monotone discriminant functions and their applications in rheumatology abstract some applications of discriminant analysis e g in rheumatology naturally require that the discriminator satisfies certain monotonicity constraints in terms of the measurements on which the classification is based this article presents a dynamic programming approach to the problem of finding the monotone function that minimizes the total misclassification cost incurred when classifying two types of cases on the basis of two variables measured on each case questions of uniqueness and convexity are explored and the way in which the solution varies with choice of misclassification costs is investigated the use of the bootstrap to estimate the accuracy of summary statistics of interest is discussed the methodology is illustrated using data on rheumatology patients some comparisons with linear discriminant functions and classification tree methods are made

testing and estimating shape constrained nonparametric density and regression in the presence of measurement error in many applications we can expect that or are interested to know if a density function or a regression curve satisfies some specific shape constraints for example when the explanatory variable x represents the value taken by a treatment or dosage the conditional mean of the response y is often anticipated to be a monotone function of x indeed if this regression mean is not monotone in the appropriate direction then the medical or commercial value of the treatment is likely to be significantly curtailed at least for values of x that lie beyond the point at which monotonicity fails in the case of a density common shape constraints include log concavity and unimodality if we can correctly guess the shape of a curve then nonparametric estimators can be improved by taking this information into account addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint and if the conclusion of the test is positive a technique for e

testing for monotonicity of a regression mean by calibrating for linear functions a new approach to testing for monotonicity of a regression mean not requiring computation of a curve estimator or a bandwidth is suggested it is based on the notion of running gradients over short intervals although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip excess mass approach for testing modality hypotheses about densities like the latter methods the new technique does not suffer difficulties caused by almost flat parts of the target function in fact it is calibrated so as to work well for flat response curves and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders in this respect as well as in its construction the running gradients approach differs from alternative techniques based on the notion of a critical bandwidth

speech perception in gated noise the effects of temporal resolution previous investigations have suggested that hearing impaired hi listeners have reduced masking release mr compared to normal hearing listeners nh when they listen in modulated noise the current study examined the following questions that have not been clearly answered first when hi listeners are amplified so that their performance is equal to that of nh listeners in quiet and in steady noise do hi listeners still show reduced mr with modulated noise when compared to nh listeners second is the masking release the same for sentences and cv syllables third does forward masking significantly contribute to the variability in performance among hi listeners to compensate for reduced hearing sensitivity for hi listeners the spectrum levels of both speech and noise were adjusted based on the individual hearing loss there was no significant difference between the performance of nh listeners and that of hi listeners in steady noise and in quiet however the amount of mr for sentences and for cv syllables was significantly reduced for hi listeners for sentence recognition the amount of mr seemed to be more related to hearing sensitivity for low to mid frequencies than to forward masking in contrast forward masking thresholds appear to be a major contributor to the amount of mr for syllable recognition

mass recentred kernel smoothers the local linear smoother usually gives better performance than the nadaraya watson smoother an exception is the case of data sparsity here we discuss a modification of the nadaraya watson smoother by muller song 1993 based on a horizontal shift of the kernel weights towards the local centre of mass of the design points this gives performance similar to the local linear when that works well and better performance when it does not the new smoother also preserves monotonicity shifting towards the centre of mass is also used to develop a modified kernel density estimate which cancels the well known peak spreading effect

unified approach to testing functional hypotheses in semiparametric contexts abstract we suggest a new method with very wide applicability for testing semiparametric hypotheses about functions such as regression means and probability densities the technique is based on characterising hypotheses in terms of functionals which can be estimated root n consistently and constructing test statistics in terms of estimators of the functionals since the tests are semiparametric it is appropriate to assess them on the basis of their ability to detect departures of size n 1 2 from the null hypothesis we show that they do indeed have this property unlike tests constructed in a nonparametric setting their power does not depend critically on choice of a bandwidth and in particular smoothing parameter selection is not an issue that has to be addressed by users of the tests bootstrap methods are suggested for calibrating the tests in a regression setting applications include tests of specification such as partial linear and index models against nonparametric or semiparametric alternatives and tests of monotonicity concavity separability equality of regression functions and base independence of equivalence scales in a density setting they include tests of radial symmetry and stochastic dominance

generalized additive and index models with shape constraints summary we study generalized additive models with shape restrictions e g monotonicity convexity and concavity imposed on each component of the additive prediction function we show that this framework facilitates a non parametric estimator of each additive component obtained by maximizing the likelihood the procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals more generally our methodology can be applied to generalized additive index models here again the procedure can be justified on theoretical grounds and like the original algorithm has highly competitive finite sample performance practical utility is illustrated through the use of these methods in the analysis of two real data sets our algorithms are publicly available in the r package scar short for shape constrained additive regression

estimating smooth monotone functions many situations call for a smooth strictly monotone function f of arbitrary flexibility the family of functions defined by the differential equation d 2 f w df where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions the solution to this equation is f c 0 c 1 d 1 exp d 1 w where c 0 and c 1 are arbitrary constants and d 1 is the partial integration operator a basis for expanding w is suggested that permits explicit integration in the expression of f in fitting data it is also useful to regularize f by penalizing the integral of w 2 since this is a measure of the relative curvature in f applications are discussed to monotone nonparametric regression to the transformation of the dependent variable in non linear regression and to density estimation

low noise noise a practical method of computation is described for making periodic signals v t which have a given frequency spectrum and which minimize the variance v2 v 2 2 in power as a function of time these signals can be used to measure the spectral response of a system the transfer function they represent a significant improvement over traditional random phase and minimum peak value approaches the signals are also of psychophysical interest

transformation invariant and nonparametric monotone smooth estimation of roc curves when a new diagnostic test is developed it is of interest to evaluate its accuracy in distinguishing diseased subjects from non diseased subjects the accuracy of the test is often evaluated by receiver operating characteristic roc curves smooth roc estimates are often preferable for continuous test results when the underlying roc curves are in fact continuous nonparametric and parametric methods have been proposed by various authors to obtain smooth roc curve estimates however there are certain drawbacks with the existing methods parametric methods need specific model assumptions nonparametric methods do not always satisfy the inherent properties of the roc curves such as monotonicity and transformation invariance in this paper we propose a monotone spline approach to obtain smooth monotone roc curves our method ensures important inherent properties of the underlying roc curves which include monotonicity transformation invariance and boundary constraints we compare the finite sample performance of the newly proposed roc method with other roc smoothing methods in large scale simulation studies we illustrate our method through a real life example

calibration using constrained smoothing with applications to mass spectrometry data summary linear regressions are commonly used to calibrate the signal measurements in proteomic analysis by mass spectrometry however with or without a monotone e g log transformation data from such functional proteomic experiments are not necessarily linear or even monotone functions of protein or peptide concentration except over a very restricted range a computationally efficient spline procedure improves upon linear regression however mass spectrometry data are not necessarily homoscedastic more often the variation of measured concentrations increases disproportionately near the boundaries of the instruments measurement capability dynamic range that is the upper and lower limits of quantitation these calibration difficulties exist with other applications of mass spectrometry as well as with other broad scale calibrations therefore the method proposed here uses a functional data approach to define the calibration curve and also the limits of quantitation under the two assumptions i that the variance is a bounded convex function of concentration and ii that the calibration curve itself is monotone at least between the limits of quantitation but not necessarily outside these limits within this paradigm the limit of detection where the signal is definitely present but not measurable with any accuracy is also defined an iterative approach draws on existing smoothing methods to account simultaneously for both restrictions and is shown to achieve the global optimal convergence rate under weak conditions this approach can also be implemented when convexity is replaced by other bounded restrictions examples from addona et al 2009 nature biotechnology 27 663 641 both motivate and illustrate the effectiveness of this functional data methodology when compared with the simpler linear regressions and spline techniques

nonparametric instrumental variable estimation under monotonicity the ill posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suer from a very slow logarithmic rate of convergence in this paper we show that restricting the problem to models with monotone regression functions and monotone instruments signicantly weakens the ill posedness of the problem in stark contrast to the existing literature the presence of a monotone instrument implies boundedness of our measure of ill posedness when restricted to the space of monotone functions based on this result we derive a novel non asymptotic error bound for the constrained estimator that imposes monotonicity of the regression function for a given sample size the bound is independent of the degree of ill posedness as long as the regression function is not too steep as an implication the bound allows us to show that the constrained estimator converges at a fast polynomial rate independently of the degree of ill posedness in a large but slowly shrinking neighborhood of constant functions our simulation study demonstrates signicant nite sample performance gains from imposing monotonicity even when the regression function is rather far from being a constant we apply the constrained estimator to the problem of estimating gasoline demand functions from u s data

on a class of solutions of kdv abstract practically every book on the inverse scattering transform method for solving the cauchy problem for kdv and other integrable systems refers to this method as nonlinear fourier transform if this is indeed so the method should lead to a nonlinear analogue of the fourier expansion formula u t x u k e i kx k t dk in this paper a special class of solutions of kdv whose role is similar to that of e i kx k t is discussed the theory of these solutions referred to here as harmonic breathers is developed and it is shown that these solutions may be used to construct more general solutions of kdv similarly to how the functions e i kx t are used to perform the same task in the theory of fourier transform a nonlinear superposition formula for general solutions of kdv similar to the fourier expansion formula is conjectured

smooth isotonic additive interaction models with application to computer system architecture design the regression relationship between a predictor vector and a response is assumed to be smooth additive with low order interactions and monotone in some of the predictors we consider two modeling approaches the first approach is to fit an unconstrained additive model first and subsequently impose the isotonic constraint to cause the least perturbation of the fit the second approach optimizes the fitting criterion that includes a roughness penalty over isotonic smoothing splines the advantage of the first approach is its modularity and ease of implementation one can incorporate a variety of smoothing methods as building blocks of the unconstrained model in the article we develop the theory for this approach in particular we show that one can use a combination of off the shelf smoothing fitting and isotonic routines however it is empirically shown that fitting an isotonic smoothing spline model produces superior results over a broad range of target functions the methodology is applied to model

positon solutions of the sine gordon equation the concept of positons is introduced for the sine gordon equation exploiting its covariance under darboux transformations positon solutions represent potentials in the associated linear system corresponding to a vanishing reflection coefficient and a transmission coefficient identically one the mutual interaction of positons and the interaction of positons with solitons is considered

cauchy type determinants and integrable systems it is well known that the sylvester matrix equation ax xb c has a unique solution x if and only if 0 spec a spec b the main result of the present article are explicit formulas for the determinant of x in the case that c is one dimensional for diagonal matrices a b we reobtain a classical result by cauchy as a special case the formulas we obtain are a cornerstone in the asymptotic classification of multiple pole solutions to integrable systems like the sine gordon equation and the toda lattice we will provide a concise introduction to the background from soliton theory an operator theoretic approach originating from work of marchenko and carl and discuss examples for the application of the main results

supertransparent potentials for the dirac equation an extension of the classical darboux transformations is applied to the one dimensional dirac equation in order to construct von neumann wigner potentials allowing embedded eigenvalues these potentials lead to a novel type of scattering problem with a trivial s matrix composed of vanishing reflection coefficients and a trivial transmission coefficient related topics like the underlying symmetry of the dirac equation and the connection with positon solutions of nonlinear evolution equations are discussed

multivariate convex regression with adaptive partitioning we propose a new nonparametric method for multivariate regression subject to convexity or concavity constraints on the response function convexity constraints are common in economics statistics operations research financial engineering and optimization but there is currently no multivariate method that is stable and computationally feasible for more than a few thousand observations we introduce convex adaptive partitioning cap which creates a globally convex regression model from locally linear estimates fit on adaptively selected covariate partitions cap is a computationally efficient consistent method for convex regression we demonstrate empirical performance by comparing the performance of cap to other shape constrained and unconstrained regression methods for predicting weekly wages and value function approximation for pricing american basket options

a robbins monro procedure for estimation in semiparametric regression models this paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model we implement a robbins monro procedure very efficient and easy to handle on the one hand we propose a stochastic algorithm similar to that of robbins monro in order to estimate the shift parameter a preliminary evaluation of the regression function is not necessary for estimating the shift parameter on the other hand we make use of a recursive nadaraya watson estimator for the estimation of the regression function this kernel estimator takes in account the previous estimation of the shift parameter we establish the almost sure convergence for both robbins monro and nadaraya watson estimators the asymptotic normality of our estimates is also provided

an improved afriat diewert parkan nonparametric production function estimator abstract recent developments in the production frontier literature include nonparametric estimators with shape constraints a few of these estimators rely on the afriat inequalities to provide piecewise linear approximations to the production function frontier we show in this paper that these afriat diewert parkan adp estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance we propose new estimators with lower variance and a relatively low bias we consider such alternative estimators based on weighted averages of random hinge functions with parameter restrictions small sample properties of the estimators are presented that show our new estimators outperform the existing adp estimators when moderate to large amounts of noise are present

nonparametric estimation and inference under shape restrictions abstract economic theory often provides shape restrictions on functions of interest in applications such as monotonicity convexity non increasing non decreasing returns to scale or the slutsky inequality of consumer theory but economic theory does not provide finite dimensional parametric models this motivates nonparametric estimation under shape restrictions nonparametric estimates are often very noisy shape restrictions stabilize nonparametric estimates without imposing arbitrary restrictions such as additivity or a single index structure that may be inconsistent with economic theory and the data this paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions such as the slutsky inequality the results of monte carlo experiments illustrate the finite sample performance of the method and an empirical example illustrates its use in an application

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

negaton and positon solutions of the kdv and mkdv hierarchy we give a systematic classification and a detailed discussion of the structure motion and scattering of the recently discovered negaton and positon solutions of the korteweg de vries hierarchy there are two distinct types of negaton solutions which we label and where n 1 is the order of the wronskian used in the derivation for negatons the number of singularities and zeros is finite and they show very interesting time dependence the general motion is in the positive x direction except for certain negatons which exhibit one oscillation around the origin in contrast there is just one type of positon solution which we label for positons one gets a finite number of singularities for n odd but an infinite number for even values of n the general motion of positons is in the negative x direction with periodic oscillations negatons and positons retain their identities in a scattering process and their phase shifts are discussed we obtain a simple explanation of all phase shifts by generalizing the notions of mass and centre of mass to singular solutions finally it is shown that negaton and positon solutions of the kdv hierarchy can be used to obtain corresponding new solutions of the modified kdv hierarchy

factors affecting masking release for speech in modulated noise for normal hearing and hearing impaired listeners the speech reception threshold for sentences in stationary noise and in several amplitude modulated noises was measured for 8 normal hearing listeners 29 sensorineural hearing impaired listeners and 16 normal hearing listeners with simulated hearing loss this approach makes it possible to determine whether the reduced benefit from masker modulations as often observed for hearing impaired listeners is due to a loss of signal audibility or due to suprathreshold deficits such as reduced spectral and temporal resolution which were measured in four separate psychophysical tasks results show that the reduced masking release can only partly be accounted for by reduced audibility and that when considering suprathreshold deficits the normal effects associated with a raised presentation level should be taken into account in this perspective reduced spectral resolution does not appear to qualify as an actual suprathreshold deficit while reduced temporal resolution does temporal resolution and age are shown to be the main factors governing masking release for speech in modulated noise accounting for more than half of the intersubject variance their influence appears to be related to the processing of mainly the higher stimulus frequencies results based on calculations of the speech intelligibility index in modulated noise confirm these conclusions

multisoliton multipositon multinegaton and multiperiodic solutions of a coupled volterra lattice system and their continuous limits this paper aims to find new explicit solutions including multisoliton multipositon multinegaton and multiperiodic for a coupled volterra lattice system this coupled lattice system is an integrable discrete version of the coupled korteweg devries kdv equation which has many physical applications the dynamical properties of these new solutions are discussed in detail we also prove that the theory of the coupled volterra lattice system including the lax pair the darboux transformation and explicit solutions yield the corresponding theory of the coupled kdv equation in the continuous limit

temporal masking functions for listeners with real and simulated hearing loss a functional simulation of hearing loss was evaluated in its ability to reproduce the temporal masking functions for eight listeners with mild to severe sensorineural hearing loss each audiometric loss was simulated in a group of age matched normal hearing listeners through a combination of spectrally shaped masking noise and multi band expansion temporal masking functions were obtained in both groups of listeners using a forward masking paradigm in which the level of a 110 ms masker required to just mask a 10 ms fixed level probe 5 10 db sl was measured as a function of the time delay between the masker offset and probe onset at each of four probe frequencies 500 1000 2000 and 4000 hz temporal masking functions were obtained using maskers that were 0 55 1 0 and 1 15 times the probe frequency the slopes and y intercepts of the masking functions were not significantly different for listeners with real and simulated hearing loss the y intercepts were positively correlated with level of hearing loss while the slopes were negatively correlated the ratio of the slopes obtained with the low frequency maskers relative to the on frequency maskers was similar for both groups of listeners and indicated a smaller compressive effect than that observed in normal hearing listeners

bootstrap selection of the smoothing parameter in nonparametric hazard rate estimation abstract an asymptotic representation of the mean weighted integrated squared error for the kernel based estimator of the hazard rate in the presence of right censored samples is obtained for different bootstrap resampling methods as a consequence a new bandwidth selector based on the bootstrap is introduced very satisfactory simulations results are obtained in comparison to the cross validation selector for different models using warped i e binned versions of the estimators

efficiency of thin and thick markets in this paper we propose a matching model to study the efficiency of thin and thick markets our model shows that the probabilities of matches in a thin market are significantly lower than those in a thick market when applying our results to a job search model it implies that if the ratio of job candidates to job openings remains roughly a constant the probability that a person can find a job is higher in a thick market than in a thin market we apply our matching model to the u s academic market for new phd economists consistent with the prediction of our model a field of specialization with more job openings and more candidates has a higher probability of matching

rapid estimation of high parameter auditory filter shapes a bayesian adaptive procedure the quick auditory filter qaf procedure was used to estimate auditory filter shapes that were asymmetric about their peaks in three experiments listeners who were naive to psychoacoustic experiments detected a fixed level pure tone target presented with a spectrally notched noise masker the qaf procedure adaptively manipulated the masker spectrum level and the position of the masker notch which was optimized for the efficient estimation of the five parameters of an auditory filter model experiment i demonstrated that the qaf procedure provided a convergent estimate of the auditory filter shape at 2 khz within 150 to 200 trials approximately 15 min to complete and for a majority of listeners excellent test retest reliability in experiment ii asymmetric auditory filters were estimated for target frequencies of 1 and 4 khz and target levels of 30 and 50 db sound pressure level the estimated filter shapes were generally consistent with published norms especially at the low target level it is known that the auditory filter estimates are narrower for forward masking than simultaneous masking due to peripheral suppression a result replicated in experiment iii using fewer than 200 qaf trials

completion problems and scattering problems for dirac type differential equations with singularities abstract a completion problem to recover a rational matrix function which is j unitary on the line is treated a dirac type system with singularities on the semi axis is recovered explicitly from its left reflection coefficient the close relation between these two problems is discussed

monotone smoothing with application to dose response curves and the assessment of synergism a spline based procedure for monotone curve smoothing is proposed and is illustrated by application to dose response curves it is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs

intelligibility of bandpass filtered speech steepness of slopes required to eliminate transition band contributions despite the recognition that the steepness of filter slopes can play an important role in the intelligibility of bandpass speech there has been no systematic examination of its importance the present study used high orders of finite impulse response fir filtering to produce slopes ranging from 150 to 10 000 db octave the slopes flanked 1 3 octave passbands of everyday sentences having a center frequency of 1500 hz the region of highest intelligibility for the male speaker s voice presentation levels were approximately 75 and 45 db no significant differences were found for the two presentation levels average intelligibility scores ranged from 77 at 150 db octave down to the asymptotic intelligibility score of 12 at 4800 db octave these results indicate that slopes of several thousand db octave may be required for accurate and unambiguous specification of the range of frequencies contributing to intelligibility of filtered speech in addition the extremely steep slopes are needed to ensure tha

intentionally biased bootstrap methods summary a class of weighted bootstrap techniques called biased bootstrap or b bootstrap methods is introduced it is motivated by the need to adjust empirical methods such as the uniform bootstrap in a surgical way to alter some of their features while leaving others unchanged depending on the nature of the adjustment the b bootstrap can be used to reduce bias or to reduce variance or to render some characteristic equal to a predetermined quantity examples of the last application include a b bootstrap approach to hypothesis testing in nonparametric contexts where the b bootstrap enables simulation under the null hypothesis even when the hypothesis is false and a b bootstrap competitor to tibshirani s variance stabilization method an example of the bias reduction application is adjustment of nadaraya watson kernel estimators to make them competitive with local linear smoothing other applications include density estimation under constraints outlier trimming sensitivity analysis skewness or kurtosis reduction and shrinkage

a proportional likelihood ratio model we propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate this model extends the generalized linear model by leaving the distribution unspecified and has a strong connection with semiparametric models such as the selection bias model gilbert et al 1999 the density ratio model qin 1998 fokianos kaimi 2006 the single index model ichimura 1993 and the exponential tilt regression model rathouz gao 2009 a maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived an example and simulation study illustrate the use of the model copyright 2012 oxford university press

constrained multivariate extrapolation models with application to computer cache rates in this article we propose an approach to building multivariate regression models for prediction beyond the range of the data the extrapolation model attempts to accurately estimate the high level trend of the data which can be extended in a natural way the constraints of monotonicity and convexity concavity play an important role in restricting the choice of the high level trend which otherwise would remain rather arbitrary our extrapolation model incorporates these constraints in multiple dimensions we describe the trend as a nonnegative linear combination of twice integrated multivariate b splines and their variations the specific basis functions in our approach are chosen so that any such combination is a plausible a priori model as a result basis function coefficients can be optimized to best fit the data without losing control over the high level trend of the extrapolation model our approach also allows the use of standard model selection techniques we illustrate this by applying cross va

making a non parametric density estimator more attractive and more accurate by data perturbation summary motivated by both the shortcomings of high order density estimators and the increasingly large data sets in many areas of modern science we introduce new high order non parametric density estimators that are guaranteed to be positive and do not have highly oscillatory tails our approach is based on data perturbation e g by tilting or data sharpening it leads to new estimators that are more accurate than conventional kernel techniques that use positive kernels but which nevertheless enjoy the positivity property and are far less wiggly than high order kernel estimators we investigate performance by theoretical analysis and in a numerical study

variable selection in monotone single index models via the adaptive lasso we consider the problem of variable selection for monotone single index models a single index model assumes that the expectation of the outcome is an unknown function of a linear combination of covariates assuming monotonicity of the unknown function is often reasonable and allows for more straightforward inference we present an adaptive lasso penalized least squares approach to estimating the index parameter and the unknown function in these models for continuous outcome monotone function estimates are achieved using the pooled adjacent violators algorithm followed by kernel regression in the iterative estimation process a linear approximation to the unknown function is used therefore reducing the situation to that of linear regression and allowing for the use of standard lasso algorithms such as coordinate descent results of a simulation study indicate that the proposed methods perform well under a variety of circumstances and that an assumption of monotonicity when appropriate noticeably improves performance the proposed methods are applied to data from a randomized clinical trial for the treatment of a critical illness in the intensive care unit

auditory filters and the benefit measured from spectral enhancement algorithms designed to improve speech intelligibility for those with sensorineural hearing loss snhl by enhancing peaks in a spectrum have had limited success since testing of such algorithms cannot separate the theory of the design from the implementation itself the contribution of each of these potentially limiting factors is not clear therefore psychophysical paradigms were used to test subjects with either normal hearing or snhl in detection tasks using well controlled stimuli to predict and assess the limits in performance gain from a spectrally enhancing algorithm a group of normal hearing nh and hearing impaired hi subjects listened in two experiments auditory filter measurements and detection of incremented harmonics in a harmonic spectrum the results show that nh and hi subjects have an improved ability to detect incremented harmonics when there are spectral decrements surrounding the increment various decrement widths and depths were compared against subjects equivalent rectangula

data envelope fitting with constrained polynomial splines estimation of support frontiers and boundaries often involves monotone and or concave edge data smoothing this estimation problem arises in various unrelated contexts such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programs of nuclear reactors very few constrained estimators of the support boundary of a bivariate distribution have been introduced in the literature they are based on simple envelopment techniques which often suffer from lack of precision and smoothness combining the edge estimation idea of hall park and stern with the quadratic spline smoothing method of he and shi we develop a novel constrained fit of the boundary curve which benefits from the smoothness of spline approximation and the computational efficiency of linear programs using cubic splines is also feasible and more attractive under multiple shape constraints computing the optimal spline smoother is then formulated into a second order cone programming problem both constrained quadratic and cubic spline frontiers have a similar level of computational complexity to the unconstrained fits and inherit their asymptotic properties the utility of this method is illustrated through applications to some real datasets and simulation evidence is also presented to show its superiority over the best known methods

smoothing under diffeomorphic constraints with homeomorphic splines in this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms this diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time dependent vector field this solution has a closed form expression which can be computed using classical unconstrained spline smoothing techniques this method does not require the use of quadratic or linear programming under inequality constraints and has therefore a low computational cost in a one dimensional setting incorporating diffeomorphic constraints is equivalent to imposing monotonicity thus as an illustration it is shown that such a monotone spline can be used to make monotone any unconstrained estimator of a regression function and that this monotone smoother inherits the convergence properties of the unconstrained estimator some numerical experiments are proposed to illustrate its finite sample performances and to compare them with another monotone estimator we also provide a two dimensional application on the computation of diffeomorphisms for landmark and image matching

the recognition of sentences in noise by normal hearing listeners using simulations of cochlear implant signal processors with 6 20 channels sentences were processed through simulations of cochlear implant signal processors with 6 8 12 16 and 20 channels and were presented to normal hearing listeners at 2 db s n and at 2 db s n the signal processing operations included bandpass filtering rectification and smoothing of the signal in each band estimation of the rms energy of the signal in each band computed every 4 ms and generation of sinusoids with frequencies equal to the center frequencies of the bands and amplitudes equal to the rms levels in each band the sinusoids were summed and presented to listeners for identification at issue was the number of channels necessary to reach maximum performance on tests of sentence understanding at 2 db s n the performance maximum was reached with 12 channels of stimulation at 2 db s n the performance maximum was reached with 20 channels of stimulation these results in combination with the outcome that in quiet asymptotic performance is reached with five channels of stimulation demonstrate that more channels are needed in noise than in quiet to reach a high level of sentence understanding and that as the s n becomes poorer more channels are needed to achieve a given level of performance

consistency of multidimensional convex regression convex regression is concerned with computing the best fit of a convex function to a data set of n observations in which the independent variable is possibly multidimensional such regression problems arise in operations research economics and other disciplines in which imposing a convexity constraint on the regression function is natural this paper studies a least squares estimator that is computable as the solution of a quadratic program and establishes that it converges almost surely to the true function as n under modest technical assumptions in addition to this multidimensional consistency result we identify the behavior of the estimator when the model is misspecified so that the true function is nonconvex and we extend the consistency result to settings in which the function must be both convex and nondecreasing as is needed for consumer preference utility functions

inverse scattering transformation for positons the scattering problem for the one dimensional schrodinger operator with potential equal to the positon solution of the korteweg de vries kdv equation is investigated it is shown that the transition coefficient is equal to zero and different positon potentials can have the same reflection coefficient i e the inverse scattering problem cannot be solved uniquely it is observed that the reflection coefficient calculated for the positon solutions does not change with time in accordance with the inverse scattering method for kdv

negatons positons rational like solutions and conservation laws of the korteweg de vries equation with loss and non uniformity terms solitons negatons positons rational like solutions and mixed solutions of a non isospectral equation the korteweg de vries equation with loss and non uniformity terms are obtained through the wronskian technique the non isospectral characteristics of the motion behaviours of some solutions are described with some figures made by using mathematica we also derive an infinite number of conservation laws of the equation

nonparametric state price density estimation using constrained least squares and the bootstrap the economic theory of option pricing imposes constraints on the structure of call functions and state price densities except in a few polar cases it does not prescribe functional forms this paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions such as monotonicity and convexity within a single least squares procedure the bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints we apply the techniques to option pricing data on the dax

varying coefficient panel data model in the presence of endogenous selectivity and fixed effects this paper considers a exible panel data sample selection model in which i the outcome equation is permitted to take a semiparametric varying coecient form to capture potential parameter heterogeneity in the relationship of interest ii both the outcome and parametric selection equations contain unobserved xed eects and iii selection is generalized to a polychotomous case we propose a two stage estimator given consistent parameter estimates from the selection equation obtained in the rst stage we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time the selection bias term is then asymptotically removed from the equation along with xed eects using kernel based weights the proposed estimator is consistent and asymptotically normal we rst investigate the nite sample properties of the estimator in a small monte carlo study and then apply it to study production technologies of u s retail credit unions from 2002 to 2006

modulating properties of harmonic breather solutions of kdv we show that a class of solutions of kdv can be used to modulate miscellaneous wavepackets similarly to how the trigonometric functions are used in linear theory to perform the same task

estimating features of a distribution from binomial data we propose estimators of previous termfeatures of the distributionnext term of an unobserved random variable w what is observed is previous termanext term sample of y v x where previous termanext term binary y equals one when w exceeds previous termanext term threshold v determined by experimental design and x are covariates potential applications include bioassay and destructive duration analysis our empirical application is referendum contingent valuation in resource economics where one is interested in previous termfeatures of the distributionnext term of values w willingness to pay placed by consumers on previous termanext term public good such as endangered species sample consumers with characteristics x are asked whether they favor with y 1 if yes and zero otherwise previous termanext term referendum that would provide the good at previous termanext term cost v specified by experimental design this paper provides estimators for quantiles and conditional on x moments of w under both nonparametric and semiparametric specifications

monotone nonparametric regression in monotone regression procedures one utilizes only the monotonicity of the regression function in nonparametric regression one utilizes only the assumed smoothness the analytic and asymptotic properties of the estimator are superior in the latter case however monotonicity is not guaranteed we study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators

bayesian mode regression using mixtures of triangular densities abstract bayesian semiparametric models for mean and median regressions abound but a void for mode regressions exists we fill this gap by nonparametrically modeling the error distribution in such regressions that entails constructing prior distributions on densities which exhibit flexibility while fixing the mode at 0 such priors exist when constraining the mean and median but to our knowledge there is none for the mode our solution with mixtures of triangular distributions results in a conditionally conjugate prior on the space of unimodal untruncated convex densities consistency properties of the resulting modal estimators are studied followed by simulated and real data illustrations

functional coefficient spatial autoregressive models with nonparametric spatial weights abstract we apply local linear regression and sieve estimation technique to estimate functional coefficients and an unknown spatial weighting function respectively via a nonparametric gmm estimation method where we allow both exogenous and endogenous spatial covariates a consistency result is derived to support the method moreover a two step estimator is constructed for the functional coefficients and under certain conditions we show that this estimator can be oracle efficient in the sense that its limiting distribution is the same regardless of whether or not the spatial weights are known both simulated and real data examples are used to illustrate our theory

comparison of frequency selectivity and consonant recognition among hearing impaired and masked normal hearing listeners frequency selectivity and consonant recognition were determined for normal hearing and hearing impaired listeners using techniques that facilitate comparisons of performance among listeners whose absolute thresholds vary in magnitude and configuration first for each of six subjects with cochlear hearing loss masked thresholds in notched noise and narrow band noise maskers were obtained and compared to results for three normal hearing listeners whose thresholds were precisely matched to the impaired listeners by masking with spectrally shaped broadband noise second for hearing impaired listeners and their masked normal hearing controls measurements of consonant recognition were obtained at several speech presentation levels selected on the basis of articulation index predictions to assure equal speech spectrum audibility across listeners the results suggest that frequency selectivity is poorer for hearing impaired listeners than for masked normal hearing listeners even when thresholds among subjects are equated but the deviation from normal frequency selectivity is smaller than estimated from comparisons with normal hearing listeners in quiet critical ratios for hearing impaired listeners are equivalent to normal although frequency selectivity is reduced there is no consistent difference in consonant recognition between hearing impaired subjects and masked normal hearing subjects when performance is assessed under conditions that assure equal speech spectrum audibility across subjects

on the estimation of a convex set from noisy data on its support function abstract in problems of medical imaging and robotic vision measurements of a convex set are sometimes obtained via the set s support function the standard way in which the convex set is recovered from such data is to suppose that it is polygonal model the errors as normal random variables and apply constrained maximum likelihood methods typically the number of sides assumed of the polygon is equal to or a little less than the number of data points however from a statistical viewpoint the number of sides should really be interpreted as a smoothing parameter and chosen to optimize some measure of performance additionally if the true set is not a polygon then a polygonal estimate can be aesthetically unsatisfactory in this article we suggest periodic smoothing methods for estimating the convex set

auditory filter characteristics and consonant recognition for hearing impaired listeners to examine the association between frequency resolution and speech recognition auditory filter parameters and stop consonant recognition were determined for 9 normal hearing and 24 hearing impaired subjects in an earlier investigation the relationship between stop consonant recognition and the articulation index ai had been established on normal hearing listeners based on ai predictions speech presentation levels for each subject in this experiment were selected to obtain a wide range of recognition scores this strategy provides a method of interpreting speech recognition performance among listeners who vary in magnitude and configuration of hearing loss by assuming that conditions which yield equal audible spectra will result in equivalent performance it was reasoned that an association between frequency resolution and consonant recognition may be more appropriately estimated if hearing impaired listeners performance was measured under conditions that assured equivalent audibility of the speech stimuli derived auditory filter parameters indicated that filter widths and dynamic ranges were strongly associated with threshold stop consonant recognition scores for most hearing impaired listeners were not significantly poorer than predicted by the ai model furthermore differences between observed recognition scores and those predicted by the ai were not associated with auditory filter characteristics suggesting that frequency resolution and speech recognition may appear to be associated primarily because both are degraded by threshold elevation

bayesian semiparametric isotonic regression for count data this article proposes a semiparametric bayesian approach for inference on an unknown isotonic regression function f x characterizing the relationship between a continuous predictor x and a count response variable y adjusting for covariates z a dirichlet process mixture of poisson distributions is used to avoid parametric assumptions on the conditional distribution of y given x and z then to also avoid parametric assumptions on f x a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association through the use of carefully tailored hyperprior distributions we allow for borrowing of information across different regions of x in estimating f x and in assessing hypotheses about local increases in the function due to conjugacy properties posterior computation is straightforward using a markov chain monte carlo algorithm the methods are illustrated using data from an epidemiologic study of sleep pr

measuring the critical band for speech the current experiments were designed to measure the frequency resolution employed by listeners during the perception of everyday sentences speech bands having nearly vertical filter slopes and narrow bandwidths were sharply partitioned into various numbers of equal log or erbn width subbands the temporal envelope from each partition was used to amplitude modulate a corresponding band of low noise noise and the modulated carriers were combined and presented to normal hearing listeners intelligibility increased and reached asymptote as the number of partitions increased in the mid and high frequency regions of the speech spectrum the partition bandwidth corresponding to asymptotic performance matched current estimates of psychophysical tuning across a number of conditions these results indicate that in these regions the critical band for speech matches the critical band measured using traditional psychoacoustic methods and nonspeech stimuli however in the low frequency region partition bandwidths at asymptote were somewhat narrower than would be predicted based upon psychophysical tuning it is concluded that overall current estimates of psychophysical tuning represent reasonably well the ability of listeners to extract spectral detail from running speech

nonparametric analysis of dependently interval censored failure time data failure time studies based on observational cohorts often have to deal with irregular intermittent observation of individuals which produces interval censored failure times when the observation times depend on factors related to a person s failure time the failure times may be dependently interval censored inverse intensity of visit weighting methods have been developed for irregularly observed longitudinal or repeated measures data and recently extended to parametric failure time analysis this article develops nonparametric estimation of failure time distributions using weighted generalized estimating equations and monotone smoothing techniques simulations are conducted for examination of the finite sample performance of proposed estimators this research is motivated in part by the toronto psoriatic arthritis cohort study and the proposed methodology is applied to this study

the monotone smoothing of scatterplots we consider the problem of summarizing a scatterplot with a smooth monotone curve a solution that combines local averaging and isotonic regression is proposed and we demonstrate its use with two examples in the second example the procedure is applied in a regression setting to some data from box and cox 1964 and it is shown how this new procedure generalizes box and cox s well known family of transformations in the same example the bootstrap is applied to obtain a measure of the variability of the procedure

asymptotics of the multipositon soliton τ function of the korteweg de vries equation and the supertransparency the asymptotics of the function generating the n positon m soliton solution of the korteweg de vries equation is calculated this allows to prove that solitons do not experience any phase shift in a collision with positons the positons themselves survive mutual collisions unchanged this phenomenon is called the supertransparency or super reflectionless property of the multipositon solutions the linear aspects of this phenomenon are also discussed it is demonstrated that positons acquire two additional but always finite phase shifts in collision with solitons this result admits a natural extension to any number of solitons and positons in interaction

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size

effects of spectral smearing and temporal fine structure degradation on speech masking release this study assessed the effects of spectral smearing and temporal fine structure tfs degradation on masking release mr the improvement in speech identification in amplitude modulated compared to steady noise observed for normal hearing listeners syllables and noise stimuli were processed using either a spectral smearing algorithm or a tone excited vocoder the two processing schemes simulated broadening of the auditory filters by factors of 2 and 4 simulations of the early stages of auditory processing showed that the two schemes produced comparable excitation patterns however fundamental frequency f0 information conveyed by tfs was degraded more severely by the vocoder than by the spectral smearing algorithm both schemes reduced mr but for each amount of spectral smearing the vocoder produced a greater reduction in mr than the spectral smearing algorithm consistent with the effects of each scheme on f0 representation moreover the effects of spectral smearing on mr produced by the two schemes were different for manner and voicing finally mr data for listeners with moderate hearing loss were well matched by mr data obtained for normal hearing listeners with vocoded stimuli suggesting that impaired frequency selectivity alone may not be sufficient to account for the reduced mr observed for hearing impaired listeners