using polygons to recognize and locate partially occluded objects we present computer vision algorithms that recognize and locate partially occluded objects the scene may contain unknown objects that may touch or overlap giving rise to partial occlusion the algorithms revolve around a generate test paradigm the paradigm iteratively generates and tests hypotheses for compatibility with the scene until it identifies all the scene objects polygon representations of the object s boundary guide the hypothesis generation scheme choosing the polygon representation turns out to have powerful consequences in all phases of hypothesis generation and verification special vertices of the polygon called corners help detect and locate the model in the scene polygon moment calculations lead to estimates of the dissimilarity between scene and model corners and determine the model corner location in the scene an association graph represents the matches and compatibility constraints extraction of the largest set of mutually compatible matches from the association graph forms a model hypothesis using a coordinate transform that maps the model onto the scene the hypothesis gives the proposed model s location and orientation hypothesis verification requires checking for region consistency the union of two polygons and other polygon operations combine to measure the consistency of the hypothesis with the scene experimental results give examples of all phases of recognizing and locating the objects

testing for arch in the presence of a possibly misspecified conditional mean abstract ever since the development of the autoregressive conditional heteroskedasticity arch model engle 1982 testing for the presence of arch has become a routine diagnostic one popular method of testing for arch is t times the r2 from a regression of the squared residuals on p of its lags this test has been shown to have a lagrange multiplier interpretation and is asymptotically distributed as a 2 p random variable underlying this test is the assumption of a correctly specified conditional mean in this paper we consider the properties of the arch test when there is a possibly misspecified conditional mean examples of misspecification include omitted variables structural change and parameter instability we show that in general misspecification will lead to overrejection of the null hypothesis of conditional homoskedasticity we demonstrate the use of recursive residuals to improve the fit of a first stage conditional mean regression we illustrate these results via monte carlo simulations and consider two empirical examples

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

natural representations for straight lines and the hough transform on discrete arrays the grid of discrete sampled data points in a digital image supports a limited set of lines at angles and displacements natural to that grid the effect of this implicit line quantization on the parametrization of the hough transform is presented the function describing the discrete hough transforms line detection sensitivity is derived expressions for the orientation frequency and popularity of lines in the natural set are given the results obtained are of importance to data arrays of small size the distribution of lines in the natural set is also important as it determines the precision and reliability with which straight lines can be measured on a discrete imaging array from the natural line set concept a general a d slope offset straight line parametrization is developed for which the hough transform is compact and fast to compute and which is as easy to interpret as the class p theta parametrization

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

boolean compressed sensing and noisy group testing the fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests measurements the key contribution of this paper is in adopting a new information theoretic perspective on group testing problems we formulate the group testing problem as a channel coding decoding problem and derive a single letter characterization for the total number of tests used to identify the defective set although the focus of this paper is primarily on group testing our main result is generally applicable to other compressive sensing models

rank tests for changepoint problems summary we consider procedures based on quadratic form rank statistics to test for one or more changepoints in a series of independent observations models incorporating both smooth and abrupt changes are introduced various test statistics are suggested their asymptotic null distributions are derived and tables of significance points are given a monte carlo study shows that the asymptotic significance points are applicable to moderately sized samples

an adaptive reduction procedure for the piecewise linear approximation of digitized curves a new algorithm is presented for the piecewise linear approximation of two dimensional digitized curves against a square grid the algorithm utilizes an adaptive reduction procedure in two approximation phases to select the critical points of a digitized curve such that the deviation from the digitized curve to its final approximated curve is bounded by a uniform error tolerance the time complexity of this algorithm is o m sup 2 rather than o n sup 2 on the theoretical plane in the experiments of fixing the initial and the final processing points the performance of the algorithm has been compared to those of three prominent other algorithms regarding the required number of critical points and the total execution time of the program of the four algorithms compared the present algorithm consistently has the shortest execution time of the program and it tends most to require as few critical points as the optimum algorithm that was tested

new constructions of superimposed codes kautz singleton 1964 suggested a class of binary superimposed codes which are based on the q ary reed solomon codes rs codes applying a concatenation of the binary constant weight error correcting codes and the shortened rs codes we obtain new constructions of superimposed codes tables of their parameters are given from the tables it follows that the rate of obtained codes exceeds the corresponding random coding bound

unsupervised clustering in hough space for identification of partially occluded objects an automated approach for template free identification of partially occluded objects is presented the contour of each relevant object in the analyzed scene is modeled with an approximating polygon whose edges are then projected into the hough space a structurally adaptive self organizing map neural network generates clusters of collinear and or parallel edges which are used as the basis for identifying the partially occluded objects within each polygonal approximation results on a number of cases under different conditions are provided

residual based rank specification tests for ar garch type models this paper derives the asymptotic distribution for a number of rank based and classical residual specification tests in ar garch type models we consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation residual symmetry and no structural breaks we also apply our method to backtesting value at risk for these tests we show that generally no size correction is needed in the asymptotic test distribution when applied to ar garch residuals obtained through gaussian quasi maximum likelihood estimation to be precise we give exact expressions for the limiting null distribution of the test statistics applied to standardized residuals and find that standard critical values often though not always lead to conservative tests for this result we give simple necessary and sufficient conditions simulations show that our asymptotic approximations work well for a large number of ar garch models and parameter values we also show that the rank based tests often though not always have superior power properties over the classical tests even if they are conservative an empirical application illustrates the relevance of these tests to the ar garch models for weekly stock market return indices of some major and emerging countries

serial and nonserial sign and rank statistics asymptotic representation and asymptotic normality the classical theory of rank based inference is entirely based either on ordinary ranks which do not allow for considering location nor intercept parameters or on signed ranks which require an assumption of symmetry if the median in the absence of a symmetry assumption is considered as a location parameter the maximal invariance property of ordinary ranks is lost to the ranks and the signs as shown in hallin and werker 2003 conditioning on a maximal invariant in such situations is essential if semiparametric efficiency is to be reached this new maximal invariant thus suggests a new class of statistics based on ordinary ranks and signs an asymptotic representation theory a la h ajek is developed here for such statistics both in the nonserial and in the serial case the corresponding asymptotic normality results clearly show how the signs are adding a separate contribution to the asymptotic variance hence potentially to asymptotic e ciency applications to semiparametric inference in regression and time series models with median restrictions are treated in detail in a companion paper hallin werker and vermandele 2003

an optimal o n algorithm for identifying line segments from a sequence of chain codes abstract an optimal algorithm for identifying straight lines in chain codes is described the algorithm turns the complicated problem of determining the straightness of digital arcs into a simple task by constructing a passing area around the pixels it also solves the problem of detecting all straight segments from a sequence of chain codes in o n time where n is the length of the sequence it has been found that this algorithm is not only simple and intuitive but also highly efficient

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal processes strong consistency and asymptotic normality of the quasi maximum likelihood estimator qmle are given for a general class of multidimensional causal processes for particular cases already studied in the literature for instance univariate or multivariate garch arch arma garch processes the assumptions required for establishing these results are often weaker than existing conditions the qmle asymptotic behavior is also given for numerous new examples of univariate or multivariate processes for instance tarch or nlarch processes

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

a consistent test for conditional symmetry in time series models the assumption of conditional symmetry is often invoked to validate adaptive estimation and consistent estimation of arch garch models by quasi maximum likelihood imposing conditional symmetry can increase the efficiency of bootstraps if the symmetry assumption is valid this paper proposes a procedure for testing conditional symmetry the proposed test does not require the data to be stationary or i i d and the dimension of the conditional variables can be infinite the proposed test is consistent and is asymptotically distribution free in addition the test is shown to have nontrivial power against root t local alternatives the size and power of the test are satisfactory even for small samples applying the test to various time series we reject conditional symmetry in inflation exchange rate and stock returns among the nonfinancial time series considered we find that investment the consumption of durables and manufacturing employment also reject conditional symmetry

diagnostic checking in arma models with uncorrelated errors we consider tests for lack of fit in arma models with nonindependent innovations in this framework the standard box pierce and ljung box portmanteau tests can perform poorly specifically the usual text book formulas for asymptotic distributions are based on strong assumptions and should not be applied without careful consideration in this article we derive the asymptotic covariance matrix of a vector of autocorrelations for residuals of arma models under weak assumptions on the noise the asymptotic distribution of the portmanteau statistics follows a consistent estimator of and a modification of the portmanteau tests are proposed this allows us to construct valid asymptotic significance limits for the residual autocorrelations and asymptotically valid goodness of fit tests when the underlying noise process is assumed to be noncorrelated rather than independent or a martingale difference a set of monte carlo experiments and an application to the standard poor 500 returns illustrate the p

edge replacement in the recognition of occluded objects abstract the generalized hough transform recognizes objects more successfully when all edges are visible to facilitate recognition this paper introduces a preliminary generalized hough process that restores edges which were invisible because of occlusion or because of lack of contrast between occluding and occluded areas space and time complexity of generalized hough processes are reduced by chained hashing techniques experimental results show that recognition of occluded objects via a generalized hough transform is improved if occluding objects are first recognized and subtracted out of the input picture and occluded edges are then reconstructed prior to recognition of occluded objects

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

a complete class of tests when the likelihood is locally asymptotically quadratic we construct an asymptotically complete class of tests i e for a test not within this class one can find a test within the class that has a better or equal asymptotical power function for testing one parametric restriction when the likelihood function can be approximated by a quadratic function asymptotically the coefficients of this quadratic form may be random variables so that our results apply to the problem of unit root testing we show that the lr test in the case of unit roots the df test is not within this class

combinatorial properties of frameproof and traceability codes in order to protect copyrighted material codes may be embedded in the content or codes may be associated with the keys used to recover the content codes can offer protection by providing some form of traceability ta for pirated data several researchers have studied different notions of ta and related concepts in previous years strong versions of ta allow at least one member of a coalition that constructs a pirate decoder to be traced weaker versions of this concept ensure that no coalition can frame a disjoint user or group of users all these concepts can be formulated as codes having certain combinatorial properties we study the relationships between the various notions and we discuss equivalent formulations using structures such as perfect hash families we use methods from combinatorics and coding theory to provide bounds necessary conditions and constructions sufficient conditions for the objects of interest

optimal test for markov switching parameters this paper proposes a class of optimal tests for the constancy of parameters in random coefficients models our testing procedure covers the class of hamilton s models where the parameters vary according to an unobservable markov chain but also applies to nonlinear models where the random coefficients need not be markov we show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate therefore standard approaches do not apply we use bartlett type identities for the construction of the test statistics this has several desirable properties first it only requires estimating the model under the null hypothesis where the parameters are constant second the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function we derive the asymptotic distribution of our test under the null and local alternatives asymptotically valid bootstrap critical values are also proposed

recognition of occluded objects a cluster structure algorithm clustering techniques have been used to perform image segmentation to detect lines and curves in images and to solve several other problems in pattern recognition and image analysis in this paper we apply clustering methods to a new problem domain and present a new method based on a cluster structure approach for the recognition of 2 d partially occluded objects basically the technique consists of three steps clustering of border segment transformations finding continuous sequences of segments in appropriately chosen clusters and clustering of sequence average transformation values as compared to some of the earlier methods which identify an object based on only one sequence of matched segments the new approach allows the identification of all parts of the model which match in the occluded scene we also discuss the application of the clustering techniques to 3 d scene analysis in both cases the cluster structure algorithm entails the application of clustering concepts in a hierarchical manner resulting in a decrease in the computational effort as the recognition algorithm progresses the implementation of the techniques discussed for the 2 d case has been completed and the algorithm has been evaluated with respect to a large number of examples where several objects partially occlude one another the method is able to tolerate a moderate change in scale and a significant amount of shape distortion arising as a result of segmentation and or the polygonal approximation of the boundary of the object a summary of the results is presented

on the optimality of the kautz singleton construction in probabilistic group testing we consider the probabilistic group testing problem where d random defective items in a large population of n items are identified with high probability by applying binary tests it is known that the theta d log n tests are necessary and sufficient to recover the defective set with vanishing probability of error when d o n alpha for some alpha in 0 1 however to the best of our knowledge there is no explicit deterministic construction achieving theta d log n tests in general in this paper we show that a famous construction introduced by kautz and singleton for the combinatorial group testing problem which is known to be suboptimal for combinatorial group testing for moderate values of d achieves the order optimal theta d log n tests in the probabilistic group testing problem when d omega log 2 n this provides a strongly explicit construction achieving the order optimal result in the probabilistic group testing setting for a wide range of values of d to prove the order optimality of kautz and singleton s construction in the probabilistic setting we provide a novel analysis of the probability of a non defective item being covered by a random defective set directly rather than arguing from combinatorial properties of the underlying code which has been the main approach in the literature furthermore we use a recursive technique to convert this construction into one that can also be efficiently decoded with only a log log factor increase in the number of tests

nonadaptive group testing with random set of defectives in a group testing scheme a series of tests are designed to identify a small number t of defective items that are present among a large number n of items each test takes a group of items as input and produces a binary output indicating whether any defective item is present in the group in a non adaptive scheme the tests have to be designed in one shot in this setting designing a testing scheme is equivalent to the construction of a disjunct matrix an m times n binary matrix where the union of supports of any t columns does not contain the support of any other column in principle one wants to have such a matrix with a minimum possible number m of rows in this paper we consider the scenario where defective items are random and follow simple probability distributions in particular we consider the cases where 1 each item can be defective independently with probability frac t n and 2 each t set of items can be defective with uniform probability in both the cases our aim is to design a testing matrix that successfully identifies the set of defectives with high probability both of these models have been studied in the literature before and it is known that theta t log n tests are necessary as well as sufficient via random coding in both the cases our main focus is explicit deterministic construction of the test matrices amenable to above scenarios one of the most popular ways of constructing test matrices relies on constant weight error correcting codes and their minimum distance in particular it is known that codes result in test matrices with o t 2 log n rows that identify any t defectives we go beyond the minimum distance analysis and connect the average distance of a constant weight code to the parameters of the resulting test matrix indeed we show how distance a pairwise property of the columns of the matrix translates to a t 1 wise property of the columns with our relaxed requirements we show that using explicit constant weight codes e g based on algebraic geometry codes we may achieve a number of tests equal to o t log 2 n log t for both the first and second cases while only away by a factor of log n log t from the optimal number of tests this is the best set of parameters that one can obtain from a deterministic construction and our main contribution lies in relating the group testing properties to the average and minimum distances of constant weight codes

evaluating garch models in this paper a unified framework for testing the adequacy of an estimated garch model is presented parametric lagrange multiplier lm or lm type tests of no arch in standardized errors linearity and parameter constancy are proposed the asymptotic null distributions of the tests are standard which makes application easy versions of the tests that are robust against nonnormal errors are provided the finite sample properties of the test statistics are investigated by simulation the robust tests prove superior to the nonrobust ones when the errors are nonnormal they also compare favourably in terms of power with misspecification tests previously proposed in the literature

born again group testing multiaccess communications a brief summary of the basic notions of group testing is presented together with a brief historical account one of the early papers on group testing is shown to include a description of the tree search polling algorithm of hayes the classical group testing problem is formulated including a criterion for optimality of test plans a restricted class of tests called nested testing is described and a complete description for an optimal nested strategy is given for both a finite number and an infinite number of bernoulli distributed random variables a generalization of group testing applicable to the random access communications problem is presented

semiparametric efficient adaptive estimation of asymmetric garch models abstract in this paper we derive a semiparametric efficient adaptive estimator of an asymmetric garch model applying some general results from drost et al 1997 the annals of statistics 25 786 818 we first estimate the unknown density function of the disturbances by kernel methods then apply a one step newton raphson method to obtain a more efficient estimator than the quasi maximum likelihood estimator the proposed semiparametric estimator is adaptive for parameters appearing in the conditional standard deviation model with respect to the unknown distribution of the disturbances

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

the efficiency of the estimators of the parameters in garch processes we propose a class of estimators for the parameters of a garch p q sequence we show that our estimators are consistent and asymptotically normal under mild conditions the quasi maximum likelihood and the likelihood estimators are discussed in detail we show that the maximum likelihood estimator is optimal if the tail of the distribution of the innovations is polynomial even a quasi maximum likelihood estimator based on exponential density performs better than the standard normal density based quasi likelihood estimator of lee and hansen and lumsdaine