intervals act nontrivially only in mutually orthogonal supplementary hilbert spaces

a spatial analysis of variance applied to soil water infiltration a spatial analysis of variance uses the spatial dependence among the observations to modify the usual inference procedures associated with a statistical linear model when spatial correlation is present the usual tests for presence of treatment effects may no longer be valid and erroneous conclusions may result from assuming that the usual f ratios are f distributed this is demonstrated using a spatial analysis of soil water infiltration data emphasis is placed on modeling the spatial dependence structure with geostatistical techniques and this spatial dependence structure is then used to test hypotheses about fixed effects using a nested linear model

stabilizing feedback controls for quantum systems no quantum measurement can give full information on the state of a quantum system hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory here we study the properties of controlled quantum filtering equations as classical stochastic differential equations we then develop methods using a combination of geometric control and classical probabilistic techniques for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator

signal to noise ratios performance criteria and transformations for the analysis of designed experiments taguchi uses performance criteria that he calls signal to noise sn ratios three such criteria are here denoted by sn t sn l and sn s the criterion sn t was to be used in preference to the standard deviation for the problem of achieving for some quality characteristic y the smallest mean squared error about an operating target value leon shoemaker and kacker 1987 showed how sn t was appropriate to solve this problem only when y was proportional to y on that assumption the same result could be obtained more simply by conducting the analysis in terms of log y rather than y a more general transformation approach is here introduced for other commonly met kinds of dependence between y and y including no dependence and a lambda plot is presented that uses the data to suggest an appropriate transformation the criteria sn l and sn s were for problems in which the objective was to make the response as large or as small as possible it is arg

parallel ssle algorithm for large scale constrained optimization in this paper a parallel ssle algorithm is proposed for solving large scale constrained optimization with block separable structure at each iteration the pvd sub problems are solved inexactly by the ssle algorithm which successfully overcomes the constraint inconsistency exited in most sqp type algorithm and decreases the computation amount as well without assuming the convexity of the constraints the algorithm is proved to be globally convergent to a kkt point of the original problem

second order expansion of mean squared error matrix of generalized least squares estimator with estimated parameters summary the second order expansion of the mean squared error matrix of the generalized least squares estimators for the regression parameters is obtained when the samples and the estimators for the structural parameters contained in the variance covariance matrix are independent in this paper we treat the second order expansion of the mean squared error matrix of the generalized least squares estimator fj in the statistical linear model y x u we consider the case where the variance covariance matrix v 00 of u is specified by finite parameters 00 and where a consistent estimator 0 of 00 is available which is independent of the observation y williams 1975 gave a sufficient condition concerning the order of the weak consistency of fj and commented on the asymptotic efficiency of fj but he did not obtain a result for the latter fuller rao 1978 dealt with the case where the observations fell into k groups with constant error variance for each group they obtained the asymptotic distribution of an estimator fj which used a weight matrix when the number of groups was infinite assuming the numbers of elements nij in the groups formed a fixed sequence our model corresponds to fixing k and letting ni increase

a continuous counting observation and posterior quantum dynamics a stochastic model for a continuous photon counting measurement is proposed an equation for the generating functional of the statistics of counts is found a stochastic linear equation for the unnormalised posterior state vector of atoms continuously collapsing without mixing is derived by using quantum stochastic calculus methods

the barzilai and borwein gradient method for the large scale unconstrained minimization problem the barzilai and borwein gradient method for the solution of large scale unconstrained minimization problems is considered this method requires few storage locations and very inexpensive computations furthermore it does not guarantee descent in the objective function and no line search is required recently the global convergence for the convex quadratic case has been established however for the nonquadratic case the method needs to be incorporated in a globalization scheme in this work a nonmonotone line search strategy that guarantees global convergence is combined with the barzilai and borwein method this strategy is based on the nonmonotone line search technique proposed by grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented these results indicate that the global barzilai and borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations

spatial analysis of hydraulic conductivity measured using disc infiltrometers spatial variability of surface hydraulic properties and the extrinsic e g traffic cropping etc and intrinsic e g soil type pore size distribution etc factors associated with these properties are important for infiltration and runoff processes in agricultural fields disc infiltrometers measured infiltration at 296 sites arranged on two parallel transects to examine and differentiate the factors contributing to spatial structure under different field conditions these measurements were made in the corn rows no track interrows and wheel track interrows of the field using four different soil water tensions 0 30 60 and 150 mm unsaturated hydraulic conductivity k and saturated hydraulic conductivity k were maximum in the corn rows and minimum in wheel track inter rows with no track interrows intermediate exponents cz parameters of k and k relationships k k exp av for corn rows and no track interrows were not significantly different from each other but were significantly different from q for the wheel track interrows a t p 0 01 level spatial variability o f k and k values showed some pseudoproportional effect in nugget variance for all three field conditions no track interrows clearly showed an inverse trend for semivariogram o f k with changing tension q values whereas differences were found for corn rows and wheel traffic interrows the spatial structure of y for all three field conditions were mostly white noise under corn rows in addition to random variation a small five row periodic variation at th e p 0 20 level matching the five row traffic configuration was discovered the spatial structure of a was influenced by soil type for the no track interrows spatial structure was absent in wheel track interrows indicating the destruction of pore structure due to compaction

sufficient reductions in regressions with elliptically contoured inverse predictors there are two general approaches based on inverse regression for estimating the linear sufficient reductions for the regression of y on x the moment based approach such as sir pir save and dr and the likelihood based approach such as principal fitted components pfc and likelihood acquired directions lad when the inverse predictors x y are normal by construction these methods extract information from the first two conditional moments of x y they can only estimate linear reductions and thus form the linear sufficient dimension reduction sdr methodology when var x y is constant e x y contains the reduction and it can be estimated using pfc when var x y is nonconstant pfc misses the information in the variance and second moment based methods save dr lad are used instead resulting in efficiency loss in the estimation of the mean based reduction in this article we prove that a if x y is elliptically contoured with parameters y and density gy there is no linear nontrivial suf

optimal probability weights for inference with constrained precision abstractprobability weights are used in many areas of research including complex survey designs missing data analysis and adjustment for confounding factors they are useful analytic tools but can lead to statistical inefficiencies when they contain outlying values this issue is frequently tackled by replacing large weights with smaller ones or by normalizing them through smoothing functions while these approaches are practical they are also prone to yield biased inferences this article introduces a method for obtaining optimal weights defined as those with smallest euclidean distance from target weights among all sets of weights that satisfy a constraint on the variance of the resulting weighted estimator the optimal weights yield minimum bias estimators among all estimators with specified precision the method is based on solving a constrained nonlinear optimization problem whose lagrange multipliers and objective function can help assess the trade off between bias and precision of the resulting

a model for an objective description of macroscopic state variables in quantum mechanics abstract a generalised stochastic process is obtained for the boltzmann distribution function in quantum mechanics this is an example of an objective state space description of a quantum system

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

properties and numerical performance of quasi newton methods with modified quasi newton equations quasi newton qn equation plays a core role in contemporary nonlinear optimization the usual qn equation employs only the gradients but ignores the available function value information in this paper we derive a class of modified qn equations with a vector parameter which use both available gradient and function value information the modified quasi newton methods maintain most properties of the usual quasi newton methods meanwhile they achieve a higher order accuracy in approximating the second order curvature of the problem functions than the usual ones do numerical experiments are reported which support the theoretical analyses and show the advantages of the modified qn methods over the usual ones

a note on covariate measurement error in nonlinear mixed effects models summary little is known about the effects of measurement error in intra individual covariates on inference for the nonlinear mixed effects model we investigate this issue for a controlled variable measurement error model and find that a major consequence may be substantial bias in estimates of parameters characterising intra individual variation estimation of population parameters may also be affected the dramatic effect of measurement error on estimation of intra individual variance parameters has implications not only in the repeated measurement context but also in individual nonlinear regression models

iterative weighted least squares estimation in heteroscedastic linear models this article addresses the problem of choosing weights for iterative weighted least squares estimation in heteroscedastic linear models an asymptotically optimal method for determining weights at each iteration is derived under a bayesian model for the variances the method uses a compromise between model based and model free variance estimates consider a heteroscedastic linear regression model in which responses are grouped so that the variance is constant within each group let denote the vector of regression parameters and let denote a vector of parameters determining a prior distribution for the variances iterative weighted least squares estimators are defined as follows given estimates and calculate a weight for the ith group as a function of the values in the ith group of the predictor variables and the average of the squared residuals from the estimated mean responses in the ith group given weights calculate the weighted least squares estimate and a new estimate continue until conv

quantum stochastic calculus operation valued stochastic processes and continual measurements in quantum mechanics the physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process ovsp in this article it is shown how the formalism of quantum stochastic calculus of hudson and parthasarathy allows in a simple way for constructing a large class of ovsp s that in particular contains the quantum counting processes of davies and srinivas and continual gaussian measurements this result is obtained by means of a stochastic dilation of the ovsp s at the level of the enlarged system probabilities turn out to be expressed in terms of projection valued measures associated with certain time dependent commuting self adjoint operators

optimal pointers for joint measurement of σx and σz via homodyne detection we study a model of a qubit in interaction with the electromagnetic field by means of homodyne detection the field quadrature at a t is observed continuously in time due to the interaction information about the initial state of the qubit is transferred to the field thus influencing the homodyne measurement results we construct random variables pointers on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of x and z using variational calculus we find the pointers that are optimal these optimal pointers are very close to hitting the bound imposed by heisenberg s uncertainty relation on joint measurement of two non commuting observables we close the paper by giving the probability densities of the pointers

parametric variance function estimation for nonnormal repeated measurement data zeger and liang 1986 biometrics 42 121 130 proposed a procedure for analyzing nonnormal longitudinal data in the context of the generalized linear model this procedure is extended to model variance heterogeneity allowing the observations to come from distributions with different scale parameters loss of efficiency is evaluated when heterogeneity of scale factor is ignored

mean and covariance structure analysis theoretical and practical improvements abstract the most widely used multivariate statistical models in the social and behavioral sciences involve linear structural relations among observed and latent variables in practice these variables are generally nonnormally distributed hence classical multivariate analysis based on multinomial error free variables having no simultaneous interrelations is not adequate to deal with such data a promising alternative based on asymptotically distribution free adf covariance structure analysis has been found to be virtually useless in practical model evaluation at finite sample sizes with nonnormal data we take a new look at the basic statistical theory of structural models under arbitrary distributions using the methodology of nonlinear regression and generalized least squares estimation for example we adopt the use of residual weight matrices from regression theory we develop a series of estimators and tests based on arbitrary distribution theory we obtain a type of probabilistic bartlett co

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

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

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

analysis strategies for serial multivariate ultrasonographic data that are incomplete ultrasonographic measurement of intima media thicknesses in the carotid artery has emerged as an important non invasive means of assessing atherosclerosis and has served to define primary outcome measures related to progression of arterial lesions in several large clinical trials and epidemiologic studies it is characteristic that measurements often cannot be obtained from all sites during repeated examinations this leads to incomplete multivariate serial data for which the set and number of visualized sites may vary across time we have contrasted several conditional and unconditional maximum likelihood analytical approaches and have evaluated these with a simulation experiment based on characteristics of ultrasound measurements collected during the course of the asymptomatic carotid artery plaque study we examined analyses based on unweighted and generalized least squares regression in which we estimated cross sectional summary statistics using raw means unconditional maximum likelihood estimates and full maximum likelihood estimates since the genesis of missing data is not fully clear and since the approaches we examined are based to some degree on the assumption that data are missing at random we also examined the relative impact of deviations from such an assumption on each of the approaches considered we found that maximum likelihood based approaches increased the expected efficiency of the analysis of serial ultrasound data over ignoring missing data by up to 21 per cent

efficient semiparametric marginal estimation for longitudinal clustered data we consider marginal generalized semiparametric partially linear models for clustered data lin and carroll derived the semiparametric efficient score function for this problem in the multivariate gaussian case but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound here we propose such an estimator and generalize the work to marginal generalized partially linear models we investigate asymptotic relative efficiencies of the estimators that ignore the within cluster correlation structure either in nonparametric curve estimation or throughout we evaluate the finite sample performance of these estimators through simulations and illustrate it using a longitudinal cd4 cell count dataset both theoretical and numerical results indicate that properly taking into account the within subject correlation among the responses can substantially improve efficiency

using function values in multi step quasi newton methods in previous work the authors 1993 1994 developed the concept of multi step quasi newton methods based on the use of interpolating polynomials determined by data from the m most recent steps different methods for parametrizing these polynomials were studied by the authors 1993 and several methods were shown empirically to yield substantial gains over the standard one step bfgs method for unconstrained optimization in this paper we will consider the issue of how to incorporate function value information within the framework of such multi step methods this is achieved in the case of two step methods through the use of a carefully chosen rational form to interpolate the three most recent iterates the results of numerical experiments on the new methods are reported

statistical analysis of diffusion tensors in diffusion weighted magnetic resonance imaging data diffusion tensor imaging has been widely used to reconstruct the structure and orientation of fibers in biological tissues particularly in the white matter of the brain because it can track the effective diffusion of water along those fibers the raw diffusion weighted images from which diffusion tensors are estimated however inherently contain noise noise in the images produces uncertainty in the estimation of the tensors which are 3 3 positive definite matrices and of their derived quantities including eigenvalues eigenvectors and the fiber pathways that are reconstructed based on those tensor elements the aim of this article is to provide a comprehensive theoretical framework of statistical inference for quantifying the effects of noise on diffusion tensors on their eigenvalues and eigenvectors and on their morphological classification we propose a semiparametric model to account for noise in diffusion weighted images we then develop a one step weighted least squares estimate of the t

asymptotically efficient estimation of a nonlinear model of the heteroscedasticity and the calibration of measurement systems the measurement system calibration includes the estimation of the sensor error models in order to get an optimal estimation of the measured parameters the paper is devoted to the estimation of a nonlinear parametric model of the heteroscedasticity and its application to the calibration of measurement systems the heteroscedasticity occurs in regression when the measurement noise variance is nonconstant the maximum likelihood ml estimation of variance function parameters leads to a system of nonlinear equations the iterative solution of these nonlinear equations is based entirely on a successful choice of initial conditions which is intractable in practice to overcome this difficulty another linear quasi ml estimator is proposed it is strongly consistent asymptotically gaussian and only slightly less efficient than the cramer rao lower bound by using this estimator as an initial condition an asymptotically efficient estimation is obtained by using one step noniterative newton method the theoretical findings have been applied to the calibration of the egnos gps positioning algorithm in the sub urban environments

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

a quantum analogue of hunt s representation theorem for the generator of convolution semigroups on lie groups in quantum mechanics certain operator valued measures are introduced called instruments which are an analogue of the probability measures of classical probability theory as in the classical case it is interesting to study convolution semigroups of instruments on groups and the associated semigroups of probability operators in this paper the case is considered of a finite dimensional hilbert space n level quantum system and of instruments defined on a finite dimensional lie group then the generator of a continuous semigroup of quantum probability operators is characterized in this way a quantum analogue of hunt s representation theorem for the generator of convolution semigroups on lie groups is obtained

the effect of variance function estimation on nonlinear calibration inference in immunoassay data summary often with data from immunoassays the concentration response relationship is nonlinear and intraassay response variance is heterogeneous estimation of the standard curve is usually based on a nonlinear heteroscedastic regression model for concentration response where variance is modeled as a function of mean response and additional variance parameters this paper discusses calibration inference for immunoassay data which exhibit this nonlinear heteroscedastic mean variance relationship an assessment of the effect of variance function estimation in three types of approximate large sample confidence intervals for unknown concentrations is given by theoretical and empirical investigation and application to two examples a major finding is that the accuracy of such calibration intervals depends critically on the nature of response variance and the quality with which variance parameters are estimated

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

estimation of boundary condition of two dimensional nonlinear pde with application to continuous casting abstract solidification heat transfer process of billet is described by nonlinear partial differential equation pde due to the poor productive environment the boundary condition of this nonlinear pde is difficult to be fixed therefore the identification of boundary condition of two dimensional nonlinear pde is considered this paper transforms the identification of boundary condition into a pde optimization problem the lipchitz continuous of the gradient of cost function is proved based on the dual equation in order to solve this optimization problem this paper presents a modified conjugate gradient algorithm and the global convergence of which is analyzed the results of the simulation experiment show that the modified conjugate gradient algorithm obviously reduces the iterative number and running time due to the ill posedness of the identification of boundary condition this paper combines regularization method with the modified conjugate gradient algorithm the simulation experiment illustrates that regularization method can eliminate the ill posedness of this problem finally the experimental data of a steel plant illustrate the validity of this paper s method

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

probability operators and convolution semigroups of instruments in quantum probability in quantum measurement theory a central notion is that of instrument which is a certain kind of operator valued measure in this paper instruments on locally compact groups are studied and as in classical probability theory probability operators associated with instruments are introduced then the generator of a norm continuous semigroup of probability operators is characterized

markovian limit for a reduced operation valued stochastic process operation valued stochastic processes give a formalization of the concept of continuous in time measurements in quantum mechanics in this article a first stage m of a measuring apparatus coupled to the system s is explicitly introduced and continuous measurement of some observables of m is considered one can speak of an indirect continuous measurement on s when the degrees of freedom of the measuring apparatus m are eliminated and the weak coupling limit is taken it is shown that an operation valued stochastic process describing a direct continuous observation of the system s is obtained

measurement scale network sampling scale and groundwater model parameters the scales at which model parameters are measured with local field tests distributed on a sampling network are examined two scales are defined to characterize the problem 1 the measurement scale associated with the resolution of a single field test and 2 the network scale associated with the separation between samples on a network using a spatial filtering approach it is shown that a network of measurements can only resolve a larger scale component of a parameter field the smaller scale component of the parameter field not seen by measurements here called the subgrid component can only vary on scales larger than the measurement scale and smaller than the network scale these unobserved subgrid scales give rise to the so called closure problem and consequent modeling errors when a significant proportion of the parameter variability is contained in the subgrid scales not only will the closure problem be significant but aliasing errors will also pollute the estimate of the large scale component of the parameter field these concepts are illustrated by performing simple analytical and numerical calculations

convergence of nonmonotone line search method in this paper we develop a new nonmonotone line search for general line search method and establish some global convergence theorems the new nonmonotone line search is a novel form of the nonmonotone armijo line search and allows one to choose a larger step size at each iteration which is available in constructing new line search methods and possibly reduces the function evaluations at each iteration moreover we analyze the convergence rate of some special line search methods with the new line search preliminary numerical results show that some line search methods with the new nonmonotone line search are available and efficient in practical computation

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

spatial bias in field estimated unsaturated hydraulic properties hydraulic property measurements often rely on non linear inversion models whose errors vary between samples in non linear physical measurement systems bias can be directly quantified and removed using calibration standards in hydrologic systems field calibration is often infeasible and bias must be quantified indirectly we use a monte carlo error analysis to indirectly quantify spatial bias in the saturated hydraulic conductivity k sub s and the exponential relative permeability parameter alpha estimated using a tension infiltrometer two types of observation error are considered along with one inversion model error resulting from poor contact between the instrument and the medium estimates of spatial statistics including the mean variance and variogram model parameters show significant bias across a parameter space representative of poorly to well sorted silty sand to very coarse sand when only observation errors are present spatial statistics for both parameters are best estimated in materials with high hydraulic conductivity like very coarse sand when simple contact errors are included the nature of the bias changes dramatically spatial statistics are poorly estimated even in highly conductive materials conditions that permit accurate estimation of the statistics for one of the parameters prevent accurate estimation for the other accurate regions for the two parameters do not overlap in parameter space false cross correlation between estimated parameters is created because estimates of k sub s also depend on estimates of alpha and both parameters are estimated from the same data

effective hydraulic parameters for steady state vertical flow in heterogeneous soils 1 in hydroclimate and land atmospheric interaction models effective hydraulic properties are needed at large grid scales in this study the effective soil hydraulic parameters of the areally heterogeneous soil formation are derived by conceptualizing the heterogeneous soil formation as an equivalent homogeneous medium and assuming that the equivalent homogeneous soil will approximately discharge the same total amount of flux and produce same average pressure head profile in the formation as compared to previous effective hydraulic property studies a specific feature of this study is that the derived effective hydraulic parameters are mean gradient dependent i e vary across depth although areal soil heterogeneity was formulated as parallel homogeneous stream tubes in this study our results appear to be consistent with the previous findings of mean gradient unsaturated hydraulic conductivity yeh et al 1985a 1985b three widely used hydraulic conductivity models were employed in this study i e the gardner model the brooks and corey model and the van genuchten model we examined the impact of parameter correlation boundary condition surface pressure head and elevation above the water table on the effective saturated hydraulic conductivity and shape parameter the correlation between the saturated hydraulic conductivity ks and the shape parameter increases the effective saturated hydraulic conductivity while it does not affect the effective the effective is usually smaller than the mean value of while the effective ks can be smaller or larger than the mean value depending on no correlation or full correlation between ks and fields respectively an important observation of this study is that gardner and van genuchten functions resulted in effective parameters whereas it is difficult to define effective parameters for the brooks corey model since this model uses a piecewise continuous profile for hydraulic conductivity

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

generalized stochastic processes and continual observations in quantum mechanics we give here a mathematically rigorous form to an earlier work by barchielli lanz and prosperi in which it was found that a generalized stochastic process describes the results of continual observations of the position of a quantum particle with the help of albeverio and ho egh krohn s theory of feynman path integrals we define the characteristic functional of this process and demonstrate that it possesses the necessary properties of normalization continuity and positive definiteness an explicit calculation of the feynman path integral which defines the functional allows an analysis of the process to be made

a new class of spectral conjugate gradient methods based on a modified secant equation for unconstrained optimization conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration convergence properties and their low memory requirements in this work we propose a new class of spectral conjugate gradient methods which ensures sufficient descent independent of the accuracy of the line search moreover an attractive property of our proposed methods is that they achieve a high order accuracy in approximating the second order curvature information of the objective function by utilizing the modified secant condition proposed by babaie kafaki et al s babaie kafaki r ghanbari n mahdavi amiri two new conjugate gradient methods based on modified secant equations journal of computational and applied mathematics 234 2010 1374 1386 further a global convergence result for general functions is established provided that the line search satisfies the wolfe conditions our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness

a new family of conjugate gradient methods in this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems a new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions in particular polak ribiere polyak and liu storey conjugate gradient methods are special cases of the new class of conjugate gradient methods by estimating the local lipschitz constant of the derivative of objective functions we can find an adequate step size and substantially decrease the function evaluations at each iteration numerical results show that these new conjugate gradient methods are effective in minimizing large scale non convex non quadratic functions