asymptotics of r md and lad estimators in linear regression models with long range dependent errors this paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are gaussian or a function of gaussian random variables that are strictly stationary and long range dependent this result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors the latter result in turn yields the asymptotic distribution of the jaeckel 1972 rank estimators the paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent

martingale transforms goodness of fit tests in regression models this paper discusses two goodness of fit testing problems the first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model while the second pertains to fitting a parametric regression model when the error distribution is unknown for the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes the advantage of this transform is that the corresponding tests are asymptotically distribution free for the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms a monte carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes

high moment partial sum processes of residuals in garch models and their applications in this paper we construct high moment partial sum processes based on residuals of a garch model when the mean is known to be 0 we consider partial sums of kth powers of residuals cusum processes and self normalized partial sum processes the kth power partial sum process converges to a brownian process plus a correction term where the correction term depends on the kth moment k of the innovation sequence if k 0 then the correction term is 0 and thus the kth power partial sum process converges weakly to the same gaussian process as does the kth power partial sum of the i i d innovations sequence in particular since 1 0 this holds for the first moment partial sum process but fails for the second moment partial sum process we also consider the cusum and the self normalized processes that is standardized by the residual sample variance these behave as if the residuals were asymptotically i i d we also study the joint distribution of the kth and k 1 st self normalized partial sum processes applications to change point problems and goodness of fit are considered in particular cusum statistics for testing garch model structure change and the jarque bera omnibus statistic for testing normality of the unobservable innovation distribution of a garch model the use of residuals for constructing a kernel density function estimation of the innovation distribution is discussed

inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

yates s correction for continuity and the analysis of 2 2 contingency tables despite recommendations to the contrary medical researchers still routinely use the yates corrected chisquare statistic in analyses of 2 2 contingency tables research has shown that these corrected statistics are overly conservative and that the conventional pearson chi square generally provides adequate control over type i error probabilities this paper makes a straightforward argument against use of yates s correction for continuity and fisher s exact probability test

bootstrap approximations in model checks for regression abstract let m m be a parametric model for an unknown regression function m for example m may consist of all polynomials or trigonometric polynomials with a given bound on the degree to check the full model m i e to test for h 0 m e m it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals in this article we show that the distribution of this process may be approximated by the wild bootstrap the method is applied to simulated datasets as well as to real data

r estimation in semiparametric dynamic location scale models we propose rank based estimation r estimators as an alternative to gaussian quasi likelihood and standard semiparametric estimation in time series models where conditional location and or scale depend on a euclidean parameter of interest while the unspecified innovation density is a nuisance we show how to construct r estimators achieving semiparametric efficiency at some predetermined reference density while preserving root n consistency and asymptotic normality irrespective of the actual density contrary to the standard semiparametric estimators our r estimators neither require tangent space calculations nor innovation density estimation numerical examples illustrate their good performances on simulated and real data

parametric cumulant based phase estimation of 1 d and 2 d nonminimum phase systems by allpass filtering this paper proposes a parametric cumulant based phase estimation method for one dimensional 1 d and two dimensional 2 d linear time invariant lti systems with only non gaussian measurements corrupted by additive gaussian noise the given measurements are processed by an optimum allpass filter such that a single mth order m spl ges 3 cumulant of the allpass filter output is maximum in absolute value it can be shown that the phase of the unknown system of interest is equal to the negative of the phase of the optimum allpass filter except for a linear phase term a time delay for the phase estimation of 1 d lti systems an iterative 1 d algorithm is proposed to find the optimum allpass filter modeled either by an autoregressive moving average arma model or by a fourier series based model for the phase estimation of 2 d lti systems an iterative 2 d algorithm is proposed that only uses the fourier series based allpass model a performance analysis is then presented for the proposed cumulant based 1 d and 2 d phase estimation algorithms followed by some simulation results and experimental results with real speech data to justify their efficacy and the analytic results on their performance finally the paper concludes with a discussion and some conclusions

testing multivariate distributions in garch models in this paper we consider testing distributional assumptions in multivariate garch models based on empirical processes using the fact that joint distribution carries the same amount of information as the marginal together with conditional distributions we first transform the multivariate data into univariate independent data based on the marginal and conditional cumulative distribution functions we then apply the khmaladze s martingale transformation k transformation to the empirical process in the presence of estimated parameters the k transformation eliminates the effect of parameter estimation allowing a distribution free test statistic to be constructed we show that the k transformation takes a very simple form for testing multivariate normal and multivariate t distributions the procedure is applied to a multivariate financial time series data set

testing for multivariate volatility functions using minimum volume sets and inverse regression we propose two new types of nonparametric tests for investigating multivariate regression functions the tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas involving no multivariate nonparametric regression estimation the methods proposed facilitate the investigation for different features such as if a multivariate regression function is i constant ii of a bathtub shape and iii in a given parametric form the inference based on those tests may be further enhanced through associated diagnostic plots although the potential use of those ideas is much wider we focus on the inference for multivariate volatility functions in this paper i e we test for i heteroscedasticity ii the so called smiling effect and iii some parametric volatility models the asymptotic behavior of the proposed tests is investigated and practical feasibility is shown via simulation studies we further illustrate our methods with real financial data

asymptotics of some estimators and sequential residual empiricals in nonlinear time series this paper establishes the asymptotic uniform linearity of m and r scores in a family of nonlinear time series and regression models it also gives an asymptotic expansion of the standardized sequential residual empirical process in these models these results are in turn used to obtain the asymptotic normality of certain classes of m r and minimum distance estimators of the underlying parameters the classes of estimators considered include analogs of hodges lehmann huber and lad least absolute deviation estimators some applications to the change point and testing of the goodness of fit problems in threshold and amplitude dependent exponential autoregression models are also given the paper thus offers a unified functional approach to some aspects of robust inference for a large class of nonlinear time series models

a quasi exact test for comparing two binomial proportions the use of the fisher exact test for comparing two independent binomial proportions has spawned an extensive controversy in the statistical literature many critics have faulted this test for being highly conservative partly in response to such criticism some statisticians have suggested the use of a modified non randomized version of this test namely the mid p value test this paper examines the actual type i error rates of this test for both one sided and two sided tests and for a wide range of sample sizes we show that the actual levels of significance of the mid p test tend to be closer to the nominal level as compared with various classical tests the computational effort required for the mid p test is no more than that needed for the fisher exact test further the basis for its modification is a natural adjustment for discreteness thus the test easily generalizes to r c contingency tables and other discrete data problems

a nonlinear method for robust spectral analysis a nonlinear spectral analyzer called the l p norm periodogram is obtained by replacing the least squares criterion with an l p norm criterion in the regression formulation of the ordinary periodogram in this paper we study the statistical properties of the l p norm periodogram for time series with continuous and mixed spectra we derive the asymptotic distribution of the l p norm periodogram and discover an important relationship with the so called fractional autocorrelation spectrum that can be viewed as an alternative to the power spectrum in representing the serial dependence of a random process in the frequency domain in comparison with the ordinary periodogram p 2 we show that by varying the value of p in the interval 1 2 the l p norm periodogram can strike a balance between robustness against heavy tailed noise efficiency under regular conditions and spectral leakage for time series with mixed spectra we also show that the l p norm periodogram can detect serial dependence of uncorrelated non gaussian time series that cannot be detected by the ordinary periodogram

distribution free specification tests of conditional models this article proposes a class of asymptotically distribution free specification tests for parametric conditional distributions these tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests finally neyman type smooth tests a compromise between directional and omnibus tests are discussed as a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives a small monte carlo study shows that our tests attain the nominal level already for small sample sizes

adaptive l estimation for linear models asymptotically efficient adaptive estimators for the slope parameters of the linear regression model are constructed based upon the regression quantile statistics suggested by koenker and bassett the estimators are natural analogues of the adaptive l estimators of location of sacks but employ kernel density type estimators of the optimal l estimator weight function

video orbits of the projective group a simple approach to featureless estimation of parameters we present direct featureless methods for estimating the eight parameters of an exact projective homographic coordinate transformation to register pairs of images together with the application of seamlessly combining a plurality of images of the same scene resulting in a single image or new image sequence of greater resolution or spatial extent the approach is exact for two cases of static scenes 1 images taken from the same location of an arbitrary three dimensional 3 d scene with a camera that is free to pan tilt rotate about its optical axis and zoom or 2 images of a flat scene taken from arbitrary locations the featureless projective approach generalizes interframe camera motion estimation methods that have previously used a camera model which lacks the degrees of freedom to exactly characterize such phenomena as camera pan and tilt and or which have relied upon finding points of correspondence between the image frames the featureless projective approach which operates directly on the image pixels is shown to be superior in accuracy and the ability to enhance the resolution the proposed methods work well on image data collected from both good quality and poor quality video under a wide variety of conditions sunny cloudy day night these new fully automatic methods are also shown to be robust to deviations from the assumptions of static scene and no parallax

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

least absolute deviation estimation for all pass time series models an autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all pass time series model all pass models generate uncorrelated white noise time series but these series are not independent in the non gaussian case an approximation to the likelihood of the model in the case of laplacian two sided exponential noise yields a modified absolute deviations criterion which can be used even if the underlying noise is not laplacian asymptotic normality for least absolute deviation estimators of the model parameters is established under general conditions behavior of the estimators in finite samples is studied via simulation the methodology is applied to exchange rate returns to show that linear all pass models can mimic nonlinear behavior and is applied to stock market volume data to illustrate a two step procedure for fitting noncausal autoregressions

spatial quantile estimation of multivariate threshold time series models abstract in this paper we study spatial quantile regression estimation of multivariate threshold time series models bahadur s representations for our estimators are established which naturally lead to asymptotic normality of the estimators simulations and a real example are used to evaluate the performance of the proposed estimators

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

self weighted and local quasi maximum likelihood estimators for arma garch igarch models the limit distribution of the quasi maximum likelihood estimator qmle for parameters in the arma garch model remains an open problem when the process has infinite 4th moment we propose a self weighted qmle and show that it is consistent and asymptotically normal under only a fractional moment condition based on this estimator the asymptotic normality of the local qmle is established for the arma model with garch finite variance and igarch errors using the self weighted and the local qmles we construct wald statistics for testing linear restrictions on the parameters and their limiting distributions are given in addition we show that the tail index of the igarch process is always 2 which is independently of interest

weak convergence of randomly weighted dependent residual empiricals with applications to autoregression this paper establishes the uniform closeness of a randomly weighted residual empirical process to its natural estimator via weak convergence techniques the weights need not be independent bounded or even square integrable this result is used to yield the asymptotic uniform linearity of a class of rank statistics in p th order autoregression models the latter result in turn yields the asymptotic distributions of a class of robust and jaeckel type rank estimators the main result is also used to obtain the asymptotic distributions of the least absolute deviation and certain other robust minimum distance estimators of the autoregression parameter vector

motion tracking as a constrained optimization problem in this paper we pose the problem of tracking of a varying number of points through an image sequence as a multi objective optimization problem with additional hard constraints one of the objectives is to find smooth tracks based on second order motion characteristics optimized over several frames the corresponding optimization algorithm we present is a sequential heuristic search algorithm that adequately prunes the search tree in such a way that its exponential order remains low when the algorithm is compared to other tracking algorithms it turns out that the proposed algorithm is easier to tune and generally more efficient and more accurate

rank based autoregressive order identification abstract optimal rank based procedures have been derived for testing arbitrary linear restrictions on the parameters of autoregressive moving average arma models with unspecified innovation densities the finite sample performances of these procedures are investigated here in the context of ar order identification and compared to those of classical partial correlograms and lagrange multipliers methods the results achieved by rank based methods are quite comparable in the gaussian case to those achieved by the traditional ones which under gaussian assumptions are asymptotically optimal however under non gaussian innovation densities especially heavy tailed or nonsymmetric or when outliers are present the percentages of correct order selection based on rank methods are strikingly better than those resulting from traditional approaches even in the case of very short n 25 series these empirical findings confirm the often ignored theoretical fact that the gaussian case in the arma context

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

estimating the innovation distribution in nonparametric autoregression we prove a bahadur representation for a residual based estimator of the innovation distribution function in a nonparametric autoregressive model the residuals are based on a local linear smoother for the autoregression function our result implies a functional central limit theorem for the residual based estimator

quantile correlations and quantile autoregressive modeling in this article we propose two important measures quantile correlation qcor and quantile partial correlation qpcor we then apply them to quantile autoregressive qar models and introduce two valuable quantities the quantile autocorrelation function qacf and the quantile partial autocorrelation function qpacf this allows us to extend the box jenkins three stage procedure model identification model parameter estimation and model diagnostic checking from classical autoregressive models to quantile autoregressive models specifically the qpacf of an observed time series can be employed to identify the autoregressive order while the qacf of residuals obtained from the fitted model can be used to assess the model adequacy we not only demonstrate the asymptotic properties of qcor and qpcor but also show the large sample results of qacf qpacf and the quantile version of the box pierce test moreover we obtain the bootstrap approximations to the distributions of parameter estimators and p

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

nonparametric model checks for time series this paper studies a class of tests useful for testing the goodness of fit of an autoregressive model these tests are based on a class of empirical processes marked by certain residuals the paper first gives their large sample behavior under null hypotheses then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free consistency of these tests is also discussed briefly

testing functional inequalities abstract this paper develops tests for inequality constraints of nonparametric regression functions the test statistics involve a one sided version of l p type functionals of kernel estimators 1 p drawing on the approach of poissonization this paper establishes that the tests are asymptotically distribution free admitting asymptotic normal approximation in particular the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives furthermore we establish conditions under which the tests have nontrivial local power against pitman local alternatives some results from monte carlo simulations are presented

on the range of validity of the autoregressive sieve bootstrap we explore the limits of the autoregressive ar sieve bootstrap and show that its applicability extends well beyond the realm of linear time series as has been previously thought in particular for appropriate statistics the ar sieve bootstrap is valid for stationary processes possessing a general wold type autoregressive representation with respect to a white noise in essence this includes all stationary purely nondeterministic processes whose spectral density is everywhere positive our main theorem provides a simple and effective tool in assessing whether the ar sieve bootstrap is asymptotically valid in any given situation in effect the large sample distribution of the statistic in question must only depend on the first and second order moments of the process prominent examples include the sample mean and the spectral density as a counterexample we show how the ar sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is linear

specification tests of parametric dynamic conditional quantiles this article proposes omnibus specification tests of parametric dynamic quantile models in contrast to the existing procedures we allow for a flexible specification where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data generating process since the null limit distribution of tests is not pivotal we propose a subsampling approximation of the asymptotic critical values a monte carlo study shows that the asymptotic results provide good approximations for small sample sizes finally an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

rank based estimation for all pass time series models an autoregressive moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all pass time series model all pass models are useful for identifying and modeling noncausal and noninvertible autoregressive moving average processes we establish asymptotic normality and consistency for rank based estimators of all pass model parameters the estimators are obtained by minimizing the rank based residual dispersion function given by jaeckel ann math statist 43 1972 1449 1458 these estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust the behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram

detecting independent motion the statistics of temporal continuity we consider a problem central in aerial visual surveillance applications detection and tracking of small independently moving objects in long and noisy video sequences we directly use spatiotemporal image intensity gradient measurements to compute an exact model of background motion this allows the creation of accurate mosaics over many frames and the definition of a constraint violation function which acts as an indicator of independent motion a novel temporal integration method maintains confidence measures over long subsequences without computing the optic flow requiring object models or using a kalman filter the mosaic acts as a stable feature frame allowing precise localization of the independently moving objects we present a statistical analysis of the effects of image noise on the constraint violation measure and find a good match between the predicted probability distribution function and the measured sample frequencies in a test sequence

semiparametrically efficient inference based on signs and ranks for median restricted models since the pioneering work of koenker and bassett 1978 econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest contrary to the traditional models where the noise is assumed to have mean zero median restricted models enjoy a rich group invariance structure in this paper we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models these procedures are based on residual signs and ranks and therefore insensitive to possible misspecification of the underlying innovation density yet semiparametrically efficient at correctly specified densities this latter combination is a definite advantage of these procedures over classical quasi likelihood methods the techniques we propose can be applied without additional technical difficulties to both cross sectional and time series models they do not require any explicit tangent space calculation nor any projections on these

strict stationarity testing and glad estimation of double autoregressive models abstract in this article we develop a tractable procedure for testing strict stationarity in a double autoregressive model and formulate the problem as testing if the top lyapunov exponent is negative without strict stationarity assumption we construct a consistent estimator of the associated top lyapunov exponent and employ a random weighting approach for its variance estimation which in turn are used in a t type test we also propose a glad estimation for parameters of interest relaxing key assumptions on the commonly used qmle all estimators except for the intercept are shown to be consistent and asymptotically normal in both stationary and explosive situations the finite sample performance of the proposed procedures is evaluated via monte carlo simulation studies and a real dataset of interest rates is analyzed

on alleged gains in power from lower p values the various suggestions that have been made to increase the power of fisher s test for 2 2 tables are shown to give no real increases one sided tests are examined in detail but two sided test problems are also considered the need for flexibility in use of p values is stressed

model identification for infinite variance autoregressive processes abstract we consider model identification for infinite variance autoregressive time series processes it is shown that a consistent estimate of autoregressive model order can be obtained by minimizing akaike s information criterion and we use all pass models to identify noncausal autoregressive processes and estimate the order of noncausality the number of roots of the autoregressive polynomial inside the unit circle in the complex plane we examine the performance of the order selection procedures for finite samples via simulation and use the techniques to fit a noncausal autoregressive model to stock market trading volume data

fitting an error distribution in some heteroscedastic time series models this paper addresses the problem of fltting a known distribution to the innovation distribution in a class of stationary and ergodic time series models the asymptotic null distribution of the usual kolmogorov smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution to overcome the dependence on the underlying model parameters we propose that tests be based on a vector of certain weighted residual empirical processes under the null hypothesis and under minimal moment conditions this vector of processes is shown to converge weakly to a vector of independent copies of a gaussian process whose covariance function depends only on the fltted distribution and not on the model under certain local alternatives the proposed test is shown to have nontrivial asymptotic power the monte carlo critical values of this test are tabulated when fltting standard normal and double exponential distributions the results obtained are shown to be applicable to garch and arma garch models the often used models in econometrics and flnance a simulation study shows that the test has satisfactory size and power for flnite samples at these models the paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions a result of independent interest

goodness of fit problem for errors in nonparametric regression distribution free approach this paper discusses asymptotically distribution free tests for the classical goodness of fit hypothesis of an error distribution in nonparametric regression models these tests are based on the same martingale transform of the residual empirical process as used in the one sample location model this transformation eliminates extra randomization due to covariates but not due the errors which is intrinsically present in the estimators of the regression function thus tests based on the transformed process have generally better power the results of this paper are applicable as soon as asymptotic uniform linearity of nonparametric residual empirical process is available in particular they are applicable under the conditions stipulated in recent papers of akritas and van keilegom and muller schick and wefelmeyer

center outward r estimation for semiparametric varma models we propose a new class of r estimators for semiparametric varma models in which the innovation density plays the role of the nuisance parameter our estimators are based on the novel concepts of mu

power comparison of two sided exact tests for association in 2 x 2 contingency tables using standard mid p and randomized test versions exact pearson s chi square likelihood ratio lr and fisher s tests are obtained from the conditional distribution of its test statistic given the row and column sums of the contingency table the power and obtained significance level of the standard mid p and randomized versions of these tests are compared for two sided tests in 2 x 2 tables using binomial and multinomial sampling the mid p type i error probabilities seldom exceed the nominal significance level the mid p and randomized test versions have approximately the same power and higher power than the standard test version the power of the pearson s chi square lr and fisher s test differ and they differ in approximately the same way for standard mid p and randomized test versions for any given set of parameters there is no general ranking between the three tests in many cases pearson s chi square and fisher s tests have almost equal power and higher power than lr in a few cases perhaps characterized by poorly balanced designs lr performs best fisher s test seems to be slightly more robust even if the design is poor

asymptotically distribution free tests for the volatility function of a diffusion abstract this paper develops two tests for parametric volatility function of a diffusion model based on khmaladze 1981 s martingale transformation the tests impose no restrictions on the functional form of the drift function and are shown to be asymptotically distribution free the tests are consistent against a large class of fixed alternatives and have nontrivial power against a class of root n local alternatives the paper also extends the tests of volatility to testing for joint specifications of drift and volatility monte carlo simulations show that the tests perform well in finite samples the proposed tests are then applied to testing models of short term interest using data of treasury bill rate and eurodollar deposit rate the empirical results show that the commonly used ckls volatility function of chan et al 1992 fits volatility function poorly and none of the parametric interest rate models considered in the paper fit data well

autoregression quantiles and related rank scores processes this paper develops extensions of the regression quantiles of koenker and bassett 1978 to autoregression it generalizes several results of jureckova 1992a and gutenbrunner and jureckova 1992 in linear regression to autoregression models in particular it gives the asymptotic uniform linearity of linear rank scores statistics based on residuals suitable in autoregression it also discusses the two types of l statistics appropriate in autoregression

weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models this paper establishes the weak convergence of the sequential empirical process n of the estimated residuals in nonstationary autoregressive models under some regular conditions it is shown that n converges weakly to a kiefer process when the characteristic polynomial does not include the unit root 1 otherwise n converges weakly to a kiefer process plus a functional of stochastic integrals in terms of the standard brownian motion the latter differs not only from that given by koul and levental for an explosive ar 1 model but also from that given by bai for a stationary arma model

the transfer principle a tool for complete case analysis this paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed this provides a convenient tool for obtaining the asymptotic behavior of complete case versions of established full data methods without lengthy proofs the methodology is illustrated by analyzing three inference procedures for partially linear regression models with responses missing at random we first show that complete case versions of asymptotically efficient estimators of the slope parameter for the full model are efficient thereby solving the problem of constructing efficient estimators of the slope parameter for this model secondly we derive an asymptotically distribution free test for fitting a normal distribution to the errors finally we obtain an asymptotically distribution free test for linearity i e for testing that the nonparametric component of these models is a constant this test is new both when data are fully observed and when data are missing at random

on distribution free goodness of fit testing of exponentiality there is a need to test the hypothesis of exponentiality against a wide variety of alternative hypotheses across many areas of economics and finance local or contiguous alternatives are the closest alternatives against which it is still possible to have some power hence goodness of fit tests should have some power against all or a huge majority of local alternatives such tests are often based on nonlinear statistics with a complicated asymptotic null distribution thus a second desirable property of a goodness of fit test is that its statistic will be asymptotically distribution free we suggest a whole class of goodness of fit tests with both of these properties by constructing a new version of empirical process that weakly converges to a standard brownian motion under the hypothesis of exponentiality all statistics based on this process will asymptotically behave as statistics from a standard brownian motion and so will be asymptotically distribution free we show the form of transformation is especially simple in the case of exponentiality surprisingly there are only two asymptotically distribution free versions of empirical process for this problem and only this one has a convenient limit distribution many tests of exponentiality have been suggested based on asymptotically linear functionals from the empirical process we illustrate none of these can be used as goodness of fit tests contrary to some previous recommendations of considerable interest is that a selection of well known statistics all lead to the same test asymptotically with negligible asymptotic power against a great majority of local alternatives finally we present an extension of our approach that solves the problem of multiple testing both for exponentiality and for other more general hypotheses

self weighted least absolute deviation estimation for infinite variance autoregressive models summary how to undertake statistical inference for infinite variance autoregressive models has been a long standing open problem to solve this problem we propose a self weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded furthermore a wald test statistic is developed for the linear restriction on the parameters and it is shown to have non trivial local power simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given the results are entirely different from other published results and should provide new insights for future research on heavy tailed time series

model checks for regression an innovation process approach in the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus smooth and directional goodness of fit tests since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain we propose to replace this process by its innovation martingale it turns out that the resulting tests are asymptotically distribution free under composite null models and may be readily performed a simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes

a goodness of fit test for copulas based on martingale transformation abstract this paper proposes an asymptotically distribution free test for copulas with dynamic marginal distributions such as garch and arma processes the test is based on the empirical copula process with parametrically estimated marginal distributions by applying the khmaladze 1982 1988 1993 martingale transformation method the transformed empirical process converges to a standard gaussian process so the resulting test statistics are asymptotically distribution free monte carlo simulations show that the test performs well in finite samples an empirical application to test copulas between eur usd and gbp usd exchange rates is provided

establishing motion correspondence using extended temporal scope this paper addresses the motion correspondence problem the problem of finding corresponding point measurements in an image sequence solely based on positional information the motion correspondence problem is most difficult when the target points are densely moving it becomes even harder when the point detection scheme is imperfect or when points are temporarily occluded available motion constraints should be exploited in order to rule out physically impossible assignments of measurements to point tracks the performance can be further increased by deferring the correspondence decisions that is by examining whether the consequences of candidate correspondences lead to alternate and better solutions in this paper we concentrate on the latter by introducing a scheme that extends the temporal scope over which the correspondences are optimized the consequent problem we are faced with is a multi dimensional assignment problem which is known to be np hard to restrict the consequent increase in computation time the candidate solutions are suitably ordered and then additional combined motion constraints are imposed experiments show the appropriateness of the proposed extension both with respect to performance as well as computational aspects

model checking for parametric single index models a dimension reduction model adaptive approach summary local smoothing testing based on multivariate non parametric regression estimation is one of the main model checking methodologies in the literature however the relevant tests suffer from the typical curse of dimensionality resulting in slow rates of convergence to their limits under the null hypothesis and less deviation from the null hypothesis under alternative hypotheses this problem prevents tests from maintaining the level of significance well and makes tests less sensitive to alternative hypotheses in the paper a model adaptation concept in lack of fit testing is introduced and a dimension reduction model adaptive test procedure is proposed for parametric single index models the test behaves like a local smoothing test as if the model were univariate it is consistent against any global alternative hypothesis and can detect local alternative hypotheses distinct from the null hypothesis at a fast rate that existing local smoothing tests can achieve only when the model is univariate simulations are conducted to examine the performance of our methodology an analysis of real data is shown for illustration the method can be readily extended to global smoothing methodology and other testing problems

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

generalized r estimators under conditional heteroscedasticity in this paper we extend the classical idea of rank estimation of parameters from homoscedastic problems to heteroscedastic problems in particular we define a class of rank estimators of the parameters associated with the conditional mean function of an autoregressive model through a three steps procedure and then derive their asymptotic distributions the class of models considered includes engel s arch model and the threshold heteroscedastic model the class of estimators includes an extension of wilcoxon type rank estimator the derivation of the asymptotic distributions depends on the uniform approximation of a randomly weighted empirical process by a perturbed empirical process through a very general weight dependent partitioning argument

power of testing proportions in small two sample studies when sample sizes are equal in planning experiments having two groups of equal but small size investigators face the uncertainty of power calculations that rely on asymptotic methods this paper presents a method for determining power for two sided tests i compare two randomization tests fisher s exact test fet and the mid p mid with the uncorrected chi square test chi results show power as a function of relative risk for these methods and assesses their relative power and type i error rates mid is shown to have intermediate power between chi which is the most powerful and fet the least powerful situations are shown in which chi and mid occasionally exceed the nominal level of alpha

testing for structural change in regression quantiles abstract most studies in the structural change literature focus solely on the conditional mean while under various circumstances structural change in the conditional distribution or in conditional quantiles is of key importance this paper proposes several tests for structural change in regression quantiles two types of statistics are considered namely a fluctuation type statistic based on the subgradient and a wald type statistic based on comparing parameter estimates obtained from different subsamples the former requires estimating the model under the null hypothesis and the latter involves estimation under the alternative hypothesis the tests proposed can be used to test for structural change occurring in a pre specified quantile or across quantiles which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function both single and multiple structural changes are considered we derive the limiting distributions under the null hypothesis and show they are nuisance parameter free and can be easily simulated a simulation study is conducted to assess the size and power in finite samples

stationarity of garch processes and of some nonnegative time series abstract two time series models are considered garch processes and generalized multivariate autoregressive equations x n 1 a n 1 x n b n 1 with nonnegative i i d coefficients in each case a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given

empirical process of the squared residuals of an arch sequence we derive the asymptotic distribution of the sequential empirical process of the squared residuals of an arch p sequence unlike the residuals of an arma process these residuals do not behave in this context like asymptotically independent random variables and the asymptotic distribution involves a term depending on the parameters of the model we show that in certain applications including the detection of changes in the distribution of the unobservable innovations our result leads to asymptotically distribution free statistics

testing semiparametric conditional moment restrictions using conditional martingale transforms this paper studies conditional moment restrictions that contain unknown nonparametric functions and proposes a general method of obtaining asymptotically distribution free tests via martingale transforms examples of such conditional moment restrictions are single index restrictions partially parametric regressions and partially parametric quantile regressions this paper introduces a conditional martingale transform that is conditioned on the variable in the nonparametric function and shows that we can generate distribution free tests of various semiparametric conditional moment restrictions using this martingale transform the paper proposes feasible martingale transforms using series estimation and establishes their asymptotic validity some results from a monte carlo simulation study are presented and discussed

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models