modified signed log likelihood ratio summary the signed log likelihood ratio r for a one dimensional interest parameter can be modified as r r r log u r so that r is asymptotically standard normally distributed with error of order o n 3 2 u being interpretable as a test statistic a new more direct derivation of this result is given which leads to a more explicit expression for u and provides a better handle on the error term the relation of the tail area approximation determined by r to a generalization of the lugannani rice approximation is discussed and the applicability of r to the analysis of residual variation is indicated

the analysis of rates using poisson regression models models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters estimates of the parameters can be obtained by means of iteratively reweighted least squares irls when the events of interest follow the poisson distribution the irls algorithm is equivalent to using the method of scoring to obtain maximum likelihood ml estimates the general poisson regression models include log linear quasilinear and intrinsically nonlinear models the approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model standard statistical packages that support irls can then be used to obtain ml estimates their asymptotic covariance matrix and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space applications of these methods to epidemiologic follow up studies with the data organized into a life table type of format are discussed the method is illustrated by using a nonlinear model derived from the multistage theory of carcinogenesis to analyze lung cancer death rates among british physicians who were regular cigarette smokers

the dependency of timbre on fundamental frequency the dependency of the timbre of musical sounds on their fundamental frequency f0 was examined in three experiments in experiment i subjects compared the timbres of stimuli produced by a set of 12 musical instruments with equal f0 duration and loudness there were three sessions each at a different f0 in experiment ii the same stimuli were rearranged in pairs each with the same difference in f0 and subjects had to ignore the constant difference in pitch in experiment iii instruments were paired both with and without an f0 difference within the same session and subjects had to ignore the variable differences in pitch experiment i yielded dissimilarity matrices that were similar at different f0 s suggesting that instruments kept their relative positions within timbre space experiment ii found that subjects were able to ignore the salient pitch difference while rating timbre dissimilarity dissimilarity matrices were symmetrical suggesting further that the absolute displacement of the set of i

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

on inverting permutation tests abstract polynomial time algorithms are presented for inverting permutation tests the one sample permutation test is inverted to make confidence statements about a location parameter and the two sample permutation test is inverted to make confidence statements concerning a shift in location or scale these algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time a computational method for the inversion of rank tests is also suggested the algorithms extend to stratified experiments

randomization distributions and saddlepoint approximations in generalized linear models various randomization distributions are shown to arise as conditional distributions in the setting of generalized linear models these conditional distributions admit saddlepoint approximations which can obviate the need to simulate the randomization distributions they approximate examples include multinominal and dirichlet bootstraps the jackknife and permutation distributions the double saddlepoint approximation in a regular exponential family is shown to be equivalent to conditional use of a single saddlepoint approximation when the exponential family admits to a cut

symmetric interactions and interference between pitch and timbre variations in the spectral shape of harmonic tone complexes are perceived as timbre changes and can lead to poorer fundamental frequency f0 or pitch discrimination less is known about the effects of f0 variations on spectral shape discrimination the aims of the study were to determine whether the interactions between pitch and timbre are symmetric and to test whether musical training affects listeners ability to ignore variations in irrelevant perceptual dimensions difference limens dls for f0 were measured with and without random concurrent variations in spectral centroid and vice versa additionally sensitivity was measured as the target parameter and the interfering parameter varied by the same amount in terms of individual dls results showed significant and similar interference between pitch f0 and timbre spectral centroid dimensions with upward spectral motion often confused for upward f0 motion and vice versa musicians had better f0dls than non musicians on average but similar spectral centroid dls both groups showed similar interference effects in terms of decreased sensitivity in both dimensions results reveal symmetry in the interference effects between pitch and timbre once differences in sensitivity between dimensions and subjects are controlled musical training does not reliably help to overcome these effects

conditional properties of unconditional parametric bootstrap procedures for inference in exponential families higher order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family the optimal test which is approximated is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter a bootstrap procedure that ignores the conditioning is shown to have desirable conditional properties in providing third order relative accuracy in approximation of p values associated with the optimal test in both continuous and discrete models the bootstrap approach is equivalent to third order analytical approaches and is demonstrated in a number of examples to give very accurate approximations even for very small sample sizes

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

confidence intervals for a binomial proportion and asymptotic expansions p z 2n 1 2 p 1 p 1 2 is currently in near universal use we first show that the coverage properties of the wald interval are persistently poor and defy virtually all conventional wisdom we then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their coverage probabilities and expected lengths the four additional interval methods we study in detail are the score test interval wilson the likelihood ratio test interval a jeffreys prior bayesian interval and an interval suggested by agresti and coull the asymptotic expansions for coverage show that the first three of these alternative methods have coverages that fluctuate about the nominal value while the agresti coull interval has a somewhat larger and more nearly conservative coverage function for the five interval methods we also investigate asymptotically their average coverage relative to distributions for p supported within 0 1 in terms of expected length asymptotic expansions show that the agresti coull interval is always the longest of these the remaining three are rather comparable and are shorter than the wald interval except for p near 0 or 1 these analytical calculations support and complement the findings and the recommendations in brown cai and dasgupta statist sci 2001 16 101 133

confidence intervals for the 50 per cent response dose confidence intervals for the 50 per cent response dose are usually computed using either the delta method or fieller s procedure recently confidence intervals computed by inverting the asymptotic likelihood ratio test have also been recommended there is some controversy as to which of these methods should be used by means of an extensive simulation study we examine these methods as well as confidence intervals obtained by the approximate bootstrap confidence abc procedure and an adjusted form of the likelihood ratio based confidence intervals

saddlepoint approximations as smoothers reference stat article 2002 001doi 10 1093 biomet 89 4 933view record in web of science record created on 2006 04 21 modified on 2017 05 12

perceptual components of pitch spatial representation using a multidimensional scaling technique paired comparison experiments were carried out on the pitch of 18 computer generated complex tones synthesized by slight modification of the frequency structure of shepard s endless scale sounds the results were analyzed by a multidimensional scaling technique and simple helixes were obtained in which two components of pitch tone height and tone chroma were represented some individual differences in perception of pitch were observed according to the weight that the subject gives to each component

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

empirical bayes selection of wavelet thresholds this paper explores a class of empirical bayes methods for level dependent threshold selection in wavelet shrinkage the prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy tailed density the mixing weight or sparsity parameter for each level of the transform is chosen by marginal maximum likelihood if estimation is carried out using the posterior median this is a random thresholding procedure the estimation can also be carried out using other thresholding rules with the same threshold details of the calculations needed for implementing the procedure are included in practice the estimates are quick to compute and there is software available simulations on the standard model functions show excellent performance and applications to data drawn from various fields of application are used to explore the practical performance of the approach by using a general result on the risk of the corresponding marginal maximum likelihood approach for a single sequence overall bounds on the risk of the method are found subject to membership of the unknown function in one of a wide range of besov classes covering also the case of f of bounded variation the rates obtained are optimal for any value of the parameter p in 0 simultaneously for a wide range of loss functions each dominating the lq norm of the th derivative with 0 and 0 q 2 attention is paid to the distinction between sampling the unknown function within white noise and sampling at discrete points and between placing constraints on the function itself and on the discrete wavelet transform of its sequence of values at the observation points results for all relevant combinations of these scenarios are obtained in some cases a key feature of the theory is a particular boundary corrected wavelet basis details of which are discussed overall the approach described seems so far unique in combining the properties of fast computation good theoretical properties and good performance in simulations and in practice a key feature appears to be that the estimate of sparsity adapts to three different zones of estimation first where the signal is not sparse enough for thresholding to be of benefit second where an appropriately chosen threshold results in substantially improved estimation and third where the signal is so sparse that the zero estimate gives the optimum accuracy rate

a quasi nonmetric method for multidimensional scaling via an extended euclidean model an extended two way euclidean multidimensional scaling mds model which assumes both common and specific dimensions is described and contrasted with the standard two way mds model in this extended two way euclidean model then stimuli or other objects are assumed to be characterized by coordinates onr common dimensions in addition each stimulus is assumed to have a dimension or dimensions specific to it alone the overall distance between objecti and objectj then is defined as the square root of the ordinary squared euclidean distance plus terms denoting the specificity of each object the specificity s j can be thought of as the sum of squares of coordinates on those dimensions specific to objecti all of which have nonzero coordinatesonly for objecti in practice we may think of there being just one such specific dimension for each object as this situation is mathematically indistinguishable from the case in which there are more than one we further assume that ij f d ij e ij where ij is the proximity value e g similarity or dissimilarity of objectsi andj d ij is the extended euclidean distance defined above whilee ij is an error term assumed i i d n 0 2 f is assumed either a linear function in the metric case or a monotone spline of specified form in the quasi nonmetric case a numerical procedure alternating a modified newton raphson algorithm with an algorithm for fitting an optimal monotone spline or linear function is used to secure maximum likelihood estimates of the paramstatistics can be used to test hypotheses about the number of common dimensions and or the existence of specific in addition tor common dimensions this approach is illustrated with applications to both artificial data and real data on judged similarity of nations

the likelihood ratio approximation to the conditional distribution of the maximum likelihood estimator in the discrete case summary the likelihood ratio approximation also called barndorff nielsen s approximation and often denoted by p provides a highly accurate approximation to the conditional density of a maximum likelihood estimator 0 given an ancillary statistic in this paper the properties of p are considered for the case in which the underlying random variables have a lattice distribution and 0 has a discrete but not necessarily lattice distribution if 0 has a lattice distribution then p provides a valid approximation to the density of 0 with respect to counting measure if the distribution of 0 is non lattice then p is still a valid approximation to the conditional density of 0 however the dominating measure is no longer counting measure

exact inference for categorical data recent advances and continuing controversies methods for exact small sample analyses with categorical data have been increasingly well developed in recent years a variety of exact methods exist primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics in addition a variety of algorithms now exist for implementing the methods this paper briefly summarizes the exact approaches and describes recent developments controversy continues about the appropriateness of some exact methods primarily relating to their conservative nature because of discreteness this issue is examined for two simple problems in which discreteness can be severe interval estimation of a proportion and the odds ratio in general adjusted exact methods based on the mid p value seem a reasonable way of reducing the severity of this problem

on the accuracy of fieller intervals for binary response data abstract finney proposed the use of a fiducial interval for the median response dose based on fieller s theorem an alternative is to use the asymptotic confidence interval the simulations by abdelbasit and plackett suggest that the two intervals have similar coverage probabilities we compare the two intervals theoretically and in an expanded simulation study our results show that fieller intervals are generally superior an attempt is made to characterize how and when the two intervals differ

posterior probability intervals in bayesian wavelet estimation reference stat article 2004 002doi 10 1093 biomet 91 2 497view record in web of science record created on 2006 04 21 modified on 2017 05 12

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

the nonexistence of 100 1 alpha confidence sets of finite expected diameter in errors in variables and related models on montre que pour certains modeles il est impossible de construire des intervalles de confiance pour les parametres cles qui aient a la fois une confiance positive et une longueur esperee finie

bias reduced and separation proof conditional logistic regression with small or sparse data sets conditional logistic regression is used for the analysis of binary outcomes when subjects are stratified into several subsets e g matched pairs or blocks log odds ratio estimates are usually found by maximizing the conditional likelihood this approach eliminates all strata specific parameters by conditioning on the number of events within each stratum however in the analyses of both an animal experiment and a lung cancer case control study conditional maximum likelihood cml resulted in infinite odds ratio estimates and monotone likelihood estimation can be improved by using cytel inc s well known logxact software which provides a median unbiased estimate and exact or mid p confidence intervals here we suggest and outline point and interval estimation based on maximization of a penalized conditional likelihood in the spirit of firth s biometrika 1993 80 27 38 bias correction method cfl we present comparative analyses of both studies demonstrating some advantages of cfl over competitors we report on a small sample simulation study where cfl log odds ratio estimates were almost unbiased whereas logxact estimates showed some bias and cml estimates exhibited serious bias confidence intervals and tests based on the penalized conditional likelihood had close to nominal coverage rates and yielded highest power among all methods compared respectively therefore we propose cfl as an attractive solution to the stratified analysis of binary data irrespective of the occurrence of monotone likelihood a sas program implementing cfl is available at http www muw ac at msi biometrie programs

improved exact inference about conditional association in three way contingency tables abstract we propose modified exact inferential methods for contingency tables ordinary exact inference is conservative because of the discreteness for estimating a common odds ratio in several 2 2 tables two modifications of the ordinary exact confidence interval maintain at least a fixed confidence level but tend to be much narrower one approach inverts results of a test with a modified p value utilizing the test statistic and table probabilities the second approach inverts one two sided test rather than two one sided tests this approach is much less conservative when the true odds ratio is relatively small or large we also generalize results of cohen and sackrowitz and relate modified p values to construction of exact unbiased and admissible tests for an ordinal alternative to conditional independence

conditioning to reduce the sensitivity of general estimating functions to nuisance parameters summary a conditional method is presented that renders an estimating function insensitive to nuisance parameters the approach is a generalisation of the conditional score method to a general estimating function context and does not require complete specification of the probability model we exploit the informal relationship between general estimating functions and score functions to derive simple generalisations of sufficient and partially ancillary statistics referred to as g sufficient and g ancillary statistics respectively these two types of statistic are defined in a manner that does not require complete knowledge of the probability model and thus are more suitable for use with estimating functions if we condition on a g sufficient statistic for the nuisance parameters the resulting conditional estimating function is insensitive to nuisance parameters and in particular achieves the plug in unbiasedness property furthermore if the conditioning argument is also g ancillary for the parameters of interest then the conditional estimating function possesses an attractive optimality property

the effect of fundamental frequency on the brightness dimension of timbre the dependency of the brightness dimension of timbre on fundamental frequency fo was examined experimentally subjects compared the timbres of 24 synthetic stimuli produced by the combination of six values of spectral centroid to obtain different values of expected brightness and four fo s ranging over 18 semitones subjects were instructed to ignore pitch differences dissimilarity scores were analyzed by both anova and multidimensional scaling mds results show that timbres can be compared between stimuli with different fo s over the range tested and that differences in fo affect timbre dissimilarity in two ways first dissimilarity scores reveal a term proportional to fo difference that shows up in the mds solution as a dimension correlated with fo and orthogonal to other timbre dimensions second fo affects systematically the timbre dimension brightness correlated with spectral centroid interestingly both terms covaried with differences in fo rather than chroma or consonance the first term probably corresponds to pitch the second can be eliminated if the formula for spectral centroid is modified by introducing a corrective factor dependent on fo

experimental design for binary data abstract models for binary data are usually such that the information matrix depends on the unknown parameters thus the standard criteria for optimality in regression experiments cannot be applied without modification methods of going around this difficulty include the use of initial point estimates sequential methods and bayesian analysis this article is mainly concerned with the robustness and the number of design points for methods involving initial estimates and for sequential methods in a small number of stages a final section discusses the criterion of constant information for models involving one or two parameters and summarizes recent results in this field

material identification of real impact sounds effects of size variation in steel glass wood and plexiglass plates identification of the material of struck objects of variable size was investigated previous studies on this issue assumed recognition to be based on acoustical measures of damping this assumption was tested comparing the power of a damping measure in explaining identification data with that of several other acoustical descriptors listeners performance was perfect with respect to gross material categories steel glass and wood plexiglass comprising materials of vastly different mechanical properties impaired performance was observed for materials within the same gross category identification being based on the size of the objects alone the damping descriptor accounted for the identification of the gross categories however other descriptors such as signal duration explained the results equally well materials within the same gross category were identified mainly on the basis of signal frequency overall poor support for the relevance of damping to material perception was found an analysis of the acoustical support for perfect material identification was carried out sufficient acoustical information for perfect performance was found thus procedural biases for the origin of the effects of size could be discarded pointing toward their cognitive rather than methodological nature identification performance was explained in terms of the regularities of the everyday acoustical environment

likelihood for component parameters for a statistical model with data likelihood for the scalar or vector full parameter 0 of dimension p say is typically well defined and easily computed in this paper we investigate likelihood for a component parameter 0 of dimension d p and make use of the recent likelihood theory that has been successful in producing highly accurate third order p values for scalar parameters of continuous models the theory leads under moderate regularity to a definitive third order determination of likelihood for a component parameter 0 of dimension d where 1 d p we use the simple location model on the plane with standard normal errors to motivate the development the example exhibits most of the key characteristics of the general case and the recent theory then extends the determination of likelihood to the general context for the scalar interest parameter case with d 1 the usual determinations are typically of second order accuracy the example indicates how the new determination achieves third order accuracy the implementation is straightforward and uses familiar ingredients to other determinations such as the full maximum likelihood value o the constrained value o given 0 and the observed information j o for a complementing nuisance parameter 0 it does however require a special version of the nuisance information j o a version calibrated relative to a symmetric choice of the exponential type reparameterisation 0 underlying the recent theory but this is easily computed various examples are given and the motivating example is discussed in detail

a distribution free test for symmetry based on a runs statistic abstract i present a simple test based on a runs statistic for symmetry of a continuous distribution about a known median the statistic has a binomial sampling distribution and desirable invariance properties monte carlo studies demonstrate that for a wide variety of alternative asymmetric distributions the test is more powerful than tests proposed by butler 1969 rothman and woodroofe 1972 or hill and rao 1977

small sample ld50 confidence intervals using saddlepoint approximations confidence intervals for the median lethal dose ld50 and other dose percentiles in logistic regression models are developed using a generalization of the fieller theorem for exponential families and saddlepoint approximations simulation results show that in terms of one tailed and two tailed coverage the proposed methodology generally outperforms competing confidence intervals obtained from the classical fieller likelihood ratio and score methods in terms of two tailed coverage the proposed method is comparable to the bartlett corrected likelihood ratio method but generally outperforms it in terms of one tailed coverage an extension to the competing risk setting is presented that allows binary response adjustments to be made using observed censoring times supplementary materials for this article are available online at http pubs amstat org

asymptotics and the theory of inference asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable more importantly asymptotic analysis can also provide insight into the inference process itself suggesting what information is available and how this information may be extracted the development of likelihood inference over the past twenty some years provides an illustration of the interplay between techniques of approximation and statistical theory

interval estimation of the median lethal dose summary assuming a logistic dose response curve one can construct a confidence interval for the ld50 from the asymptotic likelihood ratio test reasons are given for preferring this likelihood ratio interval to the established interval calculated by applying fieller s theorem to the maximum likelihood estimates

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

optimal self tuning filtering prediction and smoothing for discrete multivariable processes an algorithm is proposed for self tuning optimal fixed lag smoothing or filtering for linear discrete time multivariable processes a z transfer function solution to the discrete multivariable estimation problem is first presented this solution involves spectral factorization of polynomial matrices and assumes knowledge of the process parameters and the noise statistics the assumption is then made that the signal generating process and noise statistics are unknown the problem is reformulated so that the model is in an innovations signal form and implicit self tuning estimation algorithms are proposed the parameters of the innovation model of the process can be estimated using an extended kalman filter or alternatively extended recursive least squares these estimated parameters are used directly in the calculation of the predicted smoothed or filtered estimates the approach is an attempt to generalize the work of hagander and wittenmark

spike and slab gene selection for multigroup microarray data dna microarrays can provide insight into genetic changes that characterize different stages of a disease process accurate identification of these changes has significant therapeutic and diagnostic implications statistical analysis for multistage multigroup data is challenging however anova based extensions of two sample z tests a popular method for detecting differentially expressed genes in two groups do not work well in multigroup settings false detection rates are high because of variability of the ordinary least squares estimators and because of regression to the mean induced by correlated parameter estimates we develop a bayesian rescaled spike and slab hierarchical model specifically designed for the multigroup gene detection problem data preprocessing steps are introduced to deal with unique features of microarray data and to enhance selection performance we show theoretically that spike and slab models naturally encourage sparse solutions through a process called selective shrinkage t

is the improved likelihood ratio statistic really improved in the discrete case summary on the basis of some numerical studies we argue that bartlett adjustment of the likelihood ratio statistic for discrete data does not in general yield an improvement in the asymptotic error rate of the chi squared approximation also we argue that the small sample effect of the bartlett adjustment is unclear and that it is in no way comparable with the improvement obtained for continuous data

improving on exact tests by approximate conditioning summary the often conservative nature for discrete data of so called exact tests seems usually the result of unnecessarily precise conditioning we consider avoiding this by conditioning only approximately on the sufficient statistics for nuisance parameters modest relaxation of conditioning results in small loss in terms of the rationale for conditional inference but can greatly reduce the difficulties caused by discreteness exact calculation of p values based on approximate conditioning is possible but unattractive both in terms of the amount of calculation involved and in requiring explicit specification of the extent to which conditioning is to be relaxed it is shown that there is a highly accurate easily computed and very natural asymptotic approximation that avoids these difficulties

confidence intervals from randomization tests an efficient method of constructing confidence intervals that correspond to randomization tests is described the method is based on the robbins monro search process and conducts a separate search for each endpoint of the confidence interval each search requires only slightly more permutations than the number needed for a randomization test diagnostics to monitor searches are suggested and the method is illustrated with examples

h sub 2 inferential filtering prediction and smoothing with application to rolling mill gauge estimation a new minimum mean square error optimal linear estimation problem is considered where no direct measurement of the output to be estimated is available the optimal filter predictor and smoother are derived for this case where outputs must be inferred from available measurements the results cover the usual wiener or kalman filtering problems and also optimal deconvolution estimation problems however they also apply to the situation often found in industry where estimates of signals are required that can only be determined from secondary measurements a weighted h sub 2 cost function is minimized where the weighting function can be chosen to improve the robustness of the solution the optimal estimators are derived both for stable and for unstable signal source models a signal processing application is considered in detail to demonstrate the use of the optimal filter the gauge control problem in metal rolling mills is discussed where only force measurements are available

missing data model of vowel identification vowel identity correlates well with the shape of the transfer function of the vocal tract in particular the position of the first two or three formant peaks however in voiced speech the transfer function is sampled at multiples of the fundamental frequency f0 and the short term spectrum contains peaks at those frequencies rather than at formants it is not clear how the auditory system estimates the original spectral envelope from the vowel waveform cochlear excitation patterns for example resolve harmonics in the low frequency region and their shape varies strongly with f0 the problem cannot be cured by smoothing lag domain components of the spectral envelope are aliased and cause f0 dependent distortion the problem is severe at high f0 s where the spectral envelope is severely undersampled this paper treats vowel identification as a process of pattern recognition with missing data matching is restricted to available data and missing data are ignored using an f0 dependent weighting functi

spike and slab variable selection frequentist and bayesian strategies variable selection in the linear regression model takes many apparent faces from both frequentist and bayesian standpoints in this paper we introduce a variable selection method referred to as a rescaled spike and slab model we study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation specifically we study the usefulness of continuous bimodal priors to model hypervariance parameters and the effect scaling has on the posterior mean through its relationship to penalization several model selection strategies some frequentist and some bayesian in nature are developed and studied theoretically we demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification and show this is achieved using the posterior from a rescaled spike and slab model we also show how to verify a procedure s ability to reduce model uncertainty in finite samples using a specialized forward selection strategy using this tool we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty

resampling procedures to compare two survival distributions in the presence of right censored data summary in this simulation study the accuracy of the size of four classes of test procedures asymptotic normal test permutation test bootstrap hypothesis test and bootstrap interval test were compared using the logrank and prentice wilcoxon two sample test statistics sample sizes of 20 and 50 per group were used twenty observations per group yielded differences in the test procedures when the prentice wilcoxon test statistic was employed the asymptotic test procedure was the most accurate resampling procedures did not improve upon its accuracy using the logrank test statistic the permutation or bootstrap hypothesis testing procedures were closest to the nominal significance level the more popular asymptotic normal logrank test was consistently anticonservative when the number of observations in each group was increased to 50 the test procedures were comparable power comparisons were also examined the test with the greatest power was dependent upon the two survival patterns and the choice of test statistic

a simple general formula for tail probabilities for frequentist and bayesian inference summary we describe a simple general formula for approximating the p value for testing a scalar parameter in the presence of nuisance parameters the formula covers both frequentist and bayesian contexts and does not require explicit nuisance parameterisation implementation is discussed in terms of computer algebra packages examples are given and the relationship to barndorff nielsen s approximation is discussed

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

the weighted log rank class of permutation tests p values and confidence intervals using saddlepoint methods test statistics from the weighted log rank class are commonly used to compare treatment with control when there is right censoring this paper uses saddlepoint methods to determine mid p values from the null permutation distributions of tests from the weighted log rank class analytical saddlepoint computations replace the permutation simulations and provide mid p values that are virtually exact for all practical purposes the speed of these saddlepoint computations makes it practicable to invert the weighted log rank tests to determine nominal 95 confidence intervals for the treatment effect with right censored data such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation

improved likelihood inference for discrete data reference stat article 2006 001doi 10 1111 j 1467 9868 2006 00548 xview record in web of science record created on 2006 04 21 modified on 2017 05 12

technical communique descriptor wiener state estimators based on the modern time series analysis method a new time domain wiener filtering approach is presented asymptotically stable wiener state estimators are presented for discrete linear stochastic descriptor systems they can be implemented via the autoregressive moving average arma recursive filters they can handle the optimal state filtering smoothing and prediction problems in a unified framework and can simply be obtained based on the arma innovation model the solution of the diophantine equations and riccati equations is avoided so that the computational burden is reduced a simulation example shows the effectiveness of the new approach

sigmoidally constrained maximum likelihood estimation in quantal bioassay abstract in quantal bioassay doses x 1 xk of a test substance are administered to n 1 nk animal subjects let ii x denote the probability that an arbitrary subject responds in a specified way to a dose x in this article we consider maximum likelihood estimation of ii x 1 ii xk subject to the constraint that ii is sigmoid of particular interest is the nature of ii at very small x upper confidence bounds for ii x x x 1 are discussed these confidence bounds depend on an inequality that holds when ii is convex on 0 x 1 a test of concavity against the alternative under sigmoidicity and related tests are discussed rejecting concavity requires evidence that ii is convex on 0 x 1

spectral and temporal cues for perception of material and action categories in impacted sound sources in two experiments similarity ratings and categorization performance with recorded impact sounds representing three material categories wood metal glass being manipulated by three different categories of action drop strike rattle were examined previous research focusing on single impact sounds suggests that temporal cues related to damping are essential for material discrimination but spectral cues are potentially more efficient for discriminating materials manipulated by different actions that include multiple impacts e g dropping rattling perceived similarity between material categories across different actions was correlated with the distribution of long term spectral energy spectral centroid similarity between action categories was described by the temporal distribution of envelope energy temporal centroid or by the density of impacts moreover perceptual similarity correlated with the pattern of confusion in categorization judgments listeners tended to confuse materials with similar spectral centroids and actions with similar temporal centroids and onset densities to confirm the influence of these different features spectral cues were removed by applying the envelopes of the original sounds to a broadband noise carrier without spectral cues listeners retained sensitivity to action categories but not to material categories conversely listeners recognized material but not action categories after envelope scrambling that preserved long term spectral content

posterior probability intervals for wavelet thresholding summary we use cumulants to derive bayesian credible intervals for wavelet regression estimates the first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions these powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale hence a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any given data set johnson transformations then yield the credible intervals themselves simulations show that these intervals have good coverage rates even when the underlying function is inhomogeneous where standard methods fail in the case where the curve is smooth the performance of our intervals remains competitive with established nonparametric regression methods

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

genetic algorithm approach to fixed order mixed h sub 2 h sub spl infin optimal deconvolution filter designs the mixed h sub 2 h sub spl infin optimal deconvolution filter is proposed to achieve the h sub 2 optimal reconstruction and a desired robustness against the effect of uncertainties in signal processing from the h sub spl infin norm perspective however the conventional mixed h sub 2 h sub spl infin optimal design filters are very complicated and are not practical for industrial applications for simplicity of implementation and conservation of operation time the fixed order mixed h sub 2 h sub spl infin optimal deconvolution filter design is interesting for engineers in signal processing from the practical design perspective in this study to avoid the trap of local minima a design method based on the genetic algorithm is introduced to treat the nonlinear optimization design problem of the fixed order mixed h sub 2 h sub spl infin deconvolution filter the convergence property of our design algorithm is also discussed finally an example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method

saddlepoint approximation for mixture models two component mixture distributions with one component a point mass and the other a continuous density may be used as priors for bayesian inference when sparse representation of an underlying signal is required we show how saddlepoint approximation in such models can yield highly accurate quantiles for posterior distributions and illustrate this numerically using wavelet regression with point mass laplace and point mass normal prior distributions

polynomial systems approach to optimal linear filtering and prediction the solution of the optimal linear estimation problem is considered using a polynomial matrix description for the discrete system the filter or predictor is given by the solution of two diophantine equations and is equivalent to the state equation form of the steady state kalman filter or the transfer function matrix form of the wiener filter the pole zero properties of the optimal filter are more obvious in the polynomial representation and new insights into the disturbance rejection properties of the filter are obtained the plant or signal model can be stable or unstable and allowance is made for both control and disturbance input subsystems and white and coloured measurement noise or an output disturbance subsystem the model structure was determined by the needs of several industrial filtering problems the polynomial form of filter may easily be included in a self tuning algorithm and a simple adaptive estimator is described

acoustic structure of the five perceptual dimensions of timbre in orchestral instrument tones attempts to relate the perceptual dimensions of timbre to quantitative acoustical dimensions have been tenuous leading to claims that timbre is an emergent property if measurable at all here a three pronged analysis shows that the timbre space of sustained instrument tones occupies 5 dimensions and that a specific combination of acoustic properties uniquely determines gestalt perception of timbre firstly multidimensional scaling mds of dissimilarity judgments generated a perceptual timbre space in which 5 dimensions were cross validated and selected by traditional model comparisons secondly subjects rated tones on semantic scales a discriminant function analysis dfa accounting for variance of these semantic ratings across instruments and between subjects also yielded 5 significant dimensions with similar stimulus ordination the dimensions of timbre space were then interpreted semantically by rotational and reflectional projection of the mds solution into two dfa dimensions thirdly to relate this final space to acoustical structure the perceptual mds coordinates of each sound were regressed with its joint spectrotemporal modulation power spectrum sound structures correlated significantly with distances in perceptual timbre space contrary to previous studies most perceptual timbre dimensions are not the result of purely temporal or spectral features but instead depend on signature spectrotemporal patterns

a comparative investigation of methods for logistic regression with separated or nearly separated data in logistic regression analysis of small or sparse data sets results obtained by classical maximum likelihood methods cannot be generally trusted in such analyses it may even happen that the likelihood meets the convergence criteria while at least one parameter estimate diverges to infinity this situation has been termed separation and it typically occurs whenever no events are observed in one of the two groups defined by a dichotomous covariate more generally separation is caused by a linear combination of continuous or dichotomous covariates that perfectly separates events from non events separation implies infinite or zero maximum likelihood estimates of odds ratios which are usually considered unrealistic i provide some examples of separation and near separation in clinical data sets and discuss some options to analyse such data including exact logistic regression analysis and a penalized likelihood approach both methods supply finite point estimates in case of separation profile penalized likelihood confidence intervals for parameters show excellent behaviour in terms of coverage probability and provide higher power than exact confidence intervals general advantages of the penalized likelihood approach are discussed

a note on nonparametric estimation of the effective dose in quantal bioassay for the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level the estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and a classical density estimate the new method yields a simple and reliable monotone estimate of the effective dose level curve ed and is appealing to users of conventional smoothing methods as kernel estimators local polynomials series estimators or smoothing splines moreover it is computationally very efficient because it does not require a numerical inversion of a monotonized estimate of the quantile dose response curve we prove asymptotic normality of the new estimate and compare it with an available alternative estimate based on a monotonized nonparametric estimate of the dose response curve and calculation of the inverse function by means of a simulation study

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

penalized fieller s confidence interval for the ratio of bivariate normal means constructing a confidence interval for the ratio of bivariate normal means is a classical problem in statistics several methods have been proposed in the literature the fieller method is known as an exact method but can produce an unbounded confidence interval if the denominator of the ratio is not significantly deviated from 0 while the delta and some numeric methods are all bounded they are only first order correct motivated by a real world problem we propose the penalized fieller method which employs the same principle as the fieller method but adopts a penalized likelihood approach to estimate the denominator the proposed method has a simple closed form and can always produce a bounded confidence interval by selecting a suitable penalty parameter moreover the new method is shown to be second order correct under the bivariate normality assumption that is its coverage probability will converge to the nominal level faster than other bounded methods simulation results show that our proposed method generally outperforms the existing methods in terms of controlling the coverage probability and the confidence width and is particularly useful when the denominator does not have adequate power to reject being 0 finally we apply the proposed approach to the interval estimation of the median response dose in pharmacology studies to show its practical usefulness