modeling daily and subdaily cycles in rat sleep data we developed a statistical model for rat sleep wake behavior over the 24 hour day this model could be used for animals exposed to shorter cycles of light and dark conditions rat behavior was classified either as wake or sleep as determined by analysis of electrophysiological data the proposed model consists of three parts the first two explain cyclic effects relating to the lighting conditions whereas the last part reflects any acyclic effect hypothesis tests were conducted on the magnitude of the parts the model also accounts for correlated errors

multiscale inference and long run variance estimation in non parametric regression with time series errors we develop new multiscale methods to test qualitative hypotheses about the function m in the non parametric regression model yt t m t t t with time series errors t in time series applications m represents a non parametric time trend practitioners are often interested in whether the trend m has certain shape properties for example they would like to know whether m is constant or whether it is increasing or decreasing in certain time intervals our multiscale methods enable us to test for such shape properties of the trend m to perform the methods we require an estimator of the long run error variance 2 l cov e0 el we propose a new difference based estimator of 2 for the case that t belongs to the class of auto regressive ar processes in the technical part of the paper we derive asymptotic theory for the proposed multiscale test and the estimator of the long run error variance the theory is complemented by a simulation study and an empirical application to climate data

the bergman kernel of complex ovals and multivariable hypergeometric functions abstract we compute explicitly the bergman and szego kernels for a class of pseudoconvex domains the kernels are expressed in terms of appell s multivariable hypergeometric functions these explicit formulas are applied to investigate the asymptotic behavior of the bergman kernel near some weakly pseudoconvex boundary points

the explicit forms and zeros of the bergman kernel for 3 dimensional hartogs triangles abstract we compute the bergman kernel for h p 1 p 2 p 3 z 1 z 2 z 3 z 1 p 1 z 2 p 2 z 3 p 3 1 for any positive integers k p 1 p 2 p 3 using the transformation formula under a proper holomorphic mapping for example we compute the explicit forms of the bergman kernels of h k k 1 h 1 k 1 h k 1 1 using the explicit formulas we prove that the bergman kernels have zeros

visual error criteria for qualitative smoothing abstract an important gap between the classical mathematical theory and the practice and implementation of nonparametric curve estimation is due to the fact that the usual norms on function spaces measure something different from what the eye can see visually in a graphical presentation mathematical error criteria that more closely follow visual impression are developed and analyzed from both graphical and mathematical viewpoints examples from wavelet regression and kernel density estimation are considered

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

density level sets asymptotics inference and visualization abstractwe study the plug in estimator for density level sets under hausdorff loss we derive asymptotic theory for this estimator and based on this theory we develop two bootstrap confidence regions for level sets we introduce a new technique for visualizing density level sets even in multidimensions which is easy to interpret and efficient to compute supplementary materials for this article are available online

scale space view of curve estimation scale space theory from computer vision leads to an interesting and novel approach to nonparametric curve estimation the family of smooth curve estimates indexed by the smoothing parameter can be represented as a surface called the scale space surface the smoothing parameter here plays the same role as that played by the scale of resolution in a visual system in this paper we study in detail various features of that surface from a statistical viewpoint weak convergence of the empirical scale space surface to its theoretical counterpart and some related asymptotic results have been established under appropriate regularity conditions our theoretical analysis provides new insights into nonparametric smoothing procedures and yields useful techniques for statistical exploration of features in the data in particular we have used the scale space approach for the development of an effective exploratory data analytic tool called sizer

exact mean integrated squared error an exact and easily computable expression for the mean integrated squared error mise for the kernel estimator of a general normal mixture density is given for gaussian kernels of arbitrary order this provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis the family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes a number of applications of this method giving important new insights into kernel density estimation are presented among these is the discovery that the usual asymptotic approximations to the mise can be quite inaccurate especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes 1 introduction substantial research has been devoted to kernel density estimation this is because it provides a simple yet appealing context in which to study problems and issues that arise in all types of nonparametric curve estimation this includes regression spectral density and hazard estimation and also a variety of other estimators including histograms splines and orthogonal series three important and useful tools for understanding the behavior of nonparametric curve estimators are asymptotic analysis simulation and numerical calculation of error criteria each of these methods provides many useful insights into the complicated structure present in the study of curve estimation however each has its limitations as well rhe strength of asymptotic analysis is that it frequently allows simultaneous study of many different specific examples through general results applying to entire classes of settings the weakness of asymptotics is that they only describe behavior in the limit this is still very useful in many situations because the asymptotics describe the actual situation quite well however it is less useful when the asymptotics have not yet kicked in that is in studying situations where the asymptotically dominant effect has not taken over yet perhaps the biggest drawback to asymptotics is that it is very difficult to determine in a given situation which of these possibilities is occurring

the bergman kernels of generalized bergman hartogs domains abstract we define the generalized bergman hartogs domain which is the hartogs domain over the product of representative bounded homogeneous domains and compute the explicit form of the bergman kernel function as an application of this formula we show that the generalized bergman hartogs domain is a minimal domain with the origin as center in particular we get the volume of this domain in addition we also study the lu qi keng problem of the generalized bergman hartogs domain

the bergman kernel function and proper holomorphic mappings it is proved that a proper holomorphic mapping f between bounded complete reinhardt domains extends holomorphically past the boundary and that if in addition f 1 0 01 then f is a polynomial mapping the proof is accomplished via a transformation rule for the bergman kernel function under proper holomorphic mappings

multiscale clustering of nonparametric regression curves abstract in a wide range of modern applications one observes a large number of time series rather than only a single one it is often natural to suppose that there is some group structure in the observed time series when each time series is modeled by a nonparametric regression equation one may in particular assume that the observed time series can be partitioned into a small number of groups whose members share the same nonparametric regression function we develop a bandwidth free clustering method to estimate the unknown group structure from the data more precisely speaking we construct multiscale estimators of the unknown groups and their unknown number which are free of classical bandwidth or smoothing parameters in the theoretical part of the paper we analyze the statistical properties of our estimators our theoretical results are derived under general conditions which allow the data to be dependent both in time series direction and across different time series the technical analysis of the paper is complemented by simulated and real data examples

sizer for exploration of structures in curves abstract in the use of smoothing methods in data analysis an important question is which observed features are really there as opposed to being spurious sampling artifacts an approach is described based on scale space ideas originally developed in the computer vision literature assessment of significant zero crossings of derivatives results in the sizer map a graphical device for display of significance of features with respect to both location and scale here scale means level of resolution that is bandwidth

piecewise convex function estimation pilot estimators given noisy data function estimation is considered when the unknown function is known a priori to be either convex or concave on each of a small number of regions where the function when the number of regions is unknown the model selection problem is to determine the number of convexity change points for kernel estimates in gaussian noise the number of false change points is evaluated as a function of the smoothing parameter to insure that the number of false convexity change points tends to zero the smoothing level must be larger than is generically optimal for minimizing the mean integrated square error mise a two stage estimator is proposed and shown to achieve the optimal rate of convergence of the mise in the first stage the number and location of the change points is estimated using strong smoothing in the second stage a constrained smoothing spline fit is performed with the smoothing level chosen to minimize the mise the imposed constraint is that a single change point occur in a region about each empirical change point from the first stage estimate this constraint is equivalent to the requirement that the third derivative of the second stage estimate has a single sign in a small neighborhood about each first stage change point the change points from the second stage are first stage change points but need not be at the identical locations

thick pen transformation for time series traditional visualisation of time series data often consists of plotting the time series values against time and connecting the dots we propose an alternative multiscale visualisation technique motivated by the scale space approach in computer vision in brief our method also connects the dots but uses a range of pens of varying thicknesses for this purpose the resulting multiscale map termed the thick pen transform tpt corresponds to viewing the time series from a range of distances we formally prove that the tpt is a discriminatory statistic for two gaussian time series with distinct correlation structures further we show interesting possible applications of the tpt to measuring cross dependence in multivariate time series classifying time series and testing for stationarity in particular we derive the asymptotic distribution of our test statistic and argue that the test is applicable to both linear and nonlinear processes under low moment assumptions various other aspects of the methodology including other possible applications are also discussed

a discrete eoq problem is solvable in o logn time abstract the economic order quantity problem is a fundamental problem of inventory management an optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible and demand occurs at a constant rate we prove that a discrete version of this problem in which time and the product are discrete is solvable in o log n time where n is the length of the time period where the demand takes place the key elements of our approach are a reduction of the original problem to a discrete minimization problem of one variable representing the number of orders and a proof that the objective function of this problem is convex according to our approach optimal order sizes can take at most two distinct values n k and n k where k is the optimal number of orders

rigidity of proper holomorphic mappings between certain unbounded non hyperbolic domains abstract the fock bargmann hartogs domain d n m 0 in c n m is defined by the inequality w 2 e z 2 where z w c n c m which is an unbounded non hyperbolic domain in c n m recently yamamori gave an explicit formula for the bergman kernel of the fock bargmann hartogs domains in terms of the polylogarithm functions and kim ninh yamamori determined the automorphism group of the domain d n m in this article we obtain rigidity results on proper holomorphic mappings between two equidimensional fock bargmann hartogs domains our rigidity result implies that any proper holomorphic self mapping on the fock bargmann hartogs domain d n m with m 2 must be an automorphism

multiscale testing of qualitative hypotheses suppose that one observes a process y on the unit interval where dy t n1 2f t dt dw t with an unknown function parameter f given scale parameter n 1 sample size and standard brownian motion w we propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity these tests are asymptotically optimal and adaptive in a certain sense they are constructed via a new class of multiscale statistics and an extension of levy s modulus of continuity of brownian motion

confidence intervals for nonparametric curve estimates numerous nonparametric regression methods exist that yield consistent estimators of function curves often one is also interested in constructing confidence intervals for the unknown function when a function estimate is based on a single global smoothing parameter the resulting confidence intervals may hold their desired confidence level 1 on average but because bias in nonparametric estimation is not uniform they do not hold the desired level uniformly at all design points most research in this area has focused on mean squared error properties of the estimator for example mise itself a global measure in addition measures like mise are one step removed from the practical issue of coverage probability recent work that focuses on coverage probability has considered only coverage in an average sense ignoring the important issue of uniformity of coverage across the design space to deal with this problem a new estimator is developed which uses a local cross validation criterion lcv to determi

bump hunting with non gaussian kernels it is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a gaussian density there is numerical evidence of nonmonotonicity in the case of some non gaussian kernels but little additional information is available the present paper provides theoretical and numerical descriptions of the extent to which the number of modes is a nonmonotone function of bandwidth in the case of general compactly supported densities our results address popular kernels used in practice for example the epanechnikov biweight and triweight kernels and show that in such cases nonmonotonicity is present with strictly positive probability for all sample sizes n 3 in the epanechnikov and biweight cases the probability of nonmonotonicity equals 1 for all n 2 nevertheless in spite of the prevalence of lack of monotonicity revealed by these results it is shown that the notion of a critical bandwidth the smallest bandwidth above which the number of modes is guaranteed to be monotone is still well defined moreover just as in the gaussian case the critical bandwidth is of the same size as the bandwidth that minimises mean squared error of the density estimator these theoretical results and new numerical evidence show that the main effects of nonmonotonicity occur for relatively small bandwidths and have negligible impact on many aspects of bump hunting jj

some reduction and transformation formulas for the appell hypergeometric function f2 abstract an integral representation of the appell series f 2 1 2 1 2 x y is used here to obtain several finite sum expansions in terms of the less cumbersome hypergeometric functions 2f1 and 3f2 in the case when the parameters 1 2 1 and 2 are all positive integers some of our results may be seen as a generalization of the finite sum expansions of the appell series f 1 obtained by cuyt et al j comput appl math 5 1999 213 219 other important consequences as well as potential applications of our results are discussed and a listing of some useful reduction and transformation formulas is provided

the dip test of unimodality the dip test measures multimodality in a sample by the maximum difference over all sample points between the empirical distribution function and the unimodal distribution function that minimizes that maximum difference the uniform distribution is the asymptotically least favorable unimodal distribution and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform

the kernel estimate of a regression function in likelihood based models abstract smoothing splines have a penalized likelihood motivation good and gaskins 1971 allowing direct application to nonparametric regression in likelihood based models the notion of a weighted likelihood for the nonparametric kernel estimation of a regression function is proposed generalizing the local likelihood theory of tibshirani and hastie 1987 let the data be of the form xi yi i 1 n where xi 0 1 d are lattice points and the yi are independent random variables from a family of distributions with parameter i g xi with g having continuous partial derivatives of order k 2 the goal is to arrive at a nonparametric estimate o of o g xo for a fixed point xo 0 1 d we consider the estimator o that maximizes the weighted likelihood function w n i 1 w xo xi b log f yi with f the density of yi w a symmetric kernel with compact support and b the bandwidth that controls the degree of smoothing sufficient conditions for consistency and asympt

a forelli rudin construction and asymptotics of weighted bergman kernels let be a pseudoconvex domain in cn with smooth boundary two smooth defining functions for 0 such that log log are plurisubharmonic z a point at which log is strictly plurisubharmonic and m 0 an integer we show that as k the bergman kernels with respect to the weights k m have the asymptotic expansionk k m z z kn n z k z m j 0 bj z k j b0 det 2log zj zk for strongly pseudoconvex with real analytic boundary real analytic and log log strictly plurisubharmonic on we obtain also the analogous result for k k m x y for x y near the diagonal and discuss consequences for the asymptotics of the berezin transform and for the berezin quantization the proofs rely on fefferman s expansion for the bergman kernel in a certain forelli rudin type domain over as another application they also yield a generalization of the cited fefferman s expansion to a class of weighted bergman kernels

on holomorphic isometric immersions of nonhomogeneous kahler einstein manifolds into the infinite dimensional complex projective space abstract in the paper we study the existence of holomorphic isometric immersions from nonhomogeneous kahler einstein manifolds into infinite dimensional complex projective space it can also be regarded as an application of explicit solutions of complex monge ampere equations on some pseudoconvex domains

jump detection in a regression curve and its derivative curve estimation from observed noisy data has broad applications in certain applications the underlying regression curve may have singularities including jumps and roofs valleys i e jumps in the first order derivative of the regression curve at some unknown positions representing structural changes of the related process detection of such singularities is important for understanding the structural changes in the literature a number of jump detection procedures have been proposed most of which are based on estimation of the one sided first order derivatives of the true regression curve in this paper motivated by certain related research in image processing we propose an alternative jump detection procedure besides the first order derivatives we suggest using helpful information about jumps in the second order derivatives as well theoretical justifications and numerical studies show that this jump detector works well in applications this procedure is then extended for detecting roofs v

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

calibrating the excess mass and dip tests of modality summary nonparametric tests of modality are a distribution free way of assessing evidence about inhomogeneity in a population provided that the potential subpopulations are sufficiently well separated they include the excess mass and dip tests which are equivalent in univariate settings and are alternatives to the bandwidth test only very conservative forms of the excess mass and dip tests are available at present however and for that reason they are generally not competitive with the bandwidth test in the present paper we develop a practical approach to calibrating the excess mass and dip tests to improve their level accuracy and power substantially our method exploits the fact that the limiting distribution of the excess mass statistic under the null hypothesis depends on unknowns only through a constant which may be estimated our calibrated test exploits this fact and is shown to have greater power and level accuracy than the bandwidth test has the latter tends to be quite conservative even in an asymptotic sense moreover the calibrated test avoids difficulties that the bandwidth test has with spurious modes in the tails which often must be discounted through subjective intervention of the experimenter

continuation of l2 holomorphic functions let be a bounded domain in cn and let l2h be the l2 holomorphic functions on we show that the envelope of holomorphy and the l2h envelope of holomorphy of differ by at most a pluripolar set

analysis of long period variable stars with nonparametric tests for trend detection in astronomy the study of variable stars that is stars characterized by showing significant variation in their brightness over time has made crucial contributions to our understanding of many phenomena from stellar birth and evolution to the calibration of the extragalactic distance scale in this article we develop a method for analyzing multiple pseudo periodic time series with the goal of detecting temporal trends in their periods we allow for nonstationary noise and for clustering among the various time series we apply this method to the long standing astronomical problem of identifying variable stars whose regular brightness fluctuations have periods that change over time the results of our analysis show that such changes can be substantial raising the possibility that astronomers estimates of galactic distances can be refined two significant contributions of our approach relative to existing methods for this problem are as follows 1 the method is nonparametric making minimal assumpt

the bergman kernel function of some reinhardt domains the boundary behavior of the bergman kernel function of some reinhardt domains is studied upper and lower bounds for the bergman kernel function are found at the diagonal points z z let d be the reinhardt domain n d z cnilll 0 j 1 2 n and let k z wi be the bergman kernel function of d then there exist two positive constants m and m and a function f such that mf z z k z z mf z z holds for every z e d here n f z z r z n 1 j7j r z lzj 12 c3 1 o j 1 and r z jjzjje1 is the defining function for d the constants m and m depend only on ce cel cen and n not on z

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

properties of squeezing functions and global transformations of bounded domains the central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains we prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary in fact such an estimate is proved for the squeezing function on any domain near its globally strongly convex boundary points we also study the stability of squeezing functions on a sequence of bounded domains and give comparisons of intrinsic measures and metrics on bounded domains in terms of squeezing functions as applications we give new and simple proofs of several well known results about geometry of strongly pseudoconvex do mains and prove that all cartan hartogs domains are homogenous regular finally some related problems that ask for further study are proposed

variation diminishing transformations a direct approach to total positivity and its statistical applications abstract karlin has shown that the variation diminishing property possessed by totally positive distributions allows a unified and straightforward presentation of many basic properties of hypothesis tests his work in fact reveals that total positivity is equivalent to a suitably formulated variation diminishing property this largely expository article begins with the latter concept and consequently gives a more direct account of the theory this approach avoids the extensive mathematical preliminaries previously required and isolates the more important statistical property

explicit formulas of the bergman kernel for 3 dimensional complex ellipsoids abstract in this paper we obtain the closed forms of some hypergeometric functions with half integer values of parameters as an application we obtain the explicit forms of the bergman kernel functions for complex ellipsoids z 1 z 2 z 3 c 3 z 1 4 z 2 4 z 3 4 1 and z 1 z 2 z 3 c 3 z 1 4 z 2 4 z 3 2 1 we also investigate the boundary behavior of the bergman kernel functions near some weakly pseudoconvex boundary points

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

establishing consistent and realistic reorder intervals in production distribution systems the objective of this paper is to present a model and algorithm that can be used to find consistent and realistic reorder intervals for each item in large scale production distribution systems we assume such systems can be represented by directed acyclic graphs demand for each end item is assumed to occur at a constant and continuous rate production is instantaneous and no backorders are allowed both fixed setup costs and echelon holding costs are charged at each stage we limit our attention to nested and stationary policies furthermore we restrict the reorder interval for each stage to be a power of 2 times a base planning period the model that results from these assumptions is an integer nonlinear programming problem the optimal solution can be found using the proposed algorithm which is a polynomial time algorithm a real world example is given to illustrate the procedure

excess mass estimates and tests for multimodality abstract we propose and study a method for analyzing the modality of a distribution the method is based on the excess mass functional this functional measures excessive empirical mass in comparison with multiples of uniform distribution by the excess mass approach we separate the investigation about the number of modes from questions concerning their location for distributions on the line the excess mass functional can be estimated at a square root rate the asymptotic behavior of estimators is studied and tests for multimodality based on the excess mass are derived

bootstrap simultaneous error bars for nonparametric regression simultaneous error bars are constructed for nonparametric kernel estimates of regression functions the method is based on the bootstrap where resampling is done from a suitably estimated residual distribution the error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints applications to an economic problem are given and comparison to both pointwise and bonferroni type bars is presented through a simulation study

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

nonparametric testing of the existence of modes given a set of data drawn from an unknown density it is frequently desirable to estimate the number and location of modes of the density a test is proposed for the weight of evidence of individual observed modes the test statistic used is a measure of the size of the mode the absolute integrated difference between the estimated density and the same density with the mode in question excised at the level of the higher of its two surrounding antimodes samples are simulated from a conservative member of the composite null hypothesis to estimate p values within a monte carlo setting such a test can be used with the graphical mode tree of minnotte and scott to examine in a locally adaptive fashion not only the reality of individual modes but also roughly the overall number of modes of the density a proof of consistency of the test statistic is offered and simulation results are presented

classification based on hybridization of parametric and nonparametric classifiers parametric methods of classification assume specific parametric models for competing population densities e g gaussian population densities can lead to linear and quadratic discriminant analysis and they work well when these model assumptions are valid violation in one or more of these parametric model assumptions often leads to a poor classifier on the other hand nonparametric classifiers e g nearest neighbor and kernel based classifiers are more flexible and free from parametric model assumptions but the statistical instability of these classifiers may lead to poor performance when we have small numbers of training sample observations nonparametric methods however do not use any parametric structure of population densities therefore even when one has some additional information about population densities that important information is not used to modify the nonparametric classification rule this paper makes an attempt to overcome these limitations of parametric and nonparametric approaches and combines their strengths to develop some hybrid classification methods we use some simulated examples and benchmark data sets to examine the performance of these hybrid discriminant analysis tools asymptotic results on their misclassification rates have been derived under appropriate regularity conditions

on the role of the shrinkage parameter in local linear smoothing it has been shown that local linear smoothing possesses a variety of very attractive properties not least being its mean square performance however such results typically refer only to asymptotic mean squared error meaning the mean squared error of the asymptotic distribution and in fact the actual mean squared error is often infinite see seifert and gasser 1996 this difficulty may be overcome by shrinking the local linear estimator towards another estimator with bounded mean square however that approach requires information about the size of the shrinkage parameter from at least a theoretical viewpoint very little is known about the effects of shrinkage in particular it is not clear how small the shrinkage parameter may be chosen without affecting first order properties or whether infinitely supported kernels such as the gaussian require shrinkage in order to achieve first order optimal performance in the present paper we provide concise and definitive answers to such questions in the context of general ridged and shrunken local linear estimators we produce necessary and sufficient conditions on the size of the shrinkage parameter that ensure the traditional mean squared error formula we show that a wide variety of infinitely supported kernels with tails even lighter than those of the gaussian kernel do not require any shrinkage at all in order to achieve traditional first order optimal mean square performance

rigidity of proper holomorphic mappings between equidimensional hua domains hua domain named after chinese mathematician loo keng hua is defined as a domain in mathbb c n fibered over an irreducible bounded symmetric domain omega subset mathbb c d with the fiber over z in omega being a n d dimensional generalized complex ellipsoid sigma z in general a hua domain is a nonhomogeneous bounded pseudoconvex domain without smooth boundary the purpose of this paper is twofold firstly we obtain what seems to be the first rigidity results on proper holomorphic mappings between two equidimensional hua domains secondly we determine the explicit form of the biholomorphisms between two equidimensional hua domains as a special conclusion of this paper we completely describe the group of holomorphic automorphisms of the hua domain

determining optimal reorder intervals in capacitated production distribution systems the problem of determining consistent and realistic reorder intervals in complex production distribution environments was formulated as a large scale nonlinear integer programming problem by maxwell and muckstadt maxwell w l j a muckstadt 1985 establishing consistent and realistic reorder intervals in production distribution systems oper res 33 6 november december 1316 1341 they show how the special structure of the problem permits its solution by a standard network flow algorithm in this paper we review the maxwell muckstadt model provide necessary and sufficient conditions that characterize the solution and show that the optimal partition of nodes in the production distribution network is invariant to an arbitrary scaling of the set up and holding cost parameters we consider two capacitated versions of the model one with a single constrained work center and the other with multiple constrained work centers for single constraint problems the invariance corollary provides a simp

function spaces and reproducing kernels on bounded symmetric domains there are several natural hilbert spaces of holomorphic functions on a bounded symmetric domain such are the bergman type spaces on which the holomorphic discrete series operates and the hardy type spaces which are related to the analytic continuation of the holomorphic discrete series also closely related is the bergmann space of entire functions on the ambient which arises as the closure of the polynomials with respect to a natural inner product the space of holomorphic polynomials decomposes into irreducible subspaces under the action of the isotropy group k of the domain the main facts about this decomposition were proved by schmid 21 for another proof see 22 each irreducible subspace contains a unique normalized l invariant spherical polynomial where l is the isotropy group of the shilov boundary in k our first main result is the explicit computation of the norms of the spherical polynomials with respect to each of the hilbert spaces considered for the domains of classical type they were considered by hua 9 and for some of the hilbert spaces this was done before by upmeier 24 using different methods for certain others there are partial results in 22 we are able to do this in a fairly simple unified way by making strong use of gindikin s generalized gamma function s next we obtain a description of the reproducing kernels of the k irreducible subspaces in each of our hilbert spaces and an expansion in terms of these for

the explicit forms and zeros of the bergman kernel function for hartogs type domains abstract we define the cartan hartogs domain which is the hartogs type domain constructed over the product of bounded hermitian symmetric domains and compute the explicit form of the bergman kernel for the cartan hartogs domain using the virtual bergman kernel as the main contribution of this paper we show that the main part of the explicit form of the bergman kernel is a polynomial whose coefficients are combinations of stirling numbers of the second kind using this observation as an application we give an algorithmic procedure to determine the condition that their bergman kernel functions have zeros

lu qi keng s problem on some complex ellipsoids abstract in this note we give an improvement on the bergman kernel for the domain w z c m c n w m 2 p z n 2 1 as an application we describe how the zeroes of the kernel depend on the defining parameters p m n we also consider the domain w z c 2 w 4 z 4 1

some asymptotics for multimodality tests based on kernel density estimates a test due to b w silverman for modality of a probability density is based on counting modes of a kernel density estimator and the idea of critical smoothing an asymptotic formula is given for the expected number of modes this together with other methods establishes the rate of convergence of the critically smoothed bandwidth these ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values

applied smoothing techniques for data analysis the kernel approach with s plus illustrations 1 density estimation for exploring data 2 density estimation for inference 3 nonparametric regression for exploring data 4 inference with nonparametric regression 5 checking parametric regression models 6 comparing regression curves and surfaces 7 time series data 8 an introduction to semiparametric and additive models references

lp regularity of the bergman projection on domains covered by the polydisc abstract if a bounded domain can be covered by the polydisc through a rational proper holomorphic map then the bergman projection is l p bounded for p in a non trivial interval depending on the ramified rational covering this result can be applied to the symmetrized polydisc and to the hartogs triangle with exponent

constructing diffeomorphic representations for the groupwise analysis of nonrigid registrations of medical images groupwise nonrigid registrations of medical images define dense correspondences across a set of images defined by a continuous deformation field that relates each target image in the group to some reference image these registrations can be automatic or based on the interpolation of a set of user defined landmarks but in both cases quantifying the normal and abnormal structural variation across the group of imaged structures implies analysis of the set of deformation fields we contend that the choice of representation of the deformation fields is an integral part of this analysis this paper presents methods for constructing a general class of multi dimensional diffeomorphic representations of deformations we demonstrate for the particular case of the polyharmonic clamped plate splines that these representations are suitable for the description of deformations of medical images in both two and three dimensions using a set of two dimensional annotated mri brain slices and a set of three dimensional segmented hippocampi with optimized correspondences the class of diffeomorphic representations also defines a non euclidean metric on the space of patterns and for the case of compactly supported deformations on the corresponding diffeomorphism group in an experimental study we show that this non euclidean metric is superior to the usual ad hoc euclidean metrics in that it enables more accurate classification of legal and illegal variations

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

improved rounding procedures for the discrete version of the capacitated eoq problem we consider a transportation problem where different products have to be shipped from an origin to a destination by means of vehicles with given capacity the production rate at the origin and the demand rate at the destination are constant over time and identical for each product the problem consists in deciding when to make the shipments and how to fill the vehicles with the objective of minimizing the sum of the average transportation and inventory costs at the origin and at the destination over an infinite horizon this problem is the well known capacitated eoq economic order quantity problem and has an optimal solution in closed form in this paper we study a discrete version of this problem in which shipments are performed only at multiples of a given minimum time it is known that rounding off the optimal solution of the capacitated eoq problem to the closest lower or upper integer value gives a tight worst case ratio of 2 while the best among the possible single frequency policies has a performance ratio of 5 3 we show that the 5 3 bound can be obtained by a single frequency policy based on a rounding procedure which considers classes of instances and for each class identifies a shipping frequency by rounding off in a different way the optimal solution of the capacitated eoq problem moreover we show that the bound can be reduced to 3 2 by using two shipping frequencies obtained by a rounding procedure in one class of instances only