empirical likelihood for regression discontinuity design this paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs we consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric the proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes unlike the conventional wald type method these features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils scholastic achievements furthermore for the sharp regression discontinuity design we show that the empirical likelihood statistic admits a higher order refinement so called the bartlett correction bandwidth selection methods are also discussed

asymptotically efficient estimation of models defined by convex moment inequalities this paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest in such a setting the identified set is itself convex and hence fully characterized by its support function we provide conditions under which despite being an infinite dimensional parameter the support function admits n consistent regular estimators a semiparametric efficiency bound is then derived for its estimation and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions in addition we show that the plug in estimator is efficient and devise a consistent bootstrap procedure for estimating its limiting distribution the setting we examine is related to an incomplete linear model studied in beresteanu and molinari 2008 and bontemps magnac and maurin 2012 which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem

the bias due to incomplete matching observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group in practice there is a trade off between the desires to find matches for all treated units and to obtain matched treated control pairs that are extremely similar to each other we derive expressions for the bias in the average matched pair difference due to the failure to match all treated units incomplete matching and the failure to obtain exact matches inexact matching a practical example shows that the bias due to incomplete matching can be severe and moreover can be avoided entirely by using an appropriate multivariate nearest available matching algorithm which in the example leaves only a small residual bias due to inexact matching

local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

regression discontinuity design with many thresholds abstract numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments a common practice is to normalize all the cutoffs to zero and estimate one effect this procedure identifies the average treatment effect ate on the observed distribution of individuals local to existing cutoffs however researchers often want to make inferences on more meaningful ates computed over general counterfactual distributions of individuals rather than simply the observed distribution of individuals local to existing cutoffs this paper proposes a consistent and asymptotically normal estimator for such ates when heterogeneity follows a non parametric function of cutoff characteristics in the sharp case the proposed estimator converges at the minimax optimal rate of root n for a specific choice of tuning parameters identification in the fuzzy case with multiple cutoffs is impossible unless heterogeneity follows a finite dimensional function of cutoff characteristics under parametric heterogeneity this paper proposes an ate estimator for the fuzzy case that optimally combines observations to maximize its precision

maximum likelihood deconvolution an optimization theory perspective a large number of deconvolution procedures have appeared in the literature during the last three decades including a number of maximum likelihood deconvolution mld procedures the major advantages of the mld procedures are 1 no assumption is required about the phase of the wavelet most of the classical deconvolution techniques assume a minimum phase wavelet an assumption that may not be appropriate for many data sets 2 mld procedures can resolve closely spaced events i e they are high resolution techniques and 3 they can efficiently handle modeling and measurement errors as well as backscatter effects i e reflections from small features a comparative study of six different mld procedures for estimating the input of a linear time invariant system from measurements which have been corrupted by additive noise was made by using a common framework developed from fundamental optimization theory arguments to date only the kormylo and the chi t algorithms can be recommended

single shot compensation of image distortions and bold contrast optimization using multi echo epi for real time fmri abstract functional magnetic resonance imaging fmri is most commonly based on echo planar imaging epi with higher field strengths gradient performance and computational power real time fmri has become feasible that is brain activation can be monitored during the ongoing scan however epi suffers from geometric distortions due to inhomogeneities of the magnetic field especially close to air tissue interfaces thus functional activations might be mislocalized and assigned to the wrong anatomical structures several techniques have been reported which reduce geometric distortions for example mapping of the static magnetic field b0 or the point spread function for all voxels yet these techniques require additional reference scans and in some cases extensive computational time moreover only static field inhomogeneities can be corrected because the correction is based on a static reference scan we present an approach which allows for simultaneous acquisition and distortion correction of a functional image without a reference scan the technique is based on a modified multi echo epi data acquisition scheme using a phase encoding pe gradient with alternating polarity the images exhibit opposite distortions due to the inverted pe gradient after adjusting the contrast of the images acquired at different echo times this information is used for the distortion correction we present the theory implementation and applications of this single shot distortion correction significant reduction in geometric distortion is shown both for phantom images and human fmri data moreover sensitivity to the blood oxygen level dependent bold effect is increased by weighted summation of the undistorted images

comparison of physiological noise at 1 5 t 3 t and 7 t and optimization of fmri acquisition parameters previous studies have shown that under some conditions noise fluctuations in an fmri time course are dominated by physiological modulations of the image intensity with secondary contributions from thermal image noise and that these two sources scale differently with signal intensity susceptibility weighting te and field strength the snr of the fmri time course was found to be near its asymptotic limit for moderate spatial resolution measurements at 3 t with only marginal gains expected from acquisition at higher field strengths in this study we investigate the amplitude of image intensity fluctuations in the fmri time course at magnetic field strengths of 1 5 t 3 t and 7 t as a function of image resolution flip angle and te the time course snr was a similar function of the image snr regardless of whether the image snr was modulated by flip angle image resolution or field strength for spatial resolutions typical of those currently used in fmri e g 3 3 3 mm3 increases in image snr obtained from 7 t acquisition produced only modest increases in time course snr at this spatial resolution the ratio of physiological noise to thermal image noise was 0 61 0 89 and 2 23 for 1 5 t 3 t and 7 t at a resolution of 1 1 3 mm3 however the physiological to thermal noise ratio was 0 34 0 57 and 0 91 for 1 5 t 3 t and 7 t for te near t2 thus by reducing the signal strength using higher image resolution the ratio of physiologic to image noise could be reduced to a regime where increased sensitivity afforded by higher field strength still translated to improved snr in the fmri time series

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

conditional permutation tests and the propensity score in observational studies abstract in observational studies the distribution of treatment assignments is unknown and therefore randomization tests are not generally applicable however permutation tests that condition on sample information about the treatment assignment mechanism can be applicable in observational studies provided treatment assignment is strongly ignorable these tests use the conditional distribution of the treatment assignments given a sufficient statistic for the unknown parameter of the propensity score several tests that are commonly used in observational studies are particular instances of this general procedure moreover conditional permutation tests and covariance adjustment are closely related in the sense that the conditional permutation distribution of the covariance adjusted difference leads to the same inferences as the conditional permutation distribution of the unadjusted difference of sample means a backtrack algorithm is developed to permit efficient calculation of the exact conditional si

sample size formulae for two stage randomized trials with survival outcomes two stage randomized trials are growing in importance in developing adaptive treatment strategies i e treatment policies or dynamic treatment regimes usually the first stage involves randomization to one of the several initial treatments the second stage of treatment begins when an early nonresponse criterion or response criterion is met in the second stage nonresponding subjects are re randomized among second stage treatments sample size calculations for planning these two stage randomized trials with failure time outcomes are challenging because the variances of common test statistics depend in a complex manner on the joint distribution of time to the early nonresponse criterion or response criterion and the primary failure time outcome we produce simple albeit conservative sample size formulae by using upper bounds on the variances the resulting formulae only require the working assumptions needed to size a standard single stage randomized trial and in common settings are only mildly conservative these sample size formulae are based on either a weighted kaplan meier estimator of survival probabilities at a fixed time point or a weighted version of the log rank test

causal inference in paired two arm experimental studies under noncompliance with application to prognosis of myocardial infarction motivated by a study about prompt coronary angiography in myocardial infarction we propose a method to estimate the causal effect of a treatment in two arm experimental studies with possible noncompliance in both treatment and control arms we base the method on a causal model for repeated binary outcomes before and after the treatment which includes individual covariates and latent variables for the unobserved heterogeneity between subjects moreover given the type of noncompliance the model assumes the existence of three subpopulations of subjects compliers never takers and always takers we estimate the model using a two step estimator at the first step we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates at the second step we estimate the causal effects through a conditional logistic method the implementation of which depends on the results from the first step the estimator is approximately consistent and under certain circumstances exactly consistent we provide evidence that the bias is negligible in relevant situations we compute standard errors on the basis of a sandwich formula the application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years with a log odds of about 2 given that noncompliance is significant for patients being given the treatment because of high risk conditions classical estimators fail to detect or at least underestimate this effect copyright 2013 john wiley sons ltd

an evaluation of the use of magnetic field maps to undistort echo planar images when a head is placed in an mri scanner differences between the magnetic susceptibility of tissue bone and air distort the magnetic field while some of the resulting inhomogeneity can be corrected by the shimming process much of it cannot and this causes distortion sometimes referred to as geometric distortion of echo planar images epis one strategy for the correction of distortion is to acquire a map of the magnetic field achieved in each subject and then to use this to undistort their epis after reconstruction jezzard and balaban 1995 here we present five experiments to evaluate the application of such a strategy on data from a 3 t scanner we show that after undistortion the shape of epis is more similar to the true shape of the brain and we investigate the effect of head movement on the efficacy of undistortion if undistortion was applied first it was found that less nonlinear warping was required to transform epis into a standard space particularly in the phaseencode direction we show that if spm 99 normalization is used to perform a nonlinear warp to standard space the prior application of undistortion increases the statistical power of group studies with motor and auditory tasks we show that this increase in power is due to an increase in the overlap of activation of different subjects finally we evaluate where in the brain undistorting epis might be expected to have the greatest effect in terms both of mislocalization of activation and of a reduction in power overall undistorting epis using field maps has proved extremely successful improving the anatomical localization of activation and increasing statistical power 2002 elsevier science usa

confidence bands for regression functions abstract a method for obtaining conservative confidence bands for regression functions in low dimensions is given of particular importance is the applicability of the method to nonparametric regression computations examples and comparisons indicate the effectiveness of the method

restoration of blurred star field images by maximally sparse optimization the problem of removing blur from or sharpening astronomical star field intensity images is discussed an approach to image restoration that recovers image detail using a constrained optimization theoretic approach is introduced ideal star images may be modeled as a few point sources in a uniform background it is argued that a direct measure of image sparseness is the appropriate optimization criterion for deconvolving the image blurring function a sparseness criterion based on the l sub p is presented and candidate algorithms for solving the ensuing nonlinear constrained optimization problem are presented and reviewed synthetic and actual star image reconstruction examples are presented to demonstrate the method s superior performance as compared with several image deconvolution methods

efficient estimation of conditional variance functions in stochastic regression author s fan jianqing yao qiwei abstract conditional heteroscedasticity has been often used in modelling and understanding the variability of statistical data under a general setup which includes the nonlinear time series model as a special case we propose an e cient and adaptive method for estimating the conditional variance the basic idea is to apply a local linear regression to the squared residuals we demonstrate that without knowing the regression function we can estimate the conditional variance asymptotically as well as if the regression were given this asymptotic result established under the assumption that the observations are made from a strictly stationary and absolutely regular process is also veri ed via simulation further the asymptotic result paves the way for adapting an automatic bandwidth selection scheme an application with nancial data illustrates the usefulness of the proposed techniques

effects of data dimension on empirical likelihood summary we evaluate the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high dimensional data under a general multivariate model data dimension and dependence among components of the multivariate random vector affect the empirical likelihood directly through the trace and the eigenvalues of the covariance matrix the growth rates to infinity we obtain for the data dimension improve the rates of hjort et al 2008

from association to causation in observational studies the role of tests of strongly ignorable treatment assignment abstract if treatment assignment is strongly ignorable then adjustment for observed covariates is sufficient to produce consistent estimates of treatment effects in observational studies a general approach to testing this critical assumption is developed and applied to a study of the effects of nuclear fallout on the risk of childhood leukemia r a fisher s advice on the interpretation of observational studies was make your theories elaborate formally make causal theories sufficiently detailed that under the theory strongly ignorable assignment has testable consequences

functional mri using sensitivity encoded echo planar imaging sense epi parallel imaging methods become increasingly available on clinical mr scanners to investigate the potential of sensitivity encoded single shot epi sense epi for functional mri five imaging protocols at different sense reduction factors r and matrix sizes were compared with respect to their noise characteristics and their sensitivity toward functional activation in a motor task examination at constant echo times sense epi was either used to shorten the single volume acquisition times trmin at matrix size 128 100 22 slices from 3 9 s no sense to 2 0 s at r 3 or to increase the matrix size to 192 153 22 slices resulting in trmin 5 3 s for r 2o r trmin 3 4 s for r 3 at the lower resolution the bisection of echo train length r 2 substantially reduced distortions and blurring while signal to noise and statistical power measured by cluster size and maximum t value per unit time were hardly reduced at r 3 the additional gain in speed and distortion reduction was quite small while signal to noise and statistical power dropped significantly with enhanced spatial resolution the time course signal to noise was better than expected from theory for purely thermal noise because of a reduced contribution of physiological noise and statistical power almost reached that of the regular low resolution single shot epi with a slight drop off toward r 3 thus sense epi allows to substantially increase speed and spatial resolution in fmri at sense reduction factors up to r 2 the potential drawbacks regarding signal to noise and statistical power are almost negligible

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

adjusting treatment effect estimates by post stratification in randomized experiments summary experimenters often use post stratification to adjust estimates post stratification is akin to blocking except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment we analyse both post stratification and blocking under the neyman rubin model and compare the efficiency of these designs we derive the variances for a post stratified estimator and a simple difference in means estimator under different randomization schemes post stratification is nearly as efficient as blocking the difference in their variances is of the order of 1 n2 with a constant depending on treatment proportion post stratification is therefore a reasonable alternative to blocking when blocking is not feasible however in finite samples post stratification can increase variance if the number of strata is large and the strata are poorly chosen to examine why the estimators variances are different we extend our results by conditioning on the observed number of treated units in each stratum conditioning also provides more accurate variance estimates because it takes into account how close or far a realized random sample is from a comparable blocked experiment we then show that the practical substance of our results remains under an infinite population sampling model finally we provide an analysis of an actual experiment to illustrate our analytical results

on bartlett correction of empirical likelihood in the presence of nuisance parameters summary lazar mykland 1999 showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be bartlett correctable this paper shows that bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest we establish in the broad framework of estimating functions that the empirical likelihood is still bartlett correctable if the nuisance parameter is profiled out given the value of the parameter of interest

deconvolution of sparse spike trains by iterated window maximization a new algorithm for deconvolution of sparse spike trains is presented to maximize a joint map criterion an initial configuration is iteratively improved through a number of small changes computational savings are achieved by precomputing and storing two correlation functions and by employing a window strategy the resulting formulas are simple intuitive and efficient in addition they allow much more complicated transitions than state space solutions such as kormylo and mendel s 1982 single most likely replacement algorithm this makes it possible to reduce significantly the probability that the algorithm terminates in a local maximum synthetic data examples are presented that support these claims

empirical likelihood confidence intervals for local linear smoothers summary empirical likelihood is considered in conjunction with the local linear smoother to construct confidence intervals for a nonparametric regression function with bounded support the coverage error of the empirical likelihood confidence intervals is evaluated and is shown to be of the same order throughout the support of the regression function this is a significant improvement over confidence intervals based directly on the asymptotic normal distribution of the local linear estimator which have a larger order of coverage error near the boundary this improvement is attributable to the natural variance estimator that empirical likelihood implicitly chooses for the local linear smoother

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

unsupervised deconvolution of sparse spike trains using stochastic approximation this paper presents an unsupervised method for restoration of sparse spike trains these signals are modeled as random bernoulli gaussian processes and their unsupervised restoration requires i estimation of the hyperparameters that control the stochastic models of the input and noise signals and ii deconvolution of the pulse process classically the problem is solved iteratively using a maximum generalized likelihood approach despite questionable statistical properties the contribution of the article is threefold first we present a new core algorithm for supervised deconvolution of spike trains which exhibits enhanced numerical efficiency and reduced memory requirements second we propose an original implementation of a hyperparameter estimation procedure that is based upon a stochastic version of the expectation maximization em algorithm this procedure utilizes the same core algorithm as the supervised deconvolution method third monte carlo simulations show that the proposed unsupervised restoration method exhibits satisfactory theoretical and practical behavior and that in addition good global numerical efficiency is achieved

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

regression analysis with clustered data clustered data are found in many different types of studies for example studies involving repeated measures inter rater agreement studies household surveys crossover designs and community randomized trials analyses based on population average and cluster specific models are commonly used for estimating treatment exposure effects with clustered data this paper discusses conditions when one or both types of models are appropriate for estimating causal effects and when there is agreement between population average and cluster specific analyses applications of survey sampling methods to the robust estimation of standard errors of estimated treatment parameters are discussed

robust nonparametric confidence intervals for regression discontinuity designs in the regression discontinuity rd design units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff in this design local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects the performance of these confidence intervals in applications however may be seriously hampered by their sensitivity to the specific bandwidth employed available bandwidth selectors typically yield a large bandwidth leading to data driven confidence intervals that may be biased with empirical coverage well below their nominal target we propose new theory based more robust confidence interval estimators for average treatment effects at the cutoff in sharp rd sharp kink rd fuzzy rd and fuzzy kink rd designs our proposed confidence intervals are constructed using a bias corrected rd estimator together with a novel standard error estimator for practical implementation we discuss mean squared error optimal bandwidths which are by construction not valid for conventional confidence intervals but are valid with our robust approach and consistent standard error estimators based on our new variance formulas in a special case of practical interest our procedure amounts to running a quadratic instead of a linear local regression more generally our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed we find in a simulation study that our confidence intervals exhibit close to correct empirical coverage and good empirical interval length on average remarkably improving upon the alternatives available in the literature all results are readily available in r and stata using our companion software packages described in calonico cattaneo and titiunik 2014d 2014b

empirical likelihood as a goodness of fit measure summary the method of empirical likelihood can be viewed as one of allocating probabilities to an n cell contingency table so as to minimise a goodness of fit criterion it is shown that when the cressie read power divergence statistic is used as the criterion confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the cressie read parameter including 1 maximum entropy 0 empirical likelihood and 1 pearson s z2 it is noted that in the power divergence family empirical likelihood is the only member which is bartlettcorrectable however simulation results suggest that for the mean using a scaled f distribution yields more accurate coverage levels for moderate sample sizes

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

multichannel blind deconvolution of seismic signals a new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given to remove the inherent ambiguity in this blind deconvolution problem we introduce relevant a priori information our major assumption is sparseness of the reflectivity which corresponds to a layered earth model this allows nonminimum phase wavelets to be recovered reliably and closely spaced reflectors to be resolved to combine a priori knowledge and data we use a bayesian framework and derive a maximum a posteriori estimate computing this estimate is a difficult optimization problem solved by a suboptimal iterative procedure the procedure alternates steps of wavelet estimation and reflectivity estimation the first step only requires a simple least squares fit while the second step is solved by the iterated window maximization algorithm proposed by kaaresen this enables better efficiency and optimality than established alternatives the resulting optimization method can easily handle multichannel models with only a moderate increase of the computational load lateral continuity of the reflectors is achieved by modeling local dependencies between neighboring traces major improvements in both wavelet and reflectivity estimates are obtained by taking the wavelet to be invariant across several traces the practicality of the algorithm is demonstrated on synthetic and real seismic data an application to multivariate well log segmentation is also given

the power of bootstrap and asymptotic tests the bootstrap discrepancy measures the difference in rejection probabilities between a bootstrap test and one based on the true distribution the order of magnitude of the bootstrap discrepancy is the same under the null hypothesis and under non null processes described by pitman drift if the test statistic is not an exact pivot critical values depend on which data generating process dgp is used to determine the null distribution we propose using the dgp which minimizes the bootstrap discrepancy we also show that under an asymptotic independence condition the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation

viterbi algorithm detector for bernoulli gaussian processes this paper shows how to apply the viterbi algorithm to detect randomly located impulses which have gaussian distributed amplitudes our detector can deal with cases of severely overlapping wavelets experimental results and comparisons to kormylo and mendel s 12 single most likely replacement detector are provided using synthetic data

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

dual and simultaneous sensitivity analysis for matched pairs summary when a study shows an association between a treatment and a response before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable u might explain the observed association sensitivity analysis clarifies the properties u must have in terms of its relationship to the response and its imbalance in the groups being compared a substantial literature has investigated the imbalance or association between u and group assignment this paper develops a dual sensitivity analysis for matched pairs focusing on the strength of the relationship between u and the response required to reduce an observed association to non significance a third simultaneous form of sensitivity analysis models both relationships between u and treatment assignment and u and response the simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships the methods are illustrated by several examples

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

bold sensitivity and snr characteristics of parallel imaging accelerated single shot multi echo epi for fmri echo planar imaging epi is a standard procedure in functional magnetic resonance imaging fmri for measuring changes in the blood oxygen level dependent bold signal associated with neuronal activity the images obtained from fmri with epi however exhibit signal dropouts and geometric distortions parallel imaging pi due to its short readout accelerates image acquisition and might reduce dephasing in phase encoding direction the concomitant loss of signal to noise ratio snr might be compensated through single shot multi echo epi mepi we systematically compared the temporal snr and bold sensitivity of single echoes te 15 45 and 75ms and contrast optimized mepi with and without pi and mepi based denoising audio visual stimulation under natural viewing conditions activated distributed neural networks heterogeneous snr noise gain and sensitivity maps emerged in single echoes snr and bold sensitivity followed the predicted dependency on echo time te and were reduced under pi however the combination of echoes with mepi recovered the quality parameters and increased bold signal changes at circumscribed fronto polar and deep brain structures we suggest applying pi only in combination with mepi to reduce imaging artifacts and conserve bold sensitivity

a semi nonparametric estimator of regression discontinuity design with discrete duration outcomes abstract we consider the regression discontinuity rd design with the duration outcome which has discrete support the parameters of policy interest are treatment effects on unconditional duration effect and conditional hazard effect exiting probabilities for each discrete level we propose a novel semi nonparametric estimator which exploits a flexible separability structure of the underlying continuous time duration process simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank the peculiarity is delivered by the nature of the rd estimand and we provide solutions random censoring and competing risks can also be allowed in our framework

multichannel deconvolution of seismic signals using statistical mcmc methods in this paper we propose two multichannel blind deconvolution algorithms for the restoration of two dimensional 2d seismic data both algorithms are based on a 2d reflectivity prior model and use iterative multichannel deconvolution procedures which deconvolve the seismic data while taking into account the spatial dependency between neighboring traces the first algorithm employs in each step a modified maximum posterior mode mpm algorithm which estimates a reflectivity column from the corresponding observed trace using the estimate of the preceding reflectivity column the second algorithm takes into account estimates of both the preceding and subsequent columns in the estimation process both algorithms are applied to synthetic and real data and demonstrate better results compared to those obtained by a single channel deconvolution method expectedly the second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm

addressing complications of intention to treat analysis in the combined presence of all or none treatment noncompliance and subsequent missing outcomes summary we study the combined impact that all or none compliance and subsequent missing outcomes can have on the estimation of the intention to treat effect of assignment in randomised studies in this setting a standard analysis which drops subjects with missing outcomes and ignores compliance information can be biased for the intention to treat effect to address all or none compliance that is followed by missing outcomes we construct a new estimation procedure for the intention to treat effect that maintains good randomisation based properties under more plausible nonignorable noncompliance and nonignorable missing outcome conditions the compound exclusion restriction on the effect of assignment and the latent ignorability of the missing data mechanism we present both theoretical results and a simulation study moreover we show how the two key concepts of compound exclusion and latent ignorability are relevant in more complicated settings such as right censoring of a time to event outcome

bayesian analysis of cross section and clustered data treatment models this paper is concerned with the problem of determining the effect of a categorical treatment variable on a response given that the treatment is non randomly assigned and the response on any given subject is observed for one setting of the treatment we consider classes of models that are designed for such problems these models are subjected to a fully bayesian analysis based on markov chain monte carlo methods the analysis of the treatment effect is then based on amongst other things the posterior distribution of the potential outcomes counter factuals at the subject level which is obtained as a by product of the mcmc simulation procedure the analysis is extended to models with categorical treatments and binary and clustered outcomes the problem of model comparisons is also considered different aspects of the methodology are illustrated through two data examples

causality tests and observationally equivalent representations of econometric models abstract this article deals with the problem of observational equivalence of alternative econometric equation systems on the same data as a practical obstacle to econometricians success in applying definitions of causality by simon 1953 strotz and wold 1960 and granger 1969 to economic time series

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

identification and estimation of treatment effects with a regression discontinuity design the regression discontinuity rd data design is a quasi experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables this data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment in the first application and discussion of the rd method thistlethwaite and campbell 1960 study the effect of student scholarships on career aspirations using the fact that awards are only made if a test score exceeds a threshold more recently van der klaauw 1997 estimates the effect of financial aid offers on students decisions to attend a particular college taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students grade point average and sat score angrist and lavy 1999 estimate the effect of class size on student test scores taking advantage of a rule stipulating that another classroom be added when the average class size exceeds a threshold level finally black 1999 uses an rd approach to estimate parents willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries regression discontinuity methods have potentially broad applicability in economic research because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method although there have been several discussions and applications of rd methods in the literature important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions here we show that identifying conditions invoked in previous applications of rd methods are often overly strong and that treatment effects can be nonparametrically identified under an rd design by a weak functional form restriction the restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism we also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the wald estimator as an rd estimator

evaluation and applications of the iterated window maximization method for sparse deconvolution estimating a sparse signal from a linearly degraded and noisy data record is often desirable in seismic and ultrasonic applications bernoulli gaussian modeling and maximum a posteriori estimation has proven successful but entails computationally difficult optimization problems that must be solved by suboptimal methods the iterated window maximization iwm algorithm was proposed for such optimization by kaaresen see ibid vol 45 p 1173 83 1997 the purpose of this paper is twofold first the iwm is evaluated against several established alternatives for bernoulli gaussian deconvolution the restoration quality is quantified by various loss functions and the average performance is studied through simulation in all cases examined the iwm combined better restoration and significantly faster execution than the other algorithms this motivates extension of iwm to other models which is the second objective of this paper promising real data results are obtained from such diverse applications as robust modeling of ultrasonic nondestructive evaluation data deblurring of two dimensional 2 d astronomical star fields and segmentation of seismic well logs it is also argued that iwm can be used for other deconvolution problems as long as the function to be reconstructed is in some sense sparse

empirical likelihood based inference for nonparametric recurrent diffusions this paper provides a new approach to constructing confidence intervals for nonparametric drift and diffusion functions in the continuous time diffusion model via empirical likelihood el the log el ratios are constructed through the estimating equations satisfied by the local linear estimators limit theories are developed by means of increasing time span and shrinking observational intervals the results apply to both stationary and nonstationary recurrent diffusion processes simulations show that for both drift and diffusion functions the new procedure performs remarkably well in finite samples and clearly dominates the conventional method in constructing confidence intervals based on asymptotic normality an empirical example is provided to illustrate the usefulness of the proposed method

recovery of a sparse spike time series by l sub 1 norm deconvolution an l sub 1 norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of ultrasonic nondestructive evaluation in candu nuclear reactors for each problem parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h according to a quantified performance factor this performance factor is based on a quantified analysis of the transitions in estimates of h as the damping parameter is varied over a wide range of possible values it is shown that for the examined cases in which the true impulse response is a sparsely filled spike strain the l sub 1 norm provides significantly better results than the more commonly used l sub 2 norm minimization schemes these results are shown to be consistent with theoretical predictions

a linear theory for noncausality abstract different definitions of noncausality according to granger sims haugh and pierce are analyzed in terms of orthogonality in the hilbert space of square integrable variables conditions when necessary are given for their respective equivalence some problems of testability are mentioned finally noncausality is also analyzed in terms of rational expectations extending previous results of sims author