wavelet like bases for the fast solutions of second kind integral equations a class of vector space bases is introduced for the sparse representation of discretizations of integral operators an operator with a smooth nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix to high precision a method is presented that employs these bases for the numerical solution of second kind integral equations in time bounded by o n log 2 n where n is the number of points in the discretization numerical results are given which demonstrate the effectiveness of the approach and several generalizations and applications of the method are discussed

simplified estimation of age specific reference intervals for skewed data age specific reference intervals are commonly used in medical screening and clinical practice where interest lies in the detection of extreme values many different statistical approaches have been published on this topic the advantages of a parametric method are that they necessarily produce smooth centile curves the entire density is estimated and an explicit formula is available for the centiles the method proposed here is a simplified version of a recent approach proposed by royston and wright basic transformations of the data and multiple regression techniques are combined to model the mean standard deviation and skewness using these simple tools which are implemented in almost all statistical computer packages age specific reference intervals may be obtained the scope of the method is illustrated by fitting models to several real data sets and assessing each model using goodness of fit techniques

barycentric interpolation collocation methods for solving linear and nonlinear high dimensional fredholm integral equations abstract in this article two barycentric interpolation collocation methods are proposed for solving linear and nonlinear high dimensional f r e d h o l m integral equations of the second kind the approaches respectively utilize the modified weighted l a g r a n g e functions and the novel rational functions as the interpolation basis functions they are effective schemes for evaluating the multidimensional undetermined function through the numerical strategies and some composite quadrature formulas the linear and nonlinear f r e d h o l m integral equations are transformed into the corresponding linear and nonlinear algebraic equations further we prove that the discrete collocation methods are equivalent to the n y s t r o m quadrature methods then the convergence analysis is established by the collectively compact theory moreover the error estimation of the approximate solution and the exact solution are also provided numerical examples are presented to illustrate the capability and efficiency of the techniques by compared with the classic l a g r a n g e interpolation collocation method and other methodologies

sampling design for gaussian detection problems we propose an approach for the design of sampling schemes for gaussian hypothesis testing problems our approach for this design is based on the class of ali silvey see j royal stat soc series b vol 28 p 131 43 1996 distance measures closed forms for the bhattacharyya distance the i divergence the j divergence and the chernoff distance between the class conditional densities are obtained for the sampling design problem in the strong signal case a new member of the class of ali silvey distance measures that is suitable for the detection problem in the weak signal case is also derived sampling schemes are determined to maximize those four distance measures as well as the new distance measure for the strong signal case and the weak signal case respectively the detection performance of our sampling schemes is compared with those of various other sampling schemes by means of numerical examples comparisons show that the sampling design based on ali silvey distance measures result in superior performance

construction of age related reference centiles using absolute residuals this paper proposes a simple approach to the parametric derivation of age related reference ranges which avoids the creation of arbitrary age groups copes easily with a non linear relation between variability and age and is computationally simple after the mean is modelled as a function of age the age specific standard deviation is estimated by regressing the absolute residuals on age the method assumes that the data are or can be transformed to be normal at each age and uses the properties of the half normal distribution an example is given using 450 measurements of fetal foot length

extrapolation of nystrom solution for two dimensional nonlinear fredholm integral equations abstract in this paper we analyze the existence of asymptotic error expansion of the nystrom solution for two dimensional nonlinear fredholm integral equations of the second kind we show that the nystrom solution admits an error expansion in powers of the step size h and the step size k for a special choice of the numerical quadrature the leading terms in the error expansion for the nystrom solution contain only even powers of h and k beginning with terms h2p and k2q these expansions are useful for the application of richardson extrapolation and for obtaining sharper error bounds numerical examples show that how richardson extrapolation gives a remarkable increase of precision in addition to faster convergence

solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method in this paper we will give some results for developing the two dimensional differential transform tddt for double integrals then the tddt method will be developed for solving a class of two dimensional linear and nonlinear volterra integral equations we also give some examples to demonstrate the accuracy of the method

improved results on transmission power control for remote state estimation we consider a sensor transmission power control problem for remote state estimation in this problem a sensor sends its local estimate to a remote estimator over a wireless packet dropping communication channel the transmission power is determined by a recently proposed algorithm which uses the innovative information contained in the measurement in the current paper we focus on parameter optimization arising from the selection of design parameters for this power controller the existing work obtained a suboptimal solution to the parameter optimization problem while by using a vector rearrangement inequality argument and the vector majorization we now show that there exists an optimal solution within a subset of the whole feasible set by leveraging this property we obtain an optimal solution via solving a convex optimization problem

scheduling two gauss markov systems an optimal solution for remote state estimation under bandwidth constraint we consider scheduling two gauss markov systems two sensors each measuring the state of one of the two systems compute and report their local state estimates to a central remote estimator respectively due to the bandwidth constraint at each time only one of the sensors is allowed to communicate its estimate with the remote estimator upon receiving the data from the sensors the remote estimator computes the minimum mean squared error estimate of each system s state we provide an explicit construction of an optimal schedule which is periodic hence allows simple and efficient practical implementation and minimizes the sum of the average estimation error covariance of each system

hybrid function method and convergence analysis for two dimensional nonlinear integral equations in the current paper an efficient numerical method based on two dimensional hybrid of block pulse functions and legendre polynomials is developed to approximate the solutions of two dimensional nonlinear fredholm volterra and volterrafredholm integral equations of the second kind the main idea of the presented method is based upon some of the important benefits of the hybrid functions such as high accuracy wide applicability and adjustability of the orders of block pulse functions and legendre polynomials to achieve highly accurate numerical solutions by using the numerical integration and collocation method two dimensional nonlinear integral equations are reduced to a system of nonlinear algebraic equations the focus of this paper is to obtain an error estimate and to show the convergence analysis for the numerical approach under the l2 norm numerical results are presented and compared with the results from other existing methods to illustrate the efficiency and accuracy of the proposed method

numerical solution of linear fredholm integral equations via two dimensional modification of hat functions abstract in this work we approximate the solution of the linear fredholm integral equations by means of a new two dimensional modification of hat functions 2d mhfs and a new operational matrix of integration by this idea the basic equations will be changed into the associated systems of algebraic equations also an error analysis is provided under several mild conditions the method is computationally attractive and some numerical examples are provided to illustrate its high accuracy

regression rank scores and regression quantiles we show that regression quantiles which could be computed as solutions of a linear programming problem and the solutions of the corresponding dual problem which we call the regression rank scores generalize the duality of order statistics and of ranks from the location to the linear model noting this fact we study the regression quantile and regression rank score processes in the heteroscedastic linear regression model obtaining some new estimators and interesting comparisons with existing estimators

a computational method for solving nonlinear stochastic volterra integral equations in this paper an efficient method for solving nonlinear stochastic ito volterra integral equations nsivies is proposed by using new adjustment of hat basis functions and their stochastic operational matrix of integration the nsivie is reduced to a nonlinear system of algebraic equations also the error analysis of the proposed method is investigated and proved that the order of convergence is o h 4 finally numerical examples affirm the efficiency of the proposed method

optimal linear estimators for systems with random sensor delays multiple packet dropouts and uncertain observations this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with random sensor delays packet dropouts and uncertain observations we develop a unified model to describe the mixed uncertainties of random delays packet dropouts and uncertain observations by three bernoulli distributed random variables with known distributions based on the proposed model the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach their solutions are given in terms of a riccati equation and a lyapunov equation they can deal with the optimal linear filtering prediction and smoothing for systems with random sensor delays packet dropouts and uncertain observations in a unified framework simulation results show the effectiveness of the proposed optimal linear estimators

optimal control of volterra integral equations in two independent variables we prove an extremality condition for optimal control problems for systems of integral equations of volterra type with two independent variables these systems generalize both the hyperbolic control problems in two independent variables and the optimal control of ordinary i e with one independent variable volterra integral equations

a new approach to sample size calculation for reference interval studies a new criterion is proposed for determining the sample size required for a study performed for the purpose of establishing reference intervals the basic idea behind the criterion is to compare the empirical coverage i e the probability content of the reference region obtained from the sample with its target value e g 95 per cent and to set suitable limits delta1 delta2 to the difference between both quantities which must not be exceeded with sufficiently large probability beta e g beta 90 per cent for the most frequently used parametric and distribution free methods of estimating univariate reference limits implicit formulae are derived relating the sample size to the design parameters delta1 delta2 and beta for symmetric specification of delta1 delta2 explicit approximation formulae for the computation of n are given exact values obtained by means of suitable numerical techniques are presented in a set of tables covering specifications of delta1 delta2 and beta which can be recommended for real applications the tables can be used both for one and two sided reference intervals

extrapolation method of iterated collocation solution for two dimensional nonlinear volterra integral equations in this paper we study the numerical solution of two dimensional nonlinear volterra integral equation by collocation and iterated collocation method asymptotic error expansion of iterated collocation solution is obtained using richardson s extrapolation we show that the accuracy of numerical solution in the iterated collocation method can be improved greatly some numerical examples are given to illustrate this theory

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

constructing time specific reference ranges reference ranges which take time such as age into account are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking a method is described which is based on low order polynomial curves linear quadratic or occasionally cubic together with guidelines for when and how to apply a logarithmic transformation to the variable analysed testing for departures from normality and assessment of the adequacy of the reference range which is constructed from the regression line plus or minus a multiple of the standard deviation standard statistical packages may be used to carry out the calculations the question of comparing two or more groups of patients is addressed three examples are discussed in detail

communication over fading channels with delay constraints we consider a user communicating over a fading channel with perfect channel state information data are assumed to arrive from some higher layer application and are stored in a buffer until transmitted we study adapting the user s transmission rate and power based on the channel state information as well as the buffer occupancy the objectives are to regulate both the long term average transmission power and the average buffer delay incurred by the traffic two models for this situation are discussed one corresponding to fixed length variable rate codewords and one corresponding to variable length codewords the tradeoff between the average delay and the average transmission power required for reliable communication is analyzed a dynamic programming formulation is given to find all pareto optimal power delay operating points we then quantify the behavior of this tradeoff in the regime of asymptotically large delay in this regime we characterize simple buffer control policies which exhibit optimal characteristics connections to the delay limited capacity and the expected capacity of fading channels are also discussed

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

richardson extrapolation of iterated discrete galerkin solution for two dimensional fredholm integral equations in this paper we study the numerical solution of two dimensional fredholm integral equation by discrete galerkin and iterated discrete galerkin method we are able to derive an asymptotic error expansion of the iterated discrete galerkin solution this expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth the expansion gives rise to richardson type extrapolation schemes which rapidly improve the original rate of the convergence numerical experiments confirm our theoretical results

optimal full order and reduced order estimators for discrete time systems with multiple packet dropouts this paper is concerned with the estimation problem for discrete time stochastic linear systems with multiple packet dropouts based on a recently developed model for multiple packet dropouts the original system is transferred to a stochastic parameter system by augmentation of the state and measurement the optimal full order linear filter of the form of employing the received outputs at the current and last time instants is investigated the solution to the optimal linear filter is given in terms of a riccati difference equation governed by packet arrival rate the optimal filter is reduced to the standard kalman filter when there are no packet dropouts the steady state filter is also studied a sufficient condition for the existence of the steady state filter is given and the asymptotic stability of the optimal filter is analyzed at last a reduced order filter is investigated

sample size determination for studies designed to estimate covariate dependent reference quantile curves accuracy and sample size issues concerning the estimation of covariate dependent quantile curves are considered it is proposed to measure the precision of an estimate of the pth quantile at a given covariate value by the probability with which this estimate lies between the p1 th and p2 th quantile where p1 p p2 requiring that this probability exceeds a given confidence bound for all covariate values in a specified range leads to a sample size criterion approximate formulae for the precision and sample size are derived for the normal parametric regression approach and for the semiparametric quantile regression method a simulation study is performed to evaluate the accuracy of the approximations numerical evaluations show that rather large numbers of subjects are needed to construct quantile curves with a reasonable amount of accuracy especially if the quantile regression method is applied

a reliable treatment for mixed volterra fredholm integral equations the main goal of this paper is to demonstrate the use of the modified decomposition method for mixed nonlinear volterra fredholm integral equations the modified method combined with the noise terms phenomena may provide the exact solution by using two iterations only two numerical illustrations are given to show the pertinent features of the technique

optimal periodic transmission power schedules for remote estimation of arma processes we consider periodic sensor transmission power allocation with an average energy constraint the sensor sends its kalman filter based state estimate to the remote estimator through an unreliable link dropout probabilities depend on the power level used to encompass applications where the estimator needs to attend to multiple tasks we allow for irregular sampling following a periodic pattern using properties of an underlying markov chain model we derive an explicit expression for the estimation error covariance the results are then used to study optimal sensor power scheduling which minimizes the average error covariance

a meshfree method for solving multidimensional linear fredholm integral equations on the hypercube domains the main purpose of this article is to describe a numerical scheme for solving multidimensional linear fredholm integral equations of the second kind on the hypercube domains the method is based on interpolation by radial basis functions rbfs to approximate the solution of the linear fredholm integral equations error analysis is presented for this method finally several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method

numerical solution of a class of two dimensional nonlinear volterra integral equations using legendre polynomials in this paper a method for finding an approximate solution of a class of two dimensional nonlinear volterra integral equations is discussed the properties of two dimensional shifted legendre functions are presented the operational matrices of integration and product together with the collocation points are utilized to reduce the solution of the integral equation to the solution of a system of nonlinear algebraic equations some results concerning the error analysis are obtained we also consider the application of the method to the solution of certain partial differential equations illustrative examples are included to demonstrate the validity and applicability of the technique

numerical solution of the two dimensional fredholm integral equations using gaussian radial basis function in this paper we introduce a numerical method for the solution of two dimensional fredholm integral equations the method is based on interpolation by gaussian radial basis function based on legendre gauss lobatto nodes and weights numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method

a computational method for system of volterra fredholm integral equations adomian decomposition method has been applied for solving volterra fredholm equation by maleknejad k maleknejad m hadizadeh a new computational method for volterra fredholm integral equations comput math appl 37 1999 1 8 in 1999 in this paper we solve the system of nonlinear volterra fredholm integral equations by adomian decomposition method some examples are solved to illustrate the accuracy of this method

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

marginal versus joint box cox transformation with applications to percentile curve construction for igg subclasses and blood pressures when age specific percentile curves are constructed for several correlated variables the marginal method of handling one variable at a time has typically been used we address the question frequently asked by practitioners of whether we can achieve efficiency gains by joint estimation we focus on a simple but common method of box cox transformation and assess the statistical impact of a joint transformation to multivariate normality on the percentile curve estimation for correlated variables we find that there is little gain from the joint transformation for estimating percentiles around the median but a noticeable reduction in variances is possible for estimating extreme percentiles that are usually of main interest in medical and biological applications our study is motivated by problems in constructing percentile charts for igg subclasses of children and for blood pressures in adult populations both of which are discussed in the paper as examples and yet our general findings are applicable to a wide range of other problems