analysis and vlsi architecture for 1 d and 2 d discrete wavelet transform in this paper a detailed analysis of very large scale integration vlsi architectures for the one dimensional 1 d and two dimensional 2 d discrete wavelet transform dwt is presented in many aspects and three related architectures are proposed as well the 1 d dwt and inverse dwt idwt architectures are classified into three categories convolution based lifting based and b spline based they are discussed in terms of hardware complexity critical path and registers as for the 2 d dwt the large amount of the frame memory access and the die area occupied by the embedded internal buffer become the most critical issues the 2 d dwt architectures are categorized and analyzed by different external memory scan methods the implementation issues of the internal buffer are also discussed and some real life experiments are given to show that the area and power for the internal buffer are highly related to memory technology and working frequency instead of the required memory size only besides the analysis the b spline based idwt architecture and the overlapped stripe based scan method are also proposed last we propose a flexible and efficient architecture for a one level 2 d dwt that exploits many advantages of the presented analysis

a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set abstract in this paper we provide a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function defined on a noncompact set our criterion is based on a new existence level introduced in this paper that describes the behavior of the function as its argument approaches the extended boundary of the minimization domain some examples are included to illustrate the efficiency of our criterion

solving the parameter identification problem of mathematical models using genetic algorithms a method for solving the parameter identification problem for ordinary second order differential equations using genetic algorithms is given the method is tested on two numerical examples

high speed vlsi implementation of 2 d discrete wavelet transform this paper presents a systematic high speed vlsi implementation of the discrete wavelet transform dwt based on hardware efficient parallel fir filter structures high speed 2 d dwt with computation time as low as n 2 12 can be easily achieved for an ntimesn image with controlled increase of hardware cost compared with recently published 2 d dwt architectures with computation time of n 2 3 and 2n 2 3 the proposed designs can also save a large amount of multipliers and or storage elements it can also be used to implement those 2 d dwt traditionally suitable for lifting or flipping based designs such as 9 7 and 6 10 dwt the throughput rate can be improved by a factor of 4 by the proposed approach but the hardware cost increases by a factor of around 3 furthermore the proposed designs have very simple control signals regular structures and 100 hardware utilization for continuous images

generalized two parameter equation of growth abstract we considered the general growth equation y ay by that encompasses the well known growth equations by bertalanffy and verhulst pearl logistic as special cases the solutions of this equation for some values of and or can be found in the literature here we present the general solution for any real and and discuss its behavior we found that the generalized gompertz growth equation y ay by ln y and its solution could be considered a limiting case of the general growth equation and its solution respectively thus all three classical growth models bertalanffy logistic and gompertz are nested within the general model this nesting relationship makes it possible to compare statistically the applicability of models to data

optimal block diagonal l_2 scaling of matrices this paper is concerned with optimal one sided and two sided scaling of a matrix with respect to the class of block diagonal matrices optimality conditions are presented a series of lower bounds for the symmetric scaling problems is introduced then for some special cases the solutions are given in a closed form finally differentiability of the best condition number as a function of a symmetric matrix is discussed

the existence of optimal parameters of the generalized logistic function the estimation of optimal parameters in a mathematical model described by the generalized logistic function with saturation level a and the asymmetry coefficient is a nonlinear least squares problem in this paper we prove the existence of optimal parameters under considerably weaker conditions than those required in 1

laplace periodogram for time series analysis a new type of periodogram called the laplace periodogram is derived by replacing least squares with least absolute deviations in the harmonic regression procedure that produces the ordinary periodogram of a time series an asymptotic analysis reveals a connection between the laplace periodogram and the zero crossing spectrum this relationship provides a theoretical justification for use of the laplace periodogram as a nonparametric tool for analyzing the serial dependence of time series data superiority of the laplace periodogram in handling heavy tailed noise and nonlinear distortion is demonstrated by simulations a real data example shows its great effectiveness in analyzing heart rate variability in the presence of ectopic events and artifacts

analytical solutions to a generalized growth equation abstract systems of the form x i i n j 1 x gij j i n j 1 x hij j i 1 n occur in the analysis of biological networks they also include as special cases the known growth laws and probability functions famous differential equations like those of bessel chebyshev and laguerre and solutions to important physical problems these systems have no known analytical solution however an important subclass comprising many of the special cases mentioned above is solved

an approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation abstract existing growth equations have been derived by hypothesizing the growth rate as self referencing although that hypothesis is appropriate for quantities with growth directly restricted to themselves it requires the solution of differential equations that are difficult to be derived however for quantities of growth that are indirectly related to themselves and for quantities that exhibit cumulative growth such as growth of diameter or volume of trees with lignification ordinary growth models with assumptions that include self referencing or implied catabolism terms might not be appropriate for such quantities the author proposes an approach for derivation of growth models based on stochastic and microscopic interpretation results show that ordinary growth models can be interpreted from the perspective the approach enables one to derive growth functions without solving differential equations based on that approach growth functions are derived by integrating cumulative distribution functions three growth functions are generated using reasonable probability distributions the fitness of the generated growth functions for real diameter growth data was compared with that of generalized ordinary growth models results show that the presented approach has high ability to generate growth models that fit data much better than ordinary growth models for a given number of parameters

fuzzy least absolutes regression using shape preserving operations the purpose of this study is to introduce a new fuzzy regression model based on the least absolutes method the fuzzy simple and fuzzy multivariate regression models with fuzzy input fuzzy output are considered in which the coefficients of the models are themselves fuzzy the proposed method is based on a new metric on the space of lr fuzzy numbers fuzzy arithmetic operations are based on the weakest triangular norm t w which is the unique triangular norm that preserves the shape of fuzzy numbers during multiplication the results of comparative studies and numerical examples indicate that using the similarity measure criterion as well as a predictive ability index the proposed method has a better performance than the least squares method especially when the data set includes some outlier data point s

flipping structure an efficient vlsi architecture for lifting based discrete wavelet transform in this paper an efficient very large scale integration vlsi architecture called flipping structure is proposed for the lifting based discrete wavelet transform it can provide a variety of hardware implementations to improve and possibly minimize the critical path as well as the memory requirement of the lifting based discrete wavelet transform by flipping conventional lifting structures the precision issues are also analyzed by case studies of the jpeg2000 default lossy 9 7 filter an integer 9 7 filter and the 6 10 filter the efficiency of the proposed flipping structure is demonstrated

precision aware self quantizing hardware architectures for the discrete wavelet transform this paper presents designs for both bit parallel bp and digit serial ds precision optimized implementations of the discrete wavelet transform dwt with specific consideration given to the impact of depth the number of levels of dwt on the overall computational accuracy these methods thus allow customizing the precision of a multilevel dwt to a given error tolerance requirement and ensuring an energy minimal implementation which increases the applicability of dwt based algorithms such as jpeg 2000 to energy constrained platforms and environments additionally quantization of dwt coefficients to a specific target step size is performed as an inherent part of the dwt computation thereby eliminating the need to have a separate downstream quantization step in applications such as jpeg 2000 experimental measurements of design performance in terms of area speed and power for 90 nm complementary metal oxide semiconductor implementation are presented results indicate that while bp designs exhibit inherent speed advantages ds designs require significantly fewer hardware resources with increasing precision and dwt level a four level dwt with medium precision for example while the bp design is four times faster than the digital serial design occupies twice the area in addition to the bp and ds designs a novel flexible dwt processor is presented which supports run time configurable dwt parameters

generalized logistic models abstract a class of models indexed by two shape parameters is introduced both to extend the scope of the standard logistic model to asymmetric probability curves and improve the fit in the noncentral probability regions one parameter subclasses can be used to examine symmetric or asymmetric deviations from the logistic model the delta algorithm is adapted to obtain maximum likelihood estimates of the parameters a review is made of other proposed generalizations the standard linear logistic model is widely used for modeling the dependence of binary data on explanatory variables its success is due to its broad applicability simplicity of form and ease of interpretation this model works well for many common applications however it assumes that the expected probability curve is skew symmetric about and that the shape of is the cumulative distribution function of the logistic distribution symmetric data with a shallower or steeper slope of ascent may not be fitted well by this model

solution of the least squares problem for logistic function given the data pi ti fi i 1 m m 3 we consider the best least squares approximation of parameters for the logistic function t f t 1 e t 0 r we give necessary and sufficient conditions which guarantee the existence of such optimal parameters

fuzzy clustering with structural constraints abstract in this paper we propose a generalization of the standard clustering problem which we call structural constrained clustering scc problem in scc problem the cluster interconnections are given by a binary relation r if this relation is empty then scc problem reduces to the standard classification problem the cluster structure imposed by r may be described by the covering graph of r for example if this graph is a rooted tree then a hierarchical structure is imposed to the clusters we formulate scc as a fuzzy clustering problem with prototype inter relation a general algorithm to solve this problem is proposed for three particular distance measures squared euclidean and l1 metric we compute the prototypes by solving a particular multifacility location problem

integer computation of lossy jpeg2000 compression in this paper an integer based cohen daubechies feauvea cdf 9 7 wavelet transform as well as an integer quantization method used in a lossy jpeg2000 compression engine is presented the conjunction of both an integer transform and quantization step allows for a complete integer computation of lossy jpeg2000 compression the lossy method of compression utilizes the cdf 9 7 wavelet filter which transforms integer input pixel values into floating point wavelet coefficients that are then quantized back into integers and finally compressed by the embedded block coding with optimal truncation tier 1 encoder integer computation of jpeg2000 allows a reduction in computational complexity of the wavelet transform as well as ease of implementation in embedded systems for higher computational performance the results of the integer computation show an equivalent rate distortion curve to the jasper jpeg2000 compression engine as well as a 30 reduction in computation time of the wavelet transform and a 56 reduction in computation time of the quantization processing on an average

origins and uses of linear programming methods for treating l1 and l regressions corrections and comments on abstract this note comments on and corrects some of the referrals and comments of castillo et al castillo e minguez r castillo c confino a s 2008 dealing with the multiplicity of solutions of the l 1 and l regression models european journal of operational research 188 460 484 concerning the origins and uses of linear programming to estimate l 1 and l statistical regressions

a mathematical model of controlling the growth of tissue in pigs a mathematical model of controlling the growth of tissues in pigs is described in this paper in that sense a method is given by which it is possible to periodically and very accurately estimate live pig weight of backfat based upon measurements done by ultrasound these estimations will be used for the purpose of predicting growth of backfat in live pigs backfat weight is estimated on the basis of measurements done by using the moving total least squares method whereas estimation of live pig backfat growth is done by using a generalized logistic function whose parameters are estimated by means of the least squares method since thereby the hessian of the corresponding minimizing function is very close to a singular matrix an additional problem analysis was necessary

approximation in normal linear spaces abstract a historical account is given of the development of methods for solving approximation problems set in normed linear spaces approximation of both real functions and real data is considered with particular reference to lp or lp and chebyshev norms as well as coverage of methods for the usual linear problems an account is given of the development of methods for approximation by functions which are nonlinear in the free parameters and special attention is paid to some particular nonlinear approximating families

a necessary and sufficient criteria for the existence of the least squares estimate for a 3 parametric exponential function given the data p i t i y i i 1 m m 3 we give necessary and sufficient conditions which guarantee the existence of the least squares estimate for a 3 parametric exponential function to this end we suggest a choice of the initial approximation and give some numerical examples

computational experience with confidence regions and confidence intervals for nonlinear least squares we present the results of a monte carlo study of the leading methods for constructing approximate confidence regions and confidence intervals for parameters estimated by nonlinear least squares we examine three variants of the linearization method the likelihood method and the lack of fit method the linearization method is computationally inexpensive produces easily understandable results and is widely used in practice the likelihood and lack of fit methods are much more expensive and more difficult to report in our tests both the likelihood and lack of fit methods perform very reliably all three variants of the linearization method however often grossly underestimate confidence regions and sometimes significantly underestimate confidence intervals the linearization method variant based solely on the jacobian matrix appears preferable to the two variants that use the full hessian matrix because it is less expensive more numerically stable and at least as accurate the bates and watts curvat

existence results for special nonlinear total least squares problem in this paper we prove an existence theorem for a special nonlinear total least squares problem we show that the optimal parameters of the generalized logistic function exist in the sense of total least squares provided the data satisfy the chebyshev s inequality

existence of optimal solution for exponential model by least squares in this paper we prove the existence theorem for the best least squares approximation of the optimal parameters for the exponential model function we give sufficient conditions which guarantee the existence of such optimal parameters using these results and methods we are able to localize a sufficiently narrow area where one can choose a good initial approximation

weighted minimum trace factor analysis in the last decade several authors discussed the so called minimum trace factor analysis mtfa which provides the greatest lower bound g l b to reliability however the mtfa fails to be scale free in this paper we propose to solve the scale problem by maximization of the g l b as the function of weights closely related to the primal problem of the g l b maximization is the dual problem we investigate the primal and dual problems utilizing convex analysis techniques the asymptotic distribution of the maximal g l b is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions finally we outline computational algorithms and consider numerical examples

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

fuzzy constrained lp norm inversion of direct current resistivity data abstractwe evaluate the use of a fuzzy c means clustering procedure to improve an inverted 2d resistivity model within the iterative error minimization procedure the algorithm is coded in matlab language for the lp norm inversion of 2d direct current resistivity data and is referred to as fuzzy constrained inversion fci two additional input parameters are required to be provided by the interpreter 1 the number of geologic units in the model i e the number of clusters and 2 the mean resistivity values of each geologic unit i e cluster center values of the geologic units the efficacy of our approach is evaluated by tests carried on the synthetic and field electrical resistivity tomography ert data inversion results from the fci algorithm are presented for conventional l1 and l2 norm minimization techniques fci indicates improvement over conventional inversion approaches in differentiating the geologic units if a proper number of the geologic units is provided to the algorithm inappro

on a modified beta function and some applications abstract in this work we study the modified beta function b 1 2 x a b 1 2 x 1 v a 1 v b 1 dv x 0 1 that appeared in marus ic and bajzer s solution m marus ic z bajzer generalized two parameter equation of growth j math anal appl 179 1993 446 462 of the generalized two parameter equation of tumor growth y ay by in particular we provide methods for computing this function for special values of the function s parameters some analytic solutions of the generalized two parameter growth equation are obtained

three points method for searching the best least absolute deviations plane in this paper a new method for estimation of optimal parameters of a best least absolute deviations plane is proposed which is based on the fact that there always exists a best least absolute deviations plane passing through at least three different data points the proposed method leads to a solution in finitely many steps moreover a modification of the aforementioned method is proposed that is especially adjusted to the case of a large number of data and the need to estimate parameters in real time both methods are illustrated by numerical examples on the basis of simulated data and by one practical example from the field of robotics

discrete total lp norm approximation problem for the exponential function in this paper we consider the total l p norm p 0 approximation problem for the exponential function we give sufficient conditions which guarantee the existence of such optimal parameters

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

a note on flipping structure an efficient vlsi architecture for lifting based discrete wavelet transform a flipping structure for the discrete wavelet transform dwt was proposed by huang et al which aimed at shortening the critical path of the lifting based one dimensional 1 d architecture and reducing the number of pipeline register used in 1 d architecture as well as the size of temporal buffer tb required in the line based two dimensional 2 d architecture in this paper we explore the intrinsic relationship between the size of tb required in the line based architecture for 2 d dwt lba2ddwt and the number of registers used in a 1 d dwt module and present a modified view on this issue that has been proposed by huang et al an improved method of mapping the registers used in 1 d dwt architecture to the tb required in lba2ddwt is presented which reduces more efficiently the size of memory required in lba2ddwt than huang s method a parallel based lifting scheme pls for dwt and its vlsi architecture are presented the proposed pls of dwt not only reduces efficiently the critical path but also results in the equality of the forward discrete wavelet transform and inverse discrete wavelet transform implementations compared with huang s method the proposed pls is more efficient in reducing critical path and or the number of registers of vlsi implementation for 1 d dwt and it can be concluded that the flipping structure of dwt is a special case of the pls based implementation

composite exponential approximations the composite exponential approximations cea arise in a natural way when one investigates the stability and order properties of a combination of several methods for the numerical solution of ordinary differential equations sequentially implemented with different step lengths some general results on the order acceptability and exponential fitting properties of cea are derived the composite pade approximations and tv approximations are explored in detail

a method for solving the parameter identification problem for ordinary differential equations of the second order we give a method for solving the parameter identification problem for ordinary differential equations of the second order using a noninterpolated moving least squares method the method is tested in two practical examples

continuous growth models in terms of generalized logarithm and exponential functions abstract consider the one parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non symmetrical hyperboles these generalizations coincide to the one obtained in the context of non extensive thermostatistics we show that these functions are suitable to describe and unify the great majority of continuous growth models which we briefly review physical interpretation to the generalization function parameter is given for the richards model which has an underlying microscopic model to justify it

two fast architectures for the direct 2 d discrete wavelet transform we propose two architectures for the direct two dimensional 2 d discrete wavelet transform dwt the first one is based on a modified recursive pyramid algorithm mrpa and performs a nonstandard decomposition i e mallat s 1989 tree of an n spl times n image in approximately 2n sup 2 3 clock cycles ccs this result consistently speeds up other known architectures that commonly need approximately n sup 2 ccs furthermore the proposed architecture is simpler than others in terms of hardware complexity subsequently we show how symmetric anti symmetric properties of linear phase wavelet filter bases can be exploited in order to further reduce the vlsi area this is used to design a second architecture that provides one processing unit for each level of decomposition pipelined approach and performs a decomposition in approximately n sup 2 2 ccs in many practical cases even this architecture is simpler than general mrpa based devices having only one processing unit

approximating surfaces by moving total least squares method we suggest a method for generating a surface approximating the given data x i y i z i e r 3 i 1 m assuming that the errors can occur both in the independent variables x and y as well as in the dependent variable z our approach is based on the moving total least squares method where the local approximants local planes are determined in the sense of total least squares the parameters of the local approximants are obtained by finding the eigenvector corresponding to the smallest eigenvalue of a certain symmetric matrix to this end we develop a procedure based on the inverse power method the method is tested on several examples

a special nonlinear least squares problem in this paper we consider the existence of the solution of a special nonlinear least squares problem we find the necessary conditions on the data which insure the existence of the optimal parameters for the asymmetric s function in the sense of the least squares

rate of convergence of shepard s global interpolation formula given any data points xl x in rw and values f x f x of a function f shepard s global interpolation formula reads as follows sof x ef xi wi x wi x i x xi i p elx xjl p where i denotes the euclidean norm in wr this interpolation scheme is stable but if p 1 the gradient of the interpolating function vanishes in all data points the interpolation operator spq is defined by replacing the values f xi in spf by taylor polynomials of f of degree q e n in this paper we investigate the approximating power of spq for all values of p q and s

dealing with the multiplicity of solutions of the l1 and l regression models abstract it is well known that the least absolute value l and the least sum of absolute deviations l1 algorithms produce estimators that are not necessarily unique in this paper it is shown how the set of all solutions of the l1 and l regression problems for moderately large sample sizes can be obtained in addition if the multiplicity of solutions wants to be avoided two new methods giving the same optimal l1 and l values but supplying unique solutions are proposed the idea consists of using two steps in the first step the optimal values of the l1 and l errors are calculated and in the second step in case of non uniqueness of solutions one of the multiple solutions is selected according to a different criterion for the l the procedure is used sequentially but removing in each iteration the data points with maximum absolute residual and adding the corresponding constraints for keeping these residuals and this process is repeated until no change in the solution is obtained in this way not only the maximum absolute residual values are minimized in the modified method but also the maximum absolute residual values of the remaining points sequentially until no further improvement is possible in the l1 case a least squares criterion is used but restricted to the l1 residual condition thus in the modified l1 method not only the l1 residual is minimized but also the sum of squared residuals subject to the l1 residual the methods are illustrated by their application to some well known examples and their performances are tested by some simulations which show that the lack of uniqueness problem cannot be corrected for some experimental designs by increasing the sample size

analysis of a parameter identification problem we consider a special parameter identification problem occurring in marketing research and give conditions on the empirical data which guarantee the existence of the solution to the problem furthermore we analyze several different approaches and methods for solving this parameter identification problem

rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis one of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries we show in this paper that the set of matrices which can be reduced to rankr has positive lebesgue measure if and only ifr is greater or equal to the ledermann bound in other words the ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix afterwards an asymptotic sampling theory of so called minimum trace factor analysis mtfa is proposed the theory is based on continuous and differential properties of functions involved in the mtfa convex analysis techniques are utilized to obtain conditions for differentiability of these functions

multivariate interpolation of arbitrarily spaced data by moving least squares methods abstract given a function f in scattered data points x1 xn r s we solve the least squares problem i 1 n j o q a j x b j x i f x i 2 v i x min in order to generate interpolants aj x bj x here the bj denote basis functions e g polynomials and the vi x are inverse distance weight functions we express the unknowns aj x the interpolant and the interpolation error in terms of moving convex combinations of functions corresponding to those of classical interpolation at q 1 points with respect to these basis functions further we discuss properties of moving least squares methods and in the case of polynomial basis functions we test various methods and give perspective plots

solving parameter estimation problem in new product diffusion models in this paper we propose a new method for the parameter identification in new product diffusion models the method can be used regardless of whether the analytical solution of the differential equation describing the model is known or not this is the main advantage of our method over the known methods another advantage of this method is the simplicity of its implementation and negligible computing time the method is based on finite differences method and the moving least squares method for data smoothing

optimal block diagonal scaling of block 2 cyclic matrices abstract we describe a class of optimal block diagonal scalings preconditionings of a symmetric positive definite block 2 cyclic matrix generalizing a result of forsythe and strauss 1 for point 2 cyclic matrices

validating clusters with the lower bound for sum of squares error given that a minor condition holds e g the number of variables is greater than the number of clusters a nontrivial lower bound for the sum of squares error criterion in k means clustering is derived by calculating the lower bound for several different situations a method is developed to determine the adequacy of cluster solution based on the observed sum of squares error as compared to the minimum sum of squares error

estimation of parameters of the shifted gompertz distribution using least squares maximum likelihood and moments methods nonlinear least squares procedures for estimating the parameters of the shifted gompertz distribution are proposed simulation studies are carried out to compare weighted and unweighted least squares methods the maximum likelihood method and method of moments this work concludes that least squares methods via weighting factors to estimate the parameters of this probability distribution give a better performance than unweighted least squares methods showing the importance of weighting factors besides results of this simulation study show that a good performance is obtained using the maximum likelihood method and the estimators obtained with more bias are those of the method of moments

moving least squares interpolation with thin plate splines and radial basis functions abstract moving least squares methods for interpolation or approximation of scattered data are well known and can suffer from defects such as flat spots in the shepard method and edge effects inherited from a polynomial basis in the higher degree cases we investigate methods based on thin plate splines and on other radial basis functions it turns out that a small support of the weight function leads to a small support for the spline basis and associated efficiency in the evaluation of the approximant the edge effects seem minimal and good interpolants of scattered data can be obtained

optimal two sided diagonal scaling for filter bank frames two sided diagonal scaling for transfer matrices is formulated an efficient algorithm is proposed to compute globally optimal solutions using the iterated bi section and linear matrix inequality lmi solver it is shown that the two sided scaling of filter bank fb frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal and that the frame bound ratio of fb frames can be effectively improved by such scaling explicit formulas are established for both uniform and nonuniform fb frames including detail formulas for discrete weyl heisenberg frames and tree structured fbs discrete wavelets different examples show the effectiveness of the obtained results

an interior point algorithm for nonlinear quantile regression abstract a new algorithm for computing quantile regression estimates for problems in which the response function is nonlinear in parameters is described the nonlinear l 1 estimation problem is a special median case the algorithm is closely related to recent developments on interior point methods for solving linear programs performance of the algorithm on a variety of test problems including the censored linear quantile regression problem of powell 1986 is reported

on nonlinear weighted least squares estimation of bass diffusion model the bass model is one of the most well known and widely used models of first purchase demand estimation of its parameters has been approached in the literature by various techniques the focus of this paper is on a nonlinear weighted least squares fitting approach as a main result two theorems on the existence of the least squares estimate are obtained one of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate some numerical experiments are given to illustrate the efficiency of our approach

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

on statistical data analysis based on the l1 norm and related methods an introduction to statistical data analysis l 1 norm based y dodge the place of the l 1 norm in robust estimation p j huber i historical development the historical development of the l 1 and l estimation procedures r w farebrother bounded influence inference in regression a review e ronchetti ii computational algorithms and computer packages algorithms for unconstrained l 1 linear regression j e gentle s c narula v a sposito the reduced gradient algorithm m r osborne the l 1 estimate as limiting case of an l p or huber estimate h ekblom a review of computational methods for solving the nonlinear l 1 norm estimation problem r gonin a h money fitting data through homotopy methods j p schellhorn blinwdr a fortran program for robust and bounded influence regression r dutter solving bounded influence regression problems with robsys a marazzi xplore a computing environment for exploratory regression w hardle iii estimation characterization properties and selection of variables l 1 distances in statistical inference comparison of topological functional and statistical properties i vajda the role played by l 1 in data analysis b fichet l 1 embeddings of a data structure i d g le calve assessing the accuracy of the sample median estimated standard errors vs interpolated confidence intervals s j sheather the median of a finite measure on a banach space j h b kemperman variable selection in linear model based on trimmed least squares estimator j antoch numerical techniques for finding estimates which minimize the upper bound of the absolute deviation a gaivoronski asymptotic properties of restricted l 1 estimates of regression j dupacova adaptive combination of least squares and least absolute deviations estimators y dodge j jureckova iv statistical inference procedures a comparison of asymptotic testing methods for l 1 regression r koenker least absolute errors analysis of variance j w mckean r m schrader small sample properties of least absolute errors analysis of variance r m schrader j w mckean bootstrap and inference procedures for l 1 regression g stangenhaus invariant tests in bivariate models and the l 1 criterion b m brown t p hettmansperger using regression fractiles to identify outliers s portnoy various discrepancy measures in model testing two competing regression models v v fedorov v nonparametric analysis kernel estimates of the sparsity function a h welsh what does optimal bandwidth selection mean for nonparametric regression estimation j s marron density estimation from dependent sample l gyorfi vi cluster analysis clustering by means of medoids l kaufman p j rousseeuw l 1 in fuzzy clustering e trauwaert using the l 1 norm within cluster analysis h spath vii applications an application of l 1 to astronomy p j rousseeuw

optimally scaled matrices necessary and sufficient conditions we shall in this paper consider the problem of determination a row or column scaling of a matrixa which minimizes the condition number ofa this problem was studied by several authors for the cases of the maximum norm and of the sum norm the scale problem was completely solved by bauer 1 and sluis 5 the condition ofa subordinate to the pair of euclidean norms is the ratio where and are the maximal and minimal eigenvalue of a h a 1 2 respectively the euclidean case was considered by forsythe and strauss 3 shapiro 6 proposed some approaches to a numerical solution in this case the main result of this paper is the presentation of necessary and sufficient conditions for optimal scaling in terms of maximizing and minimizing vectors a uniqueness proof for the solution is offered provided some normality assumption is satisfied

least squares fitting gompertz curve in this paper we consider the least squares ls fitting of the gompertz curve to the given nonconstant data pi ti yi i 1 m m 3 we give necessary and sufficient conditions which guarantee the existence of the ls estimate suggest a choice of a good initial approximation and give some numerical examples

efficient architectures for 1 d and 2 d lifting based wavelet transforms the lifting scheme reduces the computational complexity of the discrete wavelet transform dwt by factoring the wavelet filters into cascades of simple lifting steps that process the input samples in pairs we propose four compact and efficient hardware architectures for implementing lifting based dwts namely one dimensional 1 d and two dimensional 2 d versions of what we call recursive and dual scan architectures the 1 d recursive architecture exploits interdependencies among the wavelet coefficients by interleaving on alternate clock cycles using the same datapath hardware the calculation of higher order coefficients along with that of the first stage coefficients the resulting hardware utilization exceeds 90 in the typical case of a five stage 1 d dwt operating on 1024 samples the 1 d dual scan architecture achieves 100 datapath hardware utilization by processing two independent data streams together using shared functional blocks the recursive and dual scan architectures can be readily extended to the 2 d case the 2 d recursive architecture is roughly 25 faster than conventional implementations and it requires a buffer that stores only a few rows of the data array instead of a fixed fraction typically 25 or more of the entire array the 2 d dual scan architecture processes the column and row transforms simultaneously and the memory buffer size is comparable to existing architectures