the general properties of discrete time competitive dynamical systems abstract for strongly competitive discrete time dynamical systems on a strongly ordered topological vector space it is proved that any or limit set is unordered and lies on some invariant hypersurface with codimension one which generalizes hirsch s results for competitive autonomous systems of ordinary differential equations to competitive maps in a very general framework and implies the sarkovskii s theorem for planar strongly competitive and monotone maps we also show that the definition of competitiveness gives more restriction on homeomorphic property

in vivo estimation of the glenohumeral joint rotation center from scapular bony landmarks by linear regression in this paper a method is described for in vivo prediction of the glenohumeral joint rotation center gh r necessary for the construction of a humerus local coordinate system in shoulder kinematic studies the three dimensional positions of five scapula bony landmarks as well as a large number of data points on the surface of the glenoid and humeral head were collected at 36 sets of cadaver scapulae and adjacent humeri the position of gh r in each scapula was estimated by mathematically fitting spheres to the glenoid and humeral head gh r prediction from scapula geometry parameters by linear regression resulted in a rmse between measured and predicted gh r of 2 32 mm for the x coordinate 2 69 mm for the y coordinate and 3 04 mm for the z coordinate application in vivo revealed a random humerus orientation error due to measurement inaccuracies of 1 35 0 29 and 1 26 degrees standard deviation per rotation angle the estimated total humerus orientation error including the offset error due to the regression model inaccuracy was 2 86 0 84 and 2 69 degrees standard deviation as these errors were about 15 and 20 of respectively the intra and inter subject variability of the humerus orientations measured it is concluded that the method described in this paper allows for an adequate construction of a humerus local coordinate system

mice multiple peak identification characterization and estimation summary mice multiple peak identification characterization and estimation is a procedure for estimating a lower bound of the number of frequency peaks and for estimating the frequency peak parameters the leading application is protein structure determination using nuclear magnetic resonance nmr experiments nmr frequency data are multiple peak data where each frequency peak corresponds to two connected atoms in the three dimensional protein structure we analyze the nmr frequency data through a series of steps a preliminary step for separating the signal from the background followed by identification of local maxima up to a noise level dependent threshold estimation of the frequency peak parameters using an iterative algorithm and detection of mixtures of peaks using hypothesis testing

an alternative root n consistent estimator for panel data binary choice models in this paper we present an alternative root n consistent estimator for panel data fixed effects binary choice models the proposed estimator relaxes one of the key conditions that are required for the consistency of the estimator proposed in honore and lewbel 2002 and is shown to be consistent and asymptotically normally distributed under some sufficient conditions an easy to compute consistent estimator for the asymptotic covariance is provided

kinematics estimation of straddled movements on high bar from a limited number of skin markers using a chain model to reduce the effects of skin movement artefacts and apparent joint dislocations in the kinematics of whole body movement derived from marker locations global optimisation procedures with a chain model have been developed these procedures can also be used to reduce the number of markers when self occlusions are hard to avoid this paper assesses the kinematics precision of three marker sets 16 11 and 7 markers for movements on high bar with straddled piked posture a three dimensional person specific chain model was defined with 9 parameters and 12 degrees of freedom and an iterative procedure optimised the gymnast posture for each frame of the three marker sets the time histories of joint angles obtained from the reduced marker sets were compared with those from the 16 marker set by means of a root mean square difference measure occlusions of medial markers fixed on the lower limb occurred when the legs were together and the pelvis markers disappeared primarily during the piked posture despite these occlusions reconstruction was possible with 16 11 and 7 markers the time histories of joint angles were similar the main differences were for the thigh mediolateral rotation and the knee flexion because the knee was close to full extension when five markers were removed the average angles difference was about 3 this difference increased to 9 for the seven marker set it is concluded that kinematics of sports movement can be reconstructed using a chain model and a global optimisation procedure for a reduced number of markers

testing for monotonicity under endogeneity an application to the reservation wage function abstract this paper develops a test for monotonicity of nonparametric regression models under endogeneity which in its generality is novel in the literature the test statistic which is built upon a second order u process introduces correction terms based on control functions that purge the endogeneity the test has a non standard asymptotic distribution from which asymptotic critical values can directly be derived furthermore the test statistic is extended to accommodate multivariate exogenous regressors consistency against general alternatives is proved and the finite sample properties of the test are examined in a monte carlo experiment the test is used to formally assess the monotonicity of the reservation wage as a declining function of elapsed unemployment duration which has implications for underlying job search models this relationship is difficult to measure due to the simultaneity of both variables results for uk data indicate that reservation wage functions do in fact not decline monotonically thereby contradicting some partial equilibrium job search models

linear interpolation with a nonparametric accelerated failure time model abstract assuming a nonparametric accelerated failure time model a method is proposed for extrapolating low stress response probabilities on negative sloping line segments in the stress failure time plane the method analogous to linear interpolation in dose response studies results in simultaneous extrapolation ahead in time and down in stress in the two sample two stress level setting a goodness of fit test of the nonparametric model is considered and two hypothesis tests are proposed each pertaining to a condition that in addition to the assumed model must be met for the method to be valid the method is illustrated with censored strand life data and some simulated examples are used to consider power and robustness the failure time model is a scale family with curvature constraints the failure probability is assumed to be a sigmoid function of the product of time and a sigmoid scaling function of stress time percentiles as functions of stress are assumed to be convex the goodness of fit

mode identification of volatility in time varying autoregression in many applications time series exhibit nonstationary behavior that might reasonably be modeled as a time varying autoregressive ar process in the context of such a model we discuss the problem of testing for modality of the variance function we propose a test of modality that is local and when used iteratively can be used to identify the total number of modes in a given series this problem is closely related to peak detection and identification which has applications in many fields we propose a test that under appropriate assumptions is asymptotically distribution free under the null hypothesis even though nonparametric estimation of the ar parameter functions is involved simulation studies and applications to real datasets illustrate the behavior of the test

a simple test for moment inequality models with an application to english auctions abstract testable predictions of many economic models involve inequality comparisons between transformations of nonparametric functionals we introduce an econometric test for these types of restrictions based on one sided l p statistics that adapt asymptotically to the contact sets without having to directly estimate them monte carlo experiments show that our test is less conservative than procedures based on least favorable configurations and has power comparable to other contact set based procedures as an application we test for interdependence of bidders valuations in ascending auctions using usfs timber auction data we reject the independent private values model in favor of a model of correlated private values

point of optimal kinematic error improvement of the instantaneous helical pivot method for locating centers of rotation this paper proposes a variation of the instantaneous helical pivot technique for locating centers of rotation the point of optimal kinematic error poke which minimizes the velocity at the center of rotation may be obtained by just adding a weighting factor equal to the square of angular velocity in woltring s equation of the pivot of instantaneous helical axes piha calculations are simplified with respect to the original method since it is not necessary to make explicit calculations of the helical axis and the effect of accidental errors is reduced the improved performance of this method was validated by simulations based on a functional calibration task for the gleno humeral joint center noisy data caused a systematic dislocation of the calculated center of rotation towards the center of the arm marker cluster this error in piha could even exceed the effect of soft tissue artifacts associated to small and medium deformations but it was successfully reduced by the poke estimation

a survey of formal methods for determining the centre of rotation of ball joints abstract the determination of an accurate centre of rotation cor from segment marker positions is of interest across a wide range of applications but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee for limb alignment purposes for the first time in this survey of formal methods we classify analyse and compare different methods geometric algebraic bias compensated algebraic and pratt sphere fit methods as well as the centre transformation technique the holzreiter approach the helical pivot technique the schwartz transformation techniques the minimal amplitude point method and the stoddart approach for the determination of spherical joint centres from marker position data in addition we propose a new method the symmetrical cor estimation or score in which the coordinates of the joint centre must only remain constant relative to each segment thus not requiring the assumption that one segment should remain at rest for each method 1000 cor estimations were analysed with the application of isotropic independent and identically distributed gaussian noise standard deviation 0 1 cm to each of the marker positions to all markers on the segment simultaneously and the two in combination for the test conditions used here most techniques were capable of determining the cor to within 0 3 cm as long as the spherical range of motion rom of the joint was 45 or more under the most stringent conditions tested however the score was capable of best determining the cor to within approximately 1 2 mm with a rom of 20 the correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement

carrying simplices in nonautonomous and random competitive kolmogorov systems abstract the purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive kolmogorov systems via the skew product flows approach it is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skew product flow associated with a nonautonomous random competitive kolmogorov system

new least squares solutions for estimating the average centre of rotation and the axis of rotation a new method is proposed for estimating the parameters of ball joints also known as spherical or revolute joints and hinge joints with a fixed axis of rotation the method does not require manual adjustment of any optimisation parameters and produces closed form solutions it is a least squares solution using the whole 3d motion data set we do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation this method is compared with other methods that use similar assumptions in the cases of random measurement errors systematic skin movements and skin movements with random measurement noise simulation results indicate that the new method is superior in terms of the algorithm used the closure of the solution consistency and minimal manual parameter adjustment the method can also be adapted to joints with translational movements

convex clustering via l1 fusion penalization summary we study the large sample behaviour of a convex clustering framework which minimizes the sample within cluster sum of squares under an l1 fusion constraint on the cluster centroids this recently proposed approach has been gaining in popularity however its asymptotic properties have remained mostly unknown our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems we use this representation to provide a simple and intuitive formulation for the population clustering procedure we then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence the proof conducts a careful simultaneous analysis of a collection of m estimation problems whose cardinality grows together with the sample size on the basis of the new perspectives gained from the asymptotic investigation we propose a key post processing modification of the original clustering framework we show both theoretically and empirically that the resulting approach can be successfully used to estimate the number of clusters in the population using simulated data we compare the proposed method with existing number of clusters and modality assessment approaches and obtain encouraging results we also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single cell virology study

the centre of rotation of the shoulder complex and the effect of normalisation shoulder motions consist of a composite movement of three joints and one pseudo joint which together dictate the humerothoracic motion the purpose of this work was to quantify the location of the centre of rotation cor of the shoulder complex as a whole dynamic motion of 12 participants was recorded using optical motion tracking during coronal scapular and sagittal plane elevation the instantaneous cor was found for each angle of elevation using helical axes projected onto the three planes of motion the location of an average cor for each plane was evaluated using digitised and anthropometric measures for normalisation when conducting motion in the coronal scapular and sagittal planes respectively the coefficients for locating the cors of the shoulder complex are 61 61 and 65 of the anterior posterior dimension the vector between the midpoint of the incisura jugularis and the xiphoid process and the midpoint of the seventh cervical vertebra and the eighth thoracic vertebra 0 1 and 2 of the superior inferior dimension the vector between the midpoint of the acromioclavicular joints and the midpoint of the anterior superior iliac spines and 57 57 and 78 of the medial lateral dimension 0 129 times the height of the participant knowing the location of the cor of the shoulder complex as a whole enables improved participant positioning for evaluation and rehabilitation activities that involve movement of the hand with a fixed radius such as those that employ isokinetic dynamometers

mode testing in difficult cases usually when testing the null hypothesis that a distribution has one mode against the alternative that it has two the null hypothesis is interpreted as entailing that the density of the sampling distribution has a unique point of zero slope which is a local maximum in this paper we argue that a more appropriate null hypothesis is that the density has two points of zero slope of which one is a local maximum and the other is a shoulder we show that when a test for a mode with shoulder is properly calibrated so that it has asymptotically correct level it is generally conservative when applied to the case of a mode without a shoulder we suggest methods for calibrating both the bandwidth and dip excess mass tests in the setting of a mode with a shoulder we also provide evidence in support of the converse a test calibrated for a single mode without a shoulder tends to be anticonservative when applied to a mode with a shoulder the calibration method involves resampling from a template density with exactly one mode and one shoulder it exploits the following asymptotic factorization property for both the sample and resample forms of the test statistic all dependence of these quantities on the sampling distribution cancels asymptotically from their ratio in contrast to other approaches the method has very good adaptivity properties

jackknife multiplier bootstrap finite sample approximations to the u process supremum with applications this paper is concerned with finite sample approximations to the supremum of a non degenerate u process of a general order indexed by a function class we are primarily interested in situations where the function class as well as the underlying distribution change with the sample size and the u process itself is not weakly convergent as a process such situations arise in a variety of modern statistical problems we first consider gaussian approximations namely approximate the u process supremum by the supremum of a gaussian process and derive coupling and kolmogorov distance bounds such gaussian approximations are however not often directly applicable in statistical problems since the covariance function of the approximating gaussian process is unknown this motivates us to study bootstrap type approximations to the u process supremum we propose a novel jackknife multiplier bootstrap jmb tailored to the u process and derive coupling and kolmogorov distance bounds for the proposed jmb method all these results are non asymptotic and established under fairly general conditions on function classes and underlying distributions key technical tools in the proofs are new local maximal inequalities for u processes which may be useful in other problems we also discuss applications of the general approximation results to testing for qualitative features of nonparametric functions based on generalized local u processes

testing monotonicity of a regression function we consider the problem of testing monotonicity of the regression function in a nonparametric regression model we introduce test statistics that are functionals of a certain natural u process we study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for gaussian processes we show that the tests are consistent against general alternatives

a new method for estimating joint parameters from motion data joint centers and axes of rotation joint parameters are central to all branches of movement analysis in gait analysis the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation anthropometric regression equations and misplaced alignment devices several alternative methods have been proposed but to date none have been shown to be accurate and reliable enough for use in the clinical setting this article describes a new method for joint parameter estimation the new method can be summarized as follows i the motions of two adjacent segments spanning a single joint are tracked ii the axis of rotation between every pair of observed segment configurations is computed iii the most likely intersection of all axes effective joint center and most likely orientation of the axes effective joint axis is found initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject for the analog the center was found to be within 3 8 mm of the geometric center and 2 0 degrees of the geometric axis standard deviation for the adult subject hip centers varied on the order of 1 3 mm knee centers by 3 9 mm and knee axes by 2 0 degrees the results suggest that the new method is an objective precise and practical alternative to the standard clinical approach

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

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract recent work on joint kinematics indicates that the finite centroid centre of rotation and the finite helical axis axis of rotation screw axis twist axis are highly susceptible to measurement errors when they are experimentally determined from landmark position data this paper presents an analytical model to describe these effects under isotropic conditions for the measurement errors and for the spatial landmark distribution it appears that the position and direction errors are inversely proportional to the rotation magnitude and that they are much more error prone than the relatively well determined rotation and translation magnitudes furthermore the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis for the planar centroid the use of rigid body constraints results in considerable precision improvement relative to the classical finite reuleaux method for centroid reconstruction these analytical results can be used to define suitable measurement configurations and they are used in this paper to explain experimental results on rontgenphotogrammetrically acquired in vitro wrist joint movement

on intrinsic equivalences of the finite helical axis the instantaneous helical axis and the sara approach a mathematical perspective accurate determination of joint axes is essential for understanding musculoskeletal function whilst numerous algorithms to compute such axes exist the conditions under which each of the methods performs best remain largely unknown typically algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance we derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data finite helical axes fha instantaneous helical axes iha and sara symmetrical axis of rotation approach including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the fha and sara approach are equivalent for the analysis of two time frames moreover we show that the position of a helical axis derived from the iha using positional data is affected by a systematic error perpendicular to the true axis direction whereas the axis direction is identical to those computed with either the fha or sara approach true direction finally with an appropriate choice of weighting factors the mean fha mfha method is equivalent to the symmetrical centre of rotation estimation score algorithm for determination of a centre of rotation cor and similarly equivalent to the sara algorithm for determination of an axis of rotation aor the deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient robust methods for determining aors and cors with confidence

comparison of the score and ha methods for locating in vivo the glenohumeral joint centre a recent paper has described a new functional method the symmetrical centre of rotation score for locating joint centre position ehrig r m taylor w r duda g n heller m o 2006 a survey of formal methods for determining the centre of rotation of ball joints journal of biomechanics 39 15 2798 2809 for in vitro analyses the score method showed better precision than helical axis ha or sphere fitting methods despites ha determination is very sensitive to small angular velocity the international society of biomechanics has recommended to use ha for locating the glenohumeral joint centre this paper aims at comparing the score method with the ha method for locating in vivo the glenohumeral joint centre according to the movement characteristics nine subjects performed 10 cycles of three different movements at two different velocities for each test combination of movements the location of the centre of rotation was estimated with both methods score and ha analyses focused on the 3d location of the glenohumeral joint centre and on the repeatability of location standard deviation this study showed that score and ha methods yielded the same gh location nevertheless with score method the location of the glenohumeral joint centre was different according to the test this study evidenced that the score method was more precise than ha method error of 3 mm versus 4 6 mm and that the gh location with the score method was not affected by movements with slow velocities

the score residual a quality index to assess the accuracy of joint estimations abstract the determination of an accurate centre of rotation cor from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis despite the many functional approaches to estimate cors no non invasive analytical determination of the error in the reconstructed joint location is currently available the purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation score as a reliable indirect measure of the error of the computed joint centre to evaluate the score residual numerical simulations were performed to evaluate cor estimations at different ranges of joint motion a statistical model was developed and used to determine the theoretical relationships among the score residual the magnitude of the skin marker artefact the corrections to the marker positions and the error of the cor estimations to the known centre of rotation we found that the equation err 0 5rs provides a reliable relationship among the cor error err and the scaled score residual rs providing that any skin marker artefact is first minimised using the optimal common shape technique ocst measurements on six healthy volunteers showed a reduction of score residual from 11 to below 6 mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data this study also demonstrates the significant benefit of the ocst for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis for the first time this understanding of the score residual allows a measure of error in the non invasive assessment of joint centres this measure now enables a rapid assessment of the accuracy of the cor as well as an estimation of the reproducibility and repeatability of skeletal motion patterns

testing noisy numerical data for monotonic association rank correlation measures are intended to measure to which extent there is a monotonic association between two observables while they are mainly designed for ordinal data they are not ideally suited for noisy numerical data in order to better account for noisy data a family of rank correlation measures has previously been introduced that replaces classical ordering relations by fuzzy relations with smooth transitions thereby ensuring that the correlation measure is continuous with respect to the data the given paper briefly repeats the basic concepts behind this family of rank correlation measures and investigates it from the viewpoint of robust statistics then on this basis we introduce a framework of novel rank correlation tests an extensive experimental evaluation using a large number of simulated data sets is presented which demonstrates that the new tests indeed outperform the classical variants in terms of type ii error rates without sacrificing good performance in terms of type i error rates this is mainly due to the fact that the new tests are more robust to noise for small samples the gaussian rank correlation estimator turned out to be the best choice in situations where no prior knowledge is available about the data whereas the new family of robust gamma test provides an advantage in situations where information about the noise distribution is available an implementation of all robust rank correlation tests used in this paper is available as an r package from the cran repository

bayesian spatial monotonic multiple regression we consider monotonic multiple regression for contiguous regions the regression functions vary regionally and may exhibit spatial structure we develop bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump markov chain monte carlo techniques spatial dependence is incorporated by a flexible prior distribution which is tuned using cross validation and bayesian optimization we derive the mean and variance of the prior induced by the marked point process approach asymptotic results show consistency of the estimated functions posterior realizations enable variable selection the detection of discontinuities and prediction in simulations and in an application to a norwegian insurance data set our methodology shows better performance than existing approaches

a procedure for determining rigid body transformation parameters for many biomechanical applications it is necessary to determine the parameters which describe the transformation of a rigid body from one reference frame to another these parameters are a scaling factor an attitude matrix and a translation vector the paper presents a new procedure for the determination of these parameters incorporating the work of arun et al ieee trans pattern anal machine intell 9 698 700 1987 but expanding their analysis to allow for the determination of a scale factor the scalar weighting of the least squares problem and the problem of obtaining the incorrect determinant when determining the attitude matrix the procedure which requires the coordinates of three or more non collinear points is based around the singular value decomposition and provides a least squares estimate of the rigid body transformation parameters examples are presented of the use of this procedure for determining the attitude of a rigid body and for osteometric scaling when used for osteometric scaling mirror transformations are possible therefore a right hand specimen can be scaled to the left hand side of another specimen

the glenohumeral joint rotation centre in vivo within the framework of the current call for standardization in upper extremity research three methods to determine the glenohumeral joint rotation centre in vivo were tested therefore subjects performed humeral movements while a 3d electromagnetic tracking device registered the motion of the humerus with respect to the scapula for the first method to estimate the glenohumeral joint rotation centre five scapular bony landmarks served as input to regression equations the second method fitted a sphere through the humeral position data and the third method calculated the rotation centre determining an optimal helical axis the experiment consisted of two parts at first one subject was measured 10 times subsequently one observer measured 10 subjects twice and another observer measured these subjects once the first part of the experiment demonstrated that all methods are capable to reproduce the rotation centre within 4mm but the location of the centre differed significantly between methods p 0 001 the second part showed that inter and intra observer reliability was sufficiently for the sphere fitting method and for the helical axes method the two observations of one observer differed significantly p 0 008 using the regression method the authors prefer the helical axes method it is a reliable and valid method which can be applied in movement registration of healthy subjects and patients with a shoulder endoprosthesis it can be applied in hinge joints to determine a rotation axis instead of a rotation centre which is desirable in standardized upper extremity research and calculation time is short

in vivo estimation of the glenohumeral joint centre by functional methods accuracy and repeatability assessment abstract several algorithms have been proposed for determining the centre of rotation of ball joints these algorithms are used rather to locate the hip joint centre few studies have focused on the determination of the glenohumeral joint centre however no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre this paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre ghrc can be estimated in vivo by functional methods the reference joint centre is the glenohumeral anatomical centre obtained by medical imaging five functional methods were tested the algorithm of gamage and lasenby 2002 bias compensated halvorsen 2003 symmetrical centre of rotation estimation ehrig et al 2006 normalization method chang and pollard 2007 helical axis woltring et al 1985 the glenohumeral anatomical centre ghac was deduced from the fitting of the humeral head four subjects performed three cycles of three different movements flexion extension abduction adduction and circumduction for each test the location of the glenohumeral joint centre was estimated by the five methods analyses focused on the 3d location on the repeatability of location and on the accuracy by computing the euclidian distance between the estimated ghrc and the ghac for all the methods the error repeatability was inferior to 8 25 mm this study showed that there are significant differences between the five functional methods the smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of gamage and lasenby 2002

distribution free tests of stochastic monotonicity this article proposes an omnibus test for monotonicity of nonpara metric conditional distributions and its moments unlike previous proposals our method does not require smooth estimation of the derivatives of nonparametric curves and it can be implemented even when probability densities do not exist in fact we only require continuity of the marginal distributions under the null and xed alternatives distinguishing features of our approach are that critical values are pivotal under the null in nite samples and the test is invariant to any monotonic continuous transformation of the explanatory variable the test sta tistic is the sup norm of the dierence between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate the resulting test is able to detect local alternatives converging to the null at the parametric rate n 1 2 with n the sample size the article also discusses several applications and extensions of the proposal these include testing monotonicity of general conditional moments and the extension to multivariate explanatory variables the nite sample performance of the test is examined by means of a monte carlo experiment

on circulant populations i the algebra of semelparity we consider a class of nonlinear leslie matrix models describing the population dynamics of an age structured semelparous species semelparous species are those whose individuals reproduce only once and die afterwards competitive interaction between individuals is modelled via a one dimensional environmental quantity age classes are characterised by their impact on and their sensitivity to the environment we do not restrict ourselves to some particular form of functional dependence and keep the model otherwise as general as possible the system possesses a cyclic symmetry due to the symmetry it exhibits so called vertical bifurcations where a manifold filled with periodic orbits appears in the phase space for specific parameter combinations this bifurcation serves as a switch between the main types of behaviour coexistence of all year classes or a periodic regime with some year classes missing in particular the vertical bifurcation takes place when a certain circulant matrix is singular we also analyse the local stability of the unique coexistence equilibrium state and derive a characteristic equation for it the dynamics of populations with two and especially with three age classes are analysed in detail