quadratically constrained adaptive beamforming for coherent signals and interference severe signal cancellation often occurs in conventional adaptive beamforming if coherent interferers are present the paper proposes adding quadratic constraints to a linearly constrained minimum variance lcmv adaptive beamformer to prevent signal cancellation in coherent interference environments the additional constraint limits the beamformer output mean squared error to be less than a specified level it is shown that if the quadratic constraint is properly chosen then the original linearly constrained beamformer s signal cancellation is reduced to an arbitrarily small level while the interference cancellation is unchanged in practice the quadratic constraint is constructed based on estimates of the interference parameters sensitivity analyses show the performance of the resulting beamformer is robust with respect to this approximate constraint the effectiveness of the quadratically constrained adaptive beamformer is further illustrated through simulations

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

simulation based finite and large sample tests in multivariate regressions abstract in the context of multivariate linear regression mlr models it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection in this paper we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of mlr systems for the case of uniform linear hypotheses we present exact distributional invariance results concerning several standard test criteria these include wilks likelihood ratio lr criterion as well as trace and maximum root criteria the normality assumption is not necessary for most of the results to hold implications for inference are two fold first invariance to nuisance parameters entails that the technique of monte carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses second the invariance property of the latter statistic is exploited to derive general nuisance parameter free bounds on the distribution of the lr statistic for arbitrary hypotheses even though it may be difficult to compute these bounds analytically they can easily be simulated hence yielding exact bounds monte carlo tests illustrative simulation experiments show that the bounds perform well our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation based test methods e g the parametric bootstrap which may be applied when the bounds are not conclusive

testing for factor loading structural change under common breaks abstract this paper proposes a new test for factor loading structural change in dynamic factor models we first show that the leading test proposed by breitung and eickmeier 2011 exhibits nonmonotonic power essentially because the breaks are considered as spurious factors with stable factor loadings the proposed test eliminates the effects of the spurious factors by maximizing the test statistic over possible numbers of the original factors monte carlo simulations and an empirical example using u s treasury yield curve data clearly illustrate the usefulness of the proposed test

testing misspecification in vector time series models with exogenous variables summary in this paper we consider the application of hypothesis testing procedures to armax systems the score or lagrangian multiplier principle is used to obtain misspecification tests appropriate to these models the structure of the information or sensitivity matrix is investigated in order to discuss the identifiability of alternative models and is used to show the existence of a set of admissible alternatives that are locally equivalent to one another this notion is then developed to suggest why the score test is to be regarded as a pure significance test

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

mmc techniques for limited dependent variables models implementation by the branch and bound algorithm we propose a finite sample approach to some of the most common limited dependent variables models the method rests on the maximized monte carlo mmc test technique proposed by dufour 1998 monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics journal of econometrics this issue we provide a general way for implementing tests and confidence regions we show that the decision rule associated with a mmc test may be written as a mixed integer programming problem the branch and bound algorithm yields a global maximum in finite time an appropriate choice of the statistic yields a consistent test while fulfilling the level constraint for any sample size the technique is illustrated with numerical data for the logit model c 2005 elsevier b v all rights reserved

acceleration of maximum likelihood reconstruction using frequency amplification and attenuation compensation algorithms that calculate maximum likelihood ml and maximum a posteriori solutions using expectation maximization have been successfully applied to spect and pet these algorithms are appealing because of their solid theoretical basis and their guaranteed convergence a major drawback is the slow convergence which results in long processing times the authors present 2 new heuristic acceleration methods for maximum likelihood reconstruction of ect images the first method incorporates a frequency dependent amplification in the calculations to compensate for the low pass filtering of the backprojection operation in the second method an amplification factor is incorporated that suppresses the effect of attenuation on the updating factors both methods are compared to the 1 dimensional line search method proposed by lewitt all 3 methods accelerate the ml algorithm on the authors test images lewitt s method produced the strongest acceleration of the three individual methods however the combination of the frequency amplification with the line search method results in a new algorithm with still better performance under certain conditions an effective frequency amplification can be already achieved by skipping some of the calculations required for ml

robust tests for heteroskedasticity in the one way error components model this paper constructs tests for heteroskedasticity in one way error components models in line with baltagi et al baltagi b h bresson g pirotte a 2006 joint lm test for homoskedasticity in a one way error component model journal of econometrics 134 401 417 our tests have two additional robustness properties first standard tests for heteroskedasticity in the individual component are shown to be negatively affected by heteroskedasticity in the remainder component we derive modified tests that are insensitive to heteroskedasticity in the component not being checked and hence help identify the source of heteroskedasticity second gaussian based lm tests are shown to reject too often in the presence of heavy tailed e g t student distributions by using a conditional moment framework we derive distribution free tests that are robust to non normalities our tests are computationally convenient since they are based on simple artificial regressions after pooled ols estimation

multiple window based minimum variance spectrum estimation for multidimensional random fields spectrum analysis is viewed as the problem of estimating the power of a process contained within narrow bands this view leads naturally to consideration of filter based methods for estimating spectra multiple window based estimators where the power in a band is estimated as the average of the powers estimated at the outputs of multiple filters are considered the filters are designed using a linearly constrained minimum variance criterion commonly employed in adaptive beamforming this results in filters that automatically adjust their sidelobes to minimize leakage of energy from outside the band of interest expressions for the bias and variance of the power estimates are derived assuming the sample covariance matrix estimate is used to estimate the data covariance matrix and that the data are independent and identically gaussian distributed these expressions lead to the definition of a performance factor that indicates the degree of variance reduction obtained via multiple window processing a technique for obtaining increased suppression of energy leaking through the filter sidelobes at the expense of the response fidelity to energy in the band is presented simulations are presented to illustrate the effectiveness of the technique

doubly constrained robust capon beamformer the standard capon beamformer scb is known to have better resolution and much better interference rejection capability than the standard data independent beamformer when the array steering vector is accurately known however the major problem of the scb is that it lacks robustness in the presence of array steering vector errors in this paper we will first provide a complete analysis of a norm constrained capon beamforming nccb approach which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise our analysis of nccb is thorough and sheds more light on the choice of the norm constraint than what was commonly known we also provide a natural extension of the scb which has been obtained via covariance matrix fitting to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector viz a constant norm constraint and a spherical uncertainty set constraint which we refer to as the doubly constrained robust capon beamformer dcrcb nccb and dcrcb can both be efficiently computed at a comparable cost with that of the scb performance comparisons of nccb dcrcb and several other adaptive beamformers via a number of numerical examples are also presented

the circular harmonic transform for spect reconstruction and boundary conditions on the fourier transform of the sinogram the circular harmonic transform cht solution of the exponential randon transform ert is applied to single photon emission computed tomography spect for uniform attenuation within a convex boundary an important special case also considered is the linear unattenuated radon transform lrt the solution is on the form of an orthogonal function expansion matched to projections that are in parallel ray geometry this property allows for efficient and accurate processing of the projections with fast fourier transform fft without interpolation or beam matching the algorithm is optimized by the use of boundary conditions on the 2 d fourier transform of the sinogram these boundary conditions imply that the signal energy of the sinogram is concentrated in well defined sectors in transform space the angle defining the sectors depends in a direct way on the radius of the field view these results are also obtained for fan beam geometry and the linear radon transform the fourier chebyshev transform of the sinogram to demonstrate that the boundary conditions are a more general property of the radon transform and a not a property unique to rectangular coordinates

a generalized sidelobe canceller with soft constraints an efficient beamforming structure similar to a generalized sidelobe canceller is derived from the soft constrained minimum variance scmv method of b van veen see ibid vol 39 no 9 p 1964 72 1991 the structure greatly reduces the computational load of the scmv method and provides insight into the nature of scmv beamforming

on the invariance of the lagrange multiplier test with respect to certain changes in the alternative hypothesis this paper examines some implications of the observation that the same lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses a characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification and the consequences for finite sample power properties are examined by monte carlo experiments

a generalized em algorithm for 3 d bayesian reconstruction from poisson data using gibbs priors a generalized expectation maximization gem algorithm is developed for bayesian reconstruction based on locally correlated markov random field priors in the form of gibbs functions and on the poisson data model for the m step of the algorithm a form of coordinate gradient ascent is derived the algorithm reduces to the em maximum likelihood algorithm as the markov random field prior tends towards a uniform distribution three different gibbs function priors are examined reconstructions of 3 d images obtained from the poisson model of single photon emission computed tomography are presented

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

tests for the error component model in the presence of local misspecification it is well known that most of the standard specification tests are not valid when the alternative hypothesis is misspecified this is particularly true in the error component model when one tests for either random effects or serial correlation without taking account of the presence of the other effect in this paper we study the size and power of the standard rao s score tests analytically and by simulation when the data are contaminated by local misspecification these tests are adversely affected under misspecification we suggest simple procedures to test for random effects or serial correlation in the presence of local serial correlation or random effects and these tests require ordinary least squares residuals only our monte carlo results demonstrate that the suggested tests have good finite sample properties for local misspecification and in some cases even for far distant misspecification our tests are also capable of detecting the right direction of the departure from the null hypothesis we also provide some empirical illustrations to highlight the usefulness of our tests

an approach to testing linear times series models the purpose of this paper is to develop diagnostic tests for open loop transfer function models with autoregressive moving average stochastic disturbances using the efficient scores procedure the tests proposed are asymptotically equivalent to those based upon the likelihood ratio principle and have the advantage that they do not involve a heavy computational burden consideration is given both to the standard case of nonsingular information matrices and to the situation obtaining when there are identifiability problems and application of conventional large sample test procedures is not feasible relationships between score tests and portmanteau tests in time series analysis are also investigated some simulation evidence on the finite sample behaviour of the tests is presented and it is seen that the tests of this paper perform well

randomization matching and propensity scores in the design and analysis of experimental studies with measured baseline covariates in many experimental situations researchers have information on a number of covariates prior to randomization this information can be used to balance treatment assignment with respect to these covariates as well as in the analysis of the outcome data in this paper we investigate the use of propensity scores in both of these roles we also introduce a randomization procedure in which the balance of all measured covariates is approximately indexed by the variance of the empirical propensity scores and randomization is restricted to those permutations with the least variable propensity scores this procedure is compared with recently proposed methods in terms of resulting covariate balance and estimation efficiency properties of the estimators resulting from each procedure are compared with estimates which incorporate the propensity score in the analysis stage simulation results show that analytical adjustment for the propensity score yields results on par with those obtained through restricted randomization procedures and can be used in conjunction with such procedures to further improve inferential efficiency

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

testing for conditional heteroskedasticity with misspecified alternative hypotheses for the multiple linear regression model this paper examines the asymptotic behaviour of some tests for conditional heteroskedasticity when an alternative hypothesis is misspecified in the standard likelihood based framework a lagrange multiplier statistic based on a correctly specified alternative is ranked above one based on an overspecified alternative it is shown that this ranking does not hold for statistics that are robust to the form of conditional heterokurticity it is also shown that the ranking obtained in the standard likelihood based framework does not depend on a joint density being specified in its entirety the same ranking can be obtained when a type of information matrix equality holds

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

asymptotic relative efficiency of the classical test statistics under misspecification abstract asymptotic properties of the three classical test statistics the likelihood ratio lagrange multiplier efficient score and wald statistics are studied in the case of two types of misspecification the first misspecification is that the alternative used to construct the test is different from the true nonnull model in the second case the alternative hypothesis is correct but some of the nuisance parameters satisfy restrictions which are not taken into account in the test pitman s local alternatives and the concept of asymptotic relative efficiency are used to derive the asymptotic distributions of the test statistics and to examine the effects of the misspecifications the general results of the paper are illustrated by an example on the dynamic specification of a regression model

multi access interference suppression in canonical space time coordinates a decentralized approach we propose a decentralized space time multiuser detection scheme based on the notion of canonical space time coordinates cstcs for representing the received signal the cstc representation provides a natural framework for decentralized multi access interference mai suppression in lower dimensional subspaces that results in complexity reduction relative to existing chip rate filtering schemes the framework is based on a partitioning of the signal space into active and inactive cstcs the active cstcs contain the signal of the desired user facilitate maximal diversity exploitation and minimal complexity interference suppression the inactive cstcs only contain mai and can be included progressively to attain a desired level of mai suppression at the cost of increased complexity we develop cstc based linear coherent multiuser detectors using the linearly constrained minimum variance lcmv criterion we characterize the set of inactive coordinates and analyze the performance of the lcmv receiver as a function of the number of inactive cstcs channel estimation and detector sensitivity to channel estimation errors are discussed we demonstrate that the low complexity adaptive receivers designed via the cstc framework are more robust to channel estimation errors than existing chip domain filtering schemes

minimum variance beamforming with soft response constraints soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming a quadratic constraint on the beamformer weights is used to control the mean squared error between a desired response and the actual response in the signal direction the constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation under the assumptions of known signal direction and spectral shape the signal to noise ratio is shown to be a nondecreasing function of the mean square distortion the distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired properties of this beamforming method and its relationship to linear constrained beamforming are discussed simulations verify analytic results and illustrate the utility of the soft constrained approach

admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative this paper establishes the asymptotic admissibility of the likelihood ratio lr test for a general class of testing problems in which a nuisance parameter is present only under the alternative hypothesis the paper also establishes the finite sample admissibility of the lr test for testing problems of this sort that arise in gaussian linear regression models with known variance

rank reduction for modeling stationary signals rank reduction is developed as a general principle for trading off model bias and model variance in the analysis and synthesis of signals the principle is applied to three basic problems stationary time series modeling stationary time series whitening and vector quantization each problem brings its own surprises and insights

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

bayesian image processing in two dimensions a bayesian image processing bip formalism which incorporates a priori amplitude and spatial probability density information was applied to two dimensional source fields for valid moderately restrictive a priori information strikingly improved results for ideal and experimental radioisotope phantom imaging data compared to a standard non bayesian formalism maximum likelihood ml were obtained the applicability of a fast fourier transform technique for convolution calculations a reduced region restriction for the initial deconvolution calculations and a relaxation parameter for accelerating convergence are considered

on bayesian image reconstruction from projections uniform and nonuniform a priori source information a method that incorporates a priori uniform or nonuniform source distribution probabilistic information and data fluctuations of a poisson nature is presented the source distributions are modeled in terms of a priori source probability density functions maximum a posteriori probability solutions as determined by a system of equations are given interactive bayesian imaging algorithms for the solutions are derived using an expectation maximization technique comparisons of the a priori uniform and nonuniform bayesian algorithms to the maximum likelihood algorithm are carried out using computer generated noise free and poisson randomized projections improvement in image reconstruction from projections with the bayesian algorithm is demonstrated superior results are obtained using the a priori nonuniform source distribution

a theoretical study of some maximum likelihood algorithms for emission and transmission tomography this paper has the dual purpose of introducing some new algorithms for emission and transmission tomography and proving mathematically that these algorithms and related antecedent algorithms converge like the em algorithms for positron single photon and transmission tomography the algorithms provide maximum likelihood estimates of pixel concentration or linear attenuation parameters one particular innovation we discuss is a computationally practical scheme for modifying the em algorithms to include a bayesian prior the bayesian versions of the em algorithms are shown to have superior convergence properties in a vicinity of the maximum we anticipate that some of the other algorithms will also converge faster than the em algorithms

a multigrid expectation maximization reconstruction algorithm for positron emission tomography the problem of reconstruction in positron emission tomography pet is basically estimating the number of photon pairs emitted from the source using the concept of the maximum likelihood ml algorithm the problem of reconstruction is reduced to determining an estimate of the emitter density that maximizes the probability of observing the actual detector count data over all possible emitter density distributions a solution using this type of expectation maximization em algorithm with a fixed grid size is severely handicapped by the slow convergence rate the large computation time and the nonuniform correction efficiency of each iteration which makes the algorithm very sensitive to the image pattern an efficient knowledge based multigrid reconstruction algorithm based on the ml approach is presented to overcome these problems

stopping rule for the mle algorithm based on statistical hypothesis testing it is known that when the maximum likelihood estimator mle algorithm passes a certain point it produces images that begin to deteriorate we propose a quantitative criterion with a simple probabilistic interpretation that allows the user to stop the algorithm just before this effect begins the mle algorithm searches for the image that has the maximum probability to generate the projection data the underlying assumption of the algorithm is a poisson distribution of the data therefore the best image according to the mle algorithm is the one that results in projection means which are as close to the data as possible it is shown that this goal conflicts with the assumption that the data are poisson distributed we test a statistical hypothesis whereby the projection data could have been generated by the image produced after each iteration the acceptance or rejection of the hypothesis is based on a parameter that decreases as the images improve and increases as they deteriorate we show that the best mle images which pass the test result in somewhat lower noise in regions of high activity than the filtered back projection results and much improved images in low activity regions the applicability of the proposed stopping rule to other iterative schemes is discussed

diagnostic tests for multiple time series models this paper is concerned with the development and application of diagnostic checks for vector linear time series models a hypothesis testing procedure based upon the score or lagrangean multiplier principle is advocated and the distributions of the test statistic both under the null hypothesis and under a pitman sequence of alternatives are discussed consideration of alternative models with singular sensitivity matrices when the null hypothesis is true leads to an interpretation of the score test as a pure significance test and to a notion of an equivalence class of local alternatives portmanteau tests of model adequacy are also investigated and are seen to be equivalent to score tests

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

a non local perspective on the power properties of the cusum and cusum of squares tests for structural change abstract we consider the power properties of the cusum and cusum of squares cusq tests in the presence of a one time change in the parameters of a linear regression model a result due to ploberger and kramer 1990 the local power of the cusum and cusum of squares tests econometric theory 6 335 347 is that the cusq test has only trivial asymptotic local power in this case while the cusum test has non trivial local asymptotic power unless the change is orthogonal to the mean regressor the main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples the approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis this enables us to analyze what happens for non local to zero breaks our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors a static regression with correlated errors a dynamic regression with lagged dependent variables or whether a correction for non normality is applied in the case of the cusq we discuss in which cases the tests are subject to a non monotonic power function that goes to zero as the magnitude of the change increases and uncover some curious properties all theoretical results are verified to yield good guides to the finite sample power through simulation experiments we finally highlight the practical importance of our results

a fast reconstruction algorthm for stationary positron emission tomography based on a modified em algorithm an efficient iterative reconstruction method for positron emission tomography pet is presented the algorithm is basically an enhanced em expectation maximization algorithm with improved frequency response high frequency components of the ratio of measured to calculated projections are extracted and are taken into account for the iterative correction of image density in such a way that the correction is performed with a uniform efficiency over the image plane and with a flat frequency response as a result the convergence speed is not so sensitive to the image pattern or matrix size as the standard em algorithm and nonuniformity of the spatial resolution is significantly improved nonnegativity of the reconstructed image is preserved simulation studies have been made assuming two pet systems a scanning pet with ideal sampling and a stationary pet with sparse sampling in the latter a bank array of detectors is employed to improve the sampling in the object plane the new algorithm provides satisfactory images by two or three iterations starting from a flat image in either case the behavior of convergence is monitored by evaluating the root mean square of c b 1 where c b is the correction factor for pixel b in the em algorithm the value decreases rapidly and monotonically with iteration number although the theory is not accurate enough to assure the stability of convergence the algorithm is promising to achieve significant saving in computation compared to the standard em algorithm

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

feasible images and practical stopping rules for iterative algorithms in emission tomography the discussion of the causes of image deterioration in the maximum likelihood estimator mle method of tomographic image reconstruction initiated with the publication of a stopping rule for that iterative process e veklerov and j llacer 1987 is continued the concept of a feasible image is introduced which is a result of a reconstruction that if it were a radiation field could have generated the initial projection data by the poisson process that governs radioactive decay from the premise that the result of a reconstruction should be feasible the shape and characteristics of the region of feasibility in projection space are examined with a new rule reconstructions from real data can be tested for feasibility results of the tests and reconstructed images for the hoffman brain phantom are shown a comparative examination of the current methods of dealing with mle image deterioration is included

confidence intervals from monte carlo tests abstract monte carlo tests have exact level when the distribution of the test statistic is free of nuisance parameters confidence sets obtained by inverting such tests are also exact but may have a complicated structure the sets reduce to intervals if the sampling can be organized in a special way a sufficient condition is that the test statistic is monotone in the parameter of interest when all random drawings are kept fixed examples given include models from the one parameter exponential class a simple theory quantifying the impact of monte carlo uncertainty is also developed

p value approximations for spatial scan statistics using extreme value distributions spatial scan statistics are widely applied to identify spatial clusters in geographic disease surveillance to evaluate the statistical significance of detected clusters monte carlo hypothesis testing is often used because the null distribution of spatial scan statistics is not known a drawback of the method is that we have to increase the number of replications to obtain accurate p values gumbel based p value approximations for spatial scan statistics have recently been proposed and evaluated for poisson and bernoulli models in this study we examine the use of a generalized extreme value distribution to approximate the null distribution of spatial scan statistics as well as the gumbel distribution through simulation p value approximations using extreme value distributions for spatial scan statistics are assessed for multinomial and ordinal models in addition to poisson and bernoulli models copyright 2014 john wiley sons ltd

some results on the glejser and koenker tests for heteroskedasticity abstract the glejser and koenker studentized lagrange multiplier tests for heteroskedasticity are considered asymptotic theory and monte carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses and also the consequences of using an incorrect alternative a method for using test outcomes to select models of heteroskedasticity is critically examined glejser s test is not in general asymptotically valid under asymmetric disturbances koenker s test is asymptotically valid under asymmetric and other nonnormal disturbances but has estimated finite sample significance levels that are sometimes sensitive to skewness an adjusted version of koenker s statistic is discussed

a bayesian robust chi squared test for testing simple hypotheses abstract in this paper we introduce a new bayesian chi squared test based on an adjusted quadratic loss function for testing a simple null hypothesis we show that the asymptotic null distribution of our suggested test is a central chi squared distribution under some assumptions required for the bayesian large sample theory we refer to our test as the bayesian robust chi squared test since it is robust to parametric misspecification in the alternative model that is the limiting null distribution of our test is a central chi squared distribution irrespective of parametric misspecification in the alternative model in addition to being robust to parametric misspecification our test also shares properties of the test suggested by li et al 2015 based on a quadratic loss function we provide four examples to illustrate the implementation of our suggested bayesian test statistic

the approximate slopes of econometric tests in this paper the concept of approximate slope introduced by r r bahadur is used to make asymptotic global power comparisons of econometric tests the approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases under a given alternative a test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope two theorems which facilitate the computation and interpretation of the approximate slopes of most econometric tests are established these results are used to undertake some illustrative comparisons sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis

a maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography the expectation maximization method for maximum likelihood image reconstruction in emission tomography based on the poisson distribution of the statistically independent components of the image and measurement vectors is extended to a maximum aposteriori image reconstruction using a multivariate gaussian a priori probability distribution of the image vector the approach is equivalent to a penalized maximum likelihood estimation with a special choice of the penalty function the expectation maximization method is applied to find the a posteriori probability maximizer a simple iterative formula is derived for a penalty function that is a weighted sum of the squared deviations of image vector components from their a priori mean values the method is demonstrated to be superior to pure likelihood maximization in that the penalty function prevents the occurrence of irregular high amplitude patterns in the image with a large number of iterations the so called checkerboard effect or noise artifact

testing for common breaks in a multiple equations system abstract the issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system our framework is very general and allows integrated regressors and trends as well as stationary regressors the null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations under the alternative hypothesis the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations the test considered is the quasi likelihood ratio test assuming normal errors though as usual the limit distribution of the test remains valid with non normal errors of independent interest we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size allowing break dates not separated by a positive fraction of the sample size across equations simulations show that the test has good finite sample properties we also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness

assessing the relative power of structural break tests using a framework based on the approximate bahadur slope abstract we compare the asymptotic relative efficiency of the exp mean and sup functionals of the wald lm and lr tests for structural change analyzed by andrews andrews d w k 1993 tests for parameter instability and structural change with unknown change point econometrica 61 821 856 and andrews and ploberger andrews d w k ploberger w 1994 optimal tests when a nuisance parameter is present only under the alternative econometrica 62 1383 1414 we derive the approximate bahadur slopes of these tests using large deviations techniques these show that tests based on the mean functional are inferior to those based on the sup and exp when using the same base statistic also for a given functional the wald based test dominates the lr based test which dominates the lm based one we show that the sup and mean type tests satisfy wieand s wieand h s 1976 a condition under which the pitman and bahadur approaches to efficiency coincide annals of statistics 4 1003 1011 condition so that their slopes yield the limiting as the size tends to zero asymptotic relative pitman efficiency whether this holds for the exp type tests still remains a conjecture using this measure of efficiency the mean type tests are also inferior to the sup we also compare tests based on the wald and lm statistics modified with a hac estimator in this case the inferiority of the lm based tests is especially pronounced the relevance of our theoretical results in finite samples is assessed via simulations our results are in contrast to those obtained by the authors in the second reference cited above based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

simulation based finite sample tests for heteroskedasticity and arch effects tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations we show that the size of such tests can be perfectly controlledin nite samples through monte carlo test techniques with both gaussian and non gaussian heavy tailed disturbance distributions the procedures studied include standard heteroskedasticity tests e g glejser bartlett cochran hartley breusch pagan godfrey white szroeter as well as tests for arch type heterosked asticity sup type andcombinedtests are also proposedto allow for unknown breakpoints in the variance the fact that the proposedproced ures achieve size control andhave goodpower is demonstrated in a monte carlo simulation c 2003 elsevier b v all rights reserved

the efficiency of simulation based multiple comparisons a frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of or equivalent to a univariate linear model this problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal in other cases conservative solutions can be obtained by the methods of scheffe bonferroni or sidak 1967 journal of the american statistical association 62 626 633 here we investigate the efficiency of using a simulated critical point for exact intervals which has been suggested before but never put to serious test we find the simulation based method to be completely reliable and essentially exact sample size savings are substantial in our settings 3 19 over the sidak method 4 37 over the bonferroni method and 27 33 over the scheffe method we illustrate the efficiency and flexibility of the simulation based method with case studies in physiology and marine ecology

exact tests in single equation autoregressive distributed lag models abstract for hypotheses on the coefficient values of the lagged dependent variables in the arx class of dynamic regression models test procedures are developed which yield exact inference for given up to an unknown scale factor distribution of the innovation errors they include exact tests on the maximum lag length for structural change and on the presence of seasonal or multiple unit roots i e they cover situations where usually asymptotic and non exact t f aoc adf or hegy tests are employed the various procedures are demonstrated and compared in illustrative empirical models and the approach is critically discussed

performance evaluation of an iterative image reconstruction algorithm for positron emission tomography an image reconstruction method motivated by positron emission tomography pet is discussed the measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise the authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability map formulation of the problem an iterative approach which requires the solution of simple quadratic equations is proposed the authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing the new map algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method

implicit alternatives and the local power of test statistics the local power of test statistics is analyzed by extending the notion of pitman sequences to sequences of data generating processes dgp s that approach the null hypothesis without necessarily satisfying the alternative a space of probability densities is defined and endowed with the structure of an infinite dimensional hilbert manifold which permits a geometrical interpretation of hypothesis testing the three classical test statistics lr wald and lm are shown to tend asymptotically to the same random variable under all sequences of local dgp s the power of these statistics is seen to depend on the null the alternative and the sequence of dgp s in a simple and geometrically intuitive way moreover for any test statistic that is asymptotically chi squared under the null there exists an implicit alternative hypothesis against which that statistic will have highest power and which coincides with the explicit alternative for the classical test statistics

a rao blackwellized particle filter for adaptive beamforming with strong interference a particle filter approach is proposed for adaptive narrowband beamforming in the presence of strong interference and uncertain steering vector of interest signal from the viewpoint of subspace decomposition we first describe the known subspace projection beamformer as an orthogonal component of the steering vector that is perpendicular to the interference space then a rao blackwellized particle filter algorithm is designed to estimate the subspace projection beamforming weights all steps including the important sampling weight updating resampling and analytical computation have been discussed in detail finally the overall adaptive beamforming algorithm is summarized and the computational complexity analysis is presented the main contribution of this paper is to apply and formulate rao blackwellized particle filtering to estimate the distribution over the subspace projection beamforming weights different from other two particle filter based beamformers proposed by li and chandrasekar it is a sti based method with unknown source steering vector the sampled state variables are the signal power noise power and a model parameter for beamformer weights transition the marginalized analytical state variables are the subspace projection beamforming weights and the measurements are a series of constructed signal samples by using the estimated projection operator and random noise loading numerical simulations show that the proposed beamformer outperforms linearly constrained minimum variance subspace projection bayesian and other two particle filter based beamformers after convergence it has similar performance to the optimal max sinr beamformer which uses the true steering vector and ideal interference plus noise covariance matrix

robust adaptive beamformers based on worst case optimization and constraints on magnitude response in this paper novel robust adaptive beamformers are proposed with constraints on array magnitude response with the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight the optimization of an adaptive beamformer which is often described as a quadratic optimization problem in conventional beamforming methods is then reformulated as a linear programming lp problem unlike conventional robust beamformers the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple in practice an array has many imperfections besides steering direction error in order to make the adaptive beamformer robust against all kinds of imperfections worst case optimization is exploited to reconstruct the robust beamformer by minimizing array output power with the existence of the worst case array imperfections the robust beamforming can be expressed as a second order cone programming socp problem the resultant beamformer possesses superior robustness against arbitrary array imperfections with the proposed methods a large robust response region and a high signal to interference plus noise ratio sinr enhancement can be achieved readily simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed methods

adaptive wideband beamforming with frequency invariance constraints a response variation rv element is introduced to control the consistency of an adaptive wideband beamformer s response over the frequency range of interest by incorporating the rv element into the linearly constrained minimum variance lcmv beamformer we develop a novel linearly constrained beamformer with an improved output signal to interference plus noise ratio sinr compared to both the traditional formulation and the eigenvector based formulation due to an increased number of degrees of freedom for interference suppression in addition two novel wideband beamformers robust against look direction estimation errors are also proposed as a further application of the rv element one is designed by imposing a constraint on the rv element and simultaneously limiting the magnitude response of the beamformer within a pre defined angle range at a reference frequency the other one is obtained by combining the rv element and the worst case performance optimization method both of them are reformulated in a convex form as the second order cone soc programming problem and solved efficiently using interior point method compared with the original robust methods a more efficient and effective control over the beamformer s response at the look direction region is achieved with an improved overall performance

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

exact tests for structural change in first order dynamic models abstract several finite sample tests of parameter constancy against the presence of structural change are proposed for a linear regression model with one lagged dependent variable and independent normal disturbances the procedures derived include analysis of covariance cusum cusum of squares and predictive tests the approach used to obtain the tests involves the application of three techniques derivation of an exact confidence set for the autoregressive parameter based on using an appropriately extended regression a union intersection technique and when required randomization the tests proposed are illustrated with some artificial data and applied to a dynamic trend model of gross private domestic investment in the u s

signal waveform estimation in the presence of uncertainties about the steering vector we consider the problem of signal waveform estimation using an array of sensors where there exist uncertainties about the steering vector of interest this problem occurs in many situations including arrays undergoing deformations uncalibrated arrays scattering around the source etc in this paper we assume that some statistical knowledge about the variations of the steering vector is available within this framework two approaches are proposed depending on whether the signal is assumed to be deterministic or random in the former case the maximum likelihood ml estimator is derived it is shown that it amounts to a beamforming like processing of the observations and an iterative algorithm is presented to obtain the ml weight vector for random signals a bayesian approach is advocated and we successively derive an approximate minimum mean square error estimator and maximum a posteriori estimators numerical examples are provided to illustrate the performances of the estimators

a general class of preconditioners for statistical iterative reconstruction of emission computed tomography a major drawback of statistical iterative image reconstruction for emission computed tomography is its high computational cost the ill posed nature of tomography leads to slow convergence for standard gradient based iterative approaches such as the steepest descent or the conjugate gradient algorithm here new theory and methods for a class of preconditioners are developed for accelerating the convergence rate of iterative reconstruction to demonstrate the potential of this class of preconditioners a preconditioned conjugate gradient pcg iterative algorithm for weighted least squares reconstruction wls was formulated for emission tomography using simulated positron emission tomography pet data of the hoffman brain phantom it was shown that the convergence rate of the pcg can reduce the number of iterations of the standard conjugate gradient algorithm by a factor of 2 8 times depending on the convergence criterion