reinforced random walk leta i i 1 be a sequence of nonnegative numbers difine a nearest neighbor random motion overrightarrow x x 0 x 1 on the integers as follows initially the weight of each interval i i 1 i an integer equals 1 if at timen an interval i i 1 has been crossed exactlyk times by the motion its weight is 1 sum limits j 1 k a j given x 0 x 1 x n i0 i1 in the probability thatx n 1 isi n 1 ori n 1 is proportional to the weights at timen of the intervals i n 1 i n and i n iin 1 we prove that overrightarrow x either visits all integers infinitely often a s or visits a finite number of integers eventually oscillating between two adjacent integers a s and that mathop lim limits n to infty x n n 0 a s for much more general reinforcement schemes we provep overrightarrow x visits all integers infinitely often p overrightarrow x has finite range 1

drawing the complexity of colombian climate from non extensive extreme behavior abstract we evaluate the complexity of the colombian climate from extreme behavior of gauge temperature and precipitation using the novel tsallis non extensive entropy principle based on physical information we find the spatial structure of non additive universal categories q index and compare them with some complex systems with the potential to have some degree of dynamical affinity our results evidence the high dynamical variability of regional climate expressed in the broad range of values of q index and the high degree of non extensivity for both temperature and precipitation

incomplete generalized l statistics given data x 1 x n and a kernel h with m arguments serfling introduced the class of generalized l statistics gl statistics which is defined by taking linear combinations of the ordered h x i1 x im where i 1 i m ranges over all n n m distinct m tuples of 1 n in this paper we derive a class of incomplete generalized l statistics igl statistics by taking linear combinations of the ordered elements from a subset of h x i1 x im with size n n a special case is the class of incomplete u statistics introduced by blom under very general conditions the igl statistic is asymptotically equivalent to the gl statistic as soon as n n n as n which makes the igl much more computationally feasible we also discuss various ways of selecting the subset of h x i x im several examples are discussed in particular some new estimates of the scale parameter in nonparametric regression are introduced it is shown that these estimates are asymptotically equivalent to an igl statistic some extensions for example functionals other than l and multivariate kernels are also addressed

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

a new and efficient estimation method for the generalized pareto distribution the generalized pareto distribution gpd is widely used to model extreme values for example exceedences over thresholds in modeling floods existing methods for estimating parameters have theoretical or computational defects an efficient new estimator is proposed which is computationally easy free from the problems observed in traditional approaches and performs well compared with existing estimators a numerical example involving heights of waves is used to illustrate the various methods and tests of fit are performed to compare them

limit theorems for functionals of mixing processes with applications to u statistics and dimension estimation in this paper we develop a general approach for investigating the asymptotic distribution of functional xn f zn k k z of absolutely regular stochastic processes zn n z such functional occur naturally as orbits of chaotic dynamical systems and thus our results can be used to study probabilistic aspects of dynamical systems we first prove some moment inequalities that are analogous to those for mixing sequences with their help several limit theorems can be proved in a rather straightforward manner we illustrate this by re proving a central limit theorem of ibragimov and linnik then we apply our techniques to u statistics matrix equation with symmetric kernel h r r r we prove a law of large numbers extending results of aaronson burton dehling gilat hill and weiss for absolutely regular processes we also prove a central limit theorem under a different set of conditions than the known results of denker and keller as our main application we establish an invariance principle for u processes un h h indexed by some class of functions we finally apply these results to study the asymptotic distribution of estimators of the fractal dimension of the attractor of a dynamical system

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

a sensitivity analysis of the music algorithm a first order analysis of the sensitivity of the music algorithm to system errors which cause differences between the array manifold used by music and the true array manifold is presented the effect of such errors on the direction of arrival estimates is investigated the ability of the music algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or the receivers or errors in the element locations is analyzed a formula for computing the failure threshold of music as a function of source separation and other system parameters is derived and tested by simulation the analysis assumes that the exact covariance matrix of array element outputs is known the infinite data case

asymptotic performance of optimal gain and phase estimators of sensor arrays for estimating angles of arrival there are three well known algorithms weighted noise subspace fitting wnsf unconditional maximum likelihood uml and conditional maximum likelihood cml these algorithms can also be used for estimating calibrating the gains and phases of sensor arrays assuming the angles of arrival are known we show that the wnsf algorithm with an optimal weight has the same statistical efficiency as the uml algorithm but more efficient than the cml algorithm this conclusion was known for angles of arrival estimation and is now confirmed for gains and phases calibration computationally the wnsf algorithm is shown to be more attractive than the other two as it can be implemented via a quadratic minimization procedure for arbitrarily shaped arrays

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

functional limit theorems for u processes un processus u est une collection de statistiques u indicees par une famille de noyaux symetriques on utilise la theorie limite classique pour demontrer pour le processus u des analogues du theoreme central limite pour les processus empiriques

quadrature receiver mismatch calibration this article introduces nonlinear regression techniques to estimate gain and phase mismatches between the in phase i and quadrature q branches of a quadrature receiver under modest assumptions the system intrinsically follows a nonlinear regression model the algorithm is effective easily implemented customizable and requires few assumptions large sample jackknife and bootstrap techniques provide on line error assessment and parameter inference

estimation of sensor gain and phase the problem of estimating the direction independent gain and phase characteristics of an array of sensors using knowledge of the true field covariance at the sensor locations is considered a concise expression for the log likelihood function is derived and several mathematical properties of this objective function are given the cramer rao c r lower bounds on the variances of gain and phase estimates are derived with the plane wave in isotropic noise considered as a special case the maximum likelihood estimates are shown to be consistent asymptotically efficient and asymptotically normal a simple estimator is proposed which is consistent and which gives good initial estimates for a newton algorithm for finding the maximum likelihood solution comparison of the maximum likelihood estimates and the c r bounds is given for the plane wave in isotropic noise example

brownian motion and random walk perturbed at extrema let bt be brownian motion we show there is a unique adapted process xt which satisfies dxt dbt except when xt is at a maximum or a minimum when it receives a push the magnitudes and directions of the pushes being the parameters of the process for some ranges of the parameters this is already known we show that if a random walk close to bt is perturbed properly its paths are close to those of xt

a review of goodness of fit tests for pareto distributions abstract pareto distributions are the most popular models in economics and finance hence it is essential to have a wide spectrum of tools for checking their goodness of fit to a given data set this paper provides the first review of known goodness of fit tests for pareto distributions over twenty tests are reviewed their powers are compared by simulation

a robust analysis of crossover designs using multisample generalized l statistics abstract in a crossover study some or all subjects receive more than one treatment sequentially using a clinical example as motivation we develop multisample generalized l statistics gl statistics to estimate and test for treatment effects in crossovers when the distribution of the response data deviates from normality the basic idea is to adapt simple l statistics such as the trimmed mean and median to data with dependencies gl statistics may be applied to crossovers with more than two periods and or sequences these designs are useful for experiments with two treatments in which carryover and treatment effects might be aliased in the commonly used two period two sequence design as well as for experiments with more than two treatments for data analysis with large samples the asymptotic properties of the gl statistics suggest that the generalized trimmed mean and generalized median often should be strongly consistent and normal a simulation study of a four sequence two period crossover desi

generalized ray knight theory and limit theorems for self interacting random walks on mathbb z 1 we consider non markovian self interacting random walks sirw on the one dimensional integer lattice the walk starts from the origin and at each step jumps to a neighboring site the probability of jumping along a bond is proportional to number of previous jumps along that lattice bond where n r is a monotone weight function exponential and subexponential weight functions were considered in earlier papers in the present paper we consider weight functions with polynomial asymptotics these weight functions define variants of the reinforced random walk we prove functional limit theorems for the local time processes of these random walks and local limit theorems for the position of the random walker at late times a generalization of the ray knight theory of local time arises

numerically stable and efficient algorithm for vector channel parameter and frequency offset estimation in this paper we present a novel and numerically efficient algorithm for vector channel and calibration vector estimation which works when frequency offset error caused by either unstable oscillator or doppler effect is present in spread spectrum antenna system we propose an estimation algorithm based on gauss seidal algorithm rather than using eigen decomposition or svd in computing eigenvalues and eigenvectors at each iteration the algorithm is based on the two step procedures one for estimating both channel and frequency offset and the other for estimating the unknown array gain and phase consequently estimates of the doas the multi path impulse response of the reference signal source and the carrier frequency offset as well as the calibration of antenna array are provided the analytic performance improvement in multiplications number is presented the performance of the proposed algorithm is investigated by means of computer simulations throughout the analytic and computer simulation we show that the proposed algorithm reduces the number of multiplications by order of one

longcrisp a test for bump hunting in longitudinal data we propose an extension of the harezlak and heckman j comput graph statist 2001 10 4 713 729 test for detecting local extrema to the longitudinal data setting we use penalized spline regression techniques statist sci 1996 11 89 102 to provide a computationally efficient method of testing for relatively large data sets we estimate the p values of our test longcrisp with a smoothed bootstrap our simulation studies indicate that the test is generally conservative and has power exceeding 70 per cent at the alpha 0 1 nominal level in most considered settings finally we apply our testing procedure to the longitudinal measurements of body mass index of former prisoners of war in vietnam and conclude that the mean population curve exhibits non monotone behaviour

estimating densities of functions of observations abstract density estimates such as histograms and more sophisticated versions are important in applied and theoretical statistics in applied statistics a density estimate gives the data analyst a graphical overview of the shape of the distribution this overview allows the data analyst to arrive immediately at a qualitative impression of the location scale and various aspects of the extremes of the distribution in theoretical statistics the shape of the density allows the researcher to link the data to families of curves perhaps indexed parametrically by estimating a density nonparametrically certain aspects of the data can be viewed without the restriction of a priori imposing limitations of a class of parametric curves in this article we introduce density estimation for functions of observations to motivate the study one type of function used is the interpoint distance between observations arising in spatial statistics from the fields of biometry and regional science a second type of func

the relationship between hadamard and conventional multiplication for positive definite matrices abstract it is known that if a is positive definite hermitian then a a 1 i in the positive semidefinite ordering our principal new result is a converse to this inequality under certain weak regularity assumptions about a function f on the positive definite matrices a f a af a for all positive definite a if and only if f a is a positive multiple of a 1 in addition to the inequality a a 1 i it is known that a a 1 t i and stronger that min a b min ab t for a b positive definite hermitian we also show that min a b min ab and note that min ab and min ab t can be quite different for a b positive definite hermitian we utilize a simple technique for dealing with the hadamard product which relates it to the conventional product and which allows us to give especially simple proofs of the closure of the positive definites under hadamard multiplication and of the inequalities mentioned

reinforced brownian motion a prototype we analyze the brownian motion limit of a prototypical unit step reinforced random walk on the half line a reinfoced random walk is one which changes the weight of any edge or vertex visited to increase the frequency of return visits the generating function for the discrete case is first derived for the joint probability distribution of s n the location of the walker at the n th step and a n the maximum location the walker achieved in n steps then the bulk of the analysis concerns the statistics of the limiting brownian walker and of its environment both parametrized by the amplitude delta of the reinforcement the walker marginal distribution can be interpreted as that of free diffusion with a source serving as a diffusing soft confinement details depending very much on the value of 1 delta infty

a goodness of fit statistic for pareto type behaviour the fit of a statistical model can be visually assessed by inspection of a quantile quantile or qq plot for the strict pareto distribution since log transformed pareto random variables are exponentially distributed it is natural to consider an exponential quantile plot based on the log transformed data in case the data originate from a pareto type distribution the pareto quantile plot will be linear but only in some of the largest observations in this paper we modify the jackson statistic originally proposed as a goodness of fit statistic for testing exponentiality in such a way that it measures the linearity of the k largest observations on the pareto quantile plot further by taking the second order tail behaviour of a pareto type model into account we construct a bias corrected jackson statistic for both statistics the limiting distribution is derived next to these asymptotic results we also evaluate the small sample behaviour on the basis of a simulation study the method is illustrated on two practical case studies

limit theorems for functionals of moving averages let x n i 1 a i e n 1 where the e i are i i d with mean 0 and finite second moment and the a i are either summable or regularly varying with index 1 1 2 the sequence x n has short memory in the former case and long memory in the latter for a large class of functions k a new approach is proposed to develop both central n rate and noncentral non n rate limit theorems for s n n 1 n k x n ek x n specifically we show that in the short memory case the central limit theorem holds for s n and in the long memory case s n can be decomposed into two asymptotically uncorrelated parts that follow a central limit and a non central limit theorem respectively further we write the noncentral part as an expansion of uncorrelated components that follow noncentral limit theorems connections with the usual hermite expansion in the gaussian setting are also explored

once edge reinforced random walk on a tree we consider a nearest neighbor walk on a regular tree with transition probabilities proportional to weights or conductances of the edges initially all edges have weight 1 and the weight of an edge is increased to c 1 when the edge is traversed for the first time after such a change the weight of an edge stays at c forever we show that such a walk is transient for all values of c ge 1 and that the walk moves off to infinity at a linear rate we also prove an invariance principle for the height of the walk

bayesian leave one out cross validation approximations for gaussian latent variable models the future predictive performance of a bayesian model can be estimated using bayesian cross validation in this article we consider gaussian latent variable models where the integration over the latent values is approximated using the laplace method or expectation propagation ep we study the properties of several bayesian leave one out loo cross validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data our main objective is to assess the accuracy of the approximative loo cross validation estimators that is for each method laplace and ep we compare the approximate fast computation with the exact brute force loo computation secondarily we evaluate the accuracy of the laplace and ep approximations themselves against a ground truth established through extensive markov chain monte carlo simulation our empirical results show that the approach based upon a gaussian approximation to the loo marginal distribution the so called cavity distribution gives the most accurate and reliable results among the fast methods

maximum likelihood narrow band direction finding and the em algorithm generalized em expectation maximization algorithms have been derived for the maximum likelihood estimation of the direction of arrival of multiple narrowband signals in noise both deterministic and stochastic signal models are considered the algorithm for the deterministic model yields estimates of the signal amplitudes while that for the stochastic model yields estimates of the powers of the signal both algorithms have the properties that their limit points are stable and satisfy the necessary maximizer conditions for maximum likelihood estimators it is shown via simulation that the maximum likelihood method allows for the resolution of the directions of arrival of signals at angular separation and noise levels for which other high resolution methods will not work algorithm convergence does depend on initial conditions however convergence to a global maximum has been observed in simulation when the initial estimates are within a significant fraction if one beamwidth componentwise of this maximum simulations also show that the deterministic model has a significant impact on the angle estimator performance