importance sampling for estimating exact probabilities in permutational inference abstract this article discusses importance sampling as an alternative to conventional monte carlo sampling for estimating exact significance levels in a broad class of two sample tests including all of the linear rank tests with or without censoring homogeneity tests based on the chi squared hypergeometric and likelihood ratio statistics the mantel haenszel trend test and zelen s test for a common odds ratio in several 2 2 contingency tables inference is based on randomly selecting 2 k contingency tables from a reference set of all such tables with fixed marginals through a network algorithm the tables are selected in proportion to their importance for reducing the variance of the estimated monte carlo p value spectacular gains up to four orders of magnitude are achieved relative to conventional monte carlo sampling the technique is illustrated on four real data sets

exact nonparametric inference when doses are measured with random errors studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose if the doses are measured with error then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response if one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0 that is the dose errors are pure errors and not say systematic underreporting of exposure then the presence of zero dose controls is all that is needed to obtain exact distribution free confidence intervals and tests and consistent point estimates the method is simpler for matched pairs than for matched sets with two or more matched subjects and it is illustrated using two studies one of each kind with matched pairs as in this first example the method uses wilcoxon s signed rank test as the basis for inference when there are several zero dos

influence functions for testing abstract influence functions for testing are defined by applying hampel s influence function to transformed p values these influence functions describe the effect of an observation and an underlying distribution on the behavior of a test because these influence functions are not based on the test statistic alone they are applicable to both unconditional and conditional e g randomization tests the influence function of a transformed p value at a null hypothesis distribution is related to an influence function based on limiting power the influence functions of several one and two sample tests for location are discussed to illustrate the utility of this approach

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

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

on the convergence of he s variational iteration method in this work we will consider he s variational iteration method for solving second order initial value problems we will discuss the use of this approach for solving several important partial differential equations this method is based on the use of lagrange multipliers for identification of optimal value of a parameter in a functional this procedure is a powerful tool for solving the large amount of problems using the variational iteration method it is possible to find the exact solution or an approximate solution of the problem this technique provides a sequence of functions which converges to the exact solution of the problem our emphasis will be on the convergence of the variational iteration method in the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important models

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

confidence intervals for uncommon but dramatic responses to treatment a small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment the ranks used in these tests are very different from conventional ranks being relatively flat for low responses and then rising steeply and the associated tests are much more powerful than conventional rank tests when indeed only a small fraction of treated subjects exhibit dramatic responses because the tests are derived from considerations of local power they do not yield a plausible family of models for effect and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests there is a similarity between these tests and another family of tests originally motivated by different considerations involving peak performance in small subsets exploiting this similarity a method for obtaining confidence statements is proposed in the case of observational studies sensitivity to unobserved bias from nonrandom assignment of treatments is also examined two examples are used as illustrations i a study of smoking during pregnancy and its effects on birth weight in which smokers are matched to six controls and ii a matched pair study of damage to dna among workers at aluminum production plants

methods for exact goodness of fit tests abstract numerous goodness of fit tests with asymptotic chi squared distributions have been proposed for discrete multivariate data and there has been much discussion about using asymptotic results for computing critical values when there are small expected cell values although exact methods would be preferred in these situations it generally is believed that such methods are computationally intractable we propose methods for calculating exact distributions and significance levels for goodness of fit statistics that are computationally feasible over a wide range of models in particular the distribution for a simple multinomial model can be evaluated in polynomial time for composite null hypotheses we calculate the distribution conditional on the sufficient statistics for the nuisance parameters we calculate the characteristic function of a distribution and invert the characteristic function using the fast fourier transform fft our approach emphasizes the relationship between exact methods and

the variational iteration method for rational solutions for kdv k 2 2 burgers and cubic boussinesq equations in this work the reliable variational iteration method is used to determine rational solutions for the kdv the k 2 2 the burgers and the cubic boussinesq equations the study highlights the efficiency of the method and its dependence on the lagrange multiplier rational solutions are obtained directly in a straightforward manner

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

improved extrapolation techniques in recursive digital filtering a comparison of least squares and prediction two extrapolation techniques for recursive digital filtering are presented and compared with common padding methods such as linear and reflection reverse mirror extrapolation the case in which the endpoints of position data lead to peak accelerations after filtering and differentiation is examined the first technique least squares is based on fitting a third degree polynomial to the final 10 data points in both the forward and backward directions and extending the signal by 20 data points using the polynomial coefficients the second technique prediction is based on a linear autoregressive model with 20 coefficients which is applied in both directions and the signal is extrapolated by 20 points the lowest cumulative error of the endpoint accelerations 22 8 rad s 2 represented just one third of the error when the common padding methods were used in optimal digital filtering 69 7 rad s 2 it also represented approximately half the lowest cumulative error in optimal smoothing with quintic splines 48 0 rad s 2

exact logistic regression theory and examples we provide an alternative to the maximum likelihood method for making inferences about the parameters of the logistic regression model the method is based appropriate permutational distributions of sufficient statistics it is useful for analysing small or unbalanced binary data with covariates it also applies to small sample clustered binary data we illustrate the method by analysing several biomedical data sets

permutation distributions via generating functions with applications to sensitivity analysis of discrete data abstract generating functions provide a simple and elegant way to describe probability or frequency distributions of discrete statistics and in particular permutation distributions they are also a computational tool many efficient algorithms including those described as fast fourier transform methods network methods and multiple shift methods are different implementations of the recursions needed to evaluate generating functions efficiently our goals here are twofold first we make the relationship between these efficient methods and generating functions explicit this establishes a language for looking at other questions in randomization exact inference and may help in finding more efficient implementations second we propose methods to examine the sensitivity of results of exact analysis of discrete data to small perturbations in the data specifically we consider two settings how the analysis would change if one outcome changed and how the analysis would change if one observation was adde

construction of permutation tests abstract a general method for constructing permutation tests for various experimental designs follows from invariance and sufficiency in this framework randomization or rerandomization tests are just special cases of permutation tests the methodology extends the applicability of permutation tests an example demonstrates a test for an interaction effect in a factorial experiment a problem thought to be unapproachable by permutation or randomization methods tests are constructed as follows the modeling of block and treatment effects closely parallels classical analysis of variance anova the anova assumptions of iid normal random errors are replaced however by the much weaker assumption of exchangeability of subsets of random errors distributional dependences on the unknown nuisance parameters for blocks covariates and untested treatments and on the unknown error distribution are eliminated by invariance and sufficiency respectively initial reduction of the data by invariance appears to ex

on obtaining permutation distributions in polynomial time abstract polynomial time algorithms are presented for finding the permutation distribution of any statistic that is a linear combination of some function of either the original observations or the ranks this class of statistics includes the original fisher two sample location statistic and such common nonparametric statistics as the wilcoxon ansari bradley savage and many others the algorithms are presented for the two sample problem and it is shown how to extend them to the multisample problem for example to find the distribution of the kruskal wallis and other extensions of the wilcoxon and to the single sample situation stratification ties and censored observations are also easily handled by the algorithms the algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time this savings is effected by first calculating and then inverting the characteristic function of the statistic

time and frequency representation of acoustic signals by means of the wigner distribution function implementation and interpretation the wigner distribution function originally introduced in quantum mechanics is shown to have a similar formulation as the fourier transform of the time dependent correlation function for a time varying signal review of its mathematical properties indicates that such an expression is suitable for representing the signal simultaneously in the time and frequency domains furthermore reformating the wigner distribution function with a certain window function leads to a proof that this modified version the pseudo wigner distribution function always has a positive value and hence can be interpreted as a proper description of the dynamics for the signal s power density spectrum change with time the implementation of the wigner distribution function for digital processing can be carried out simply by adapting the fast fourier transform algorithm examples of its application to several types of acoustic signals are used to illustrate their dynamic features jointly in time and frequency representation

detecting treatment effects with small samples the power of some tests under the randomization model randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid in addition to being exact a randomization test may also be more powerful than its parametric counterpart this was demonstrated in a simulation study which examined the conditional power of three nondirectional tests the randomization t test the wilcoxon mann whitney wmw test and the parametric t test when the treatment effect was skewed with degree of skewness correlated with the size of the effect the randomization t test was systematically more powerful than the parametric t test the relative power of the wmw test under the skewed treatment effect condition depended on the sample size ratio

multiple comparisons by rerandomization tests abstract classical methods of simultaneous inference cannot be used with rerandomization tests without risking excessive type i errors this is illustrated by examples that show some published methods to be invalid for multiple comparisons however the use of stepwise procedures is shown to remain valid with rerandomization tests in particular this article advocates an adaptation of begun and gabriel s 1981 technique and provides the algorithm for using it

estimating exact p values by the method of control variates or monte carlo rescue abstract despite algorithmic advances in exact nonparametric inference problems often occur that are too large for exact p value computations but too sparse for reliable asymptotic results in these situations monte carlo methods are a good compromise they bound the true p value within a confidence interval but a factor discouraging the use of monte carlo p values is their sensitivity to the random number sequence one can overcome this drawback by computing a 99 c i confidence interval of width less than 0001 then the estimated p values become insensitive to the random number sequence up to three decimals for all practical purposes these estimates are invariant to random number sequences the usual monte carlo method requires millions of samples to yield such an invariant estimate the monte carlo scheme presented here decreases the sample size by two to three orders of magnitude we illustrate this method with tests for r c tables two sample survival data and stratified 2 2 tables

study on nonlinear jeffery hamel flow by he s semi analytical methods and comparison with numerical results in this article the problem of jeffery hamel flow is presented and the variational iteration method and the homotopy perturbation method are employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem comparisons are made between the numerical solution nm and the results of the he s variational iteration method vim and he s homotopy perturbation method hpm the results reveal that these methods are very effective and simple and can be applied for other nonlinear problems

improving the readability of time frequency and time scale representations by the reassignment method in this paper the use of the reassignment method first applied by kodera gendrin and de villedary 1976 to the spectrogram is generalized to any bilinear time frequency or time scale distribution this method creates a modified version of a representation by moving its values away from where they are computed so as to produce a better localization of the signal components we first propose a new formulation of this method followed by a thorough theoretical study of its characteristics its practical use for a large variety of known time frequency and time scale distributions is then addressed finally some experimental results are reported to demonstrate the performance of this method

rerandomizing the median in matched pairs designs on montre que la re randomisation de la mediane a la place de la moyenne transforme un gros probleme de calcul en un probleme convenable pour une calculatrice

an algorithm for exact logistic regression abstract an efficient algorithm is given for the exact logistic analysis of a single parameter hypothesis tests and confidence intervals for a logistic regression parameter are obtained the method provides for the control of the effect of a stratification factor when making inferences concerning the regression parameter

application of singular spectrum analysis to the smoothing of raw kinematic signals motion capture systems currently used in biomechanical analysis introduce systematic measurement errors that appear in the form of noise in recorded displacement signals the noise is unacceptably amplified when differentiating displacements to obtain velocities and accelerations to avoid this phenomenon it is necessary to smooth the displacement signal prior to differentiation in order to eliminate the noise introduced by the experimental system the use of singular spectrum analysis ssa is presented in this paper as an alternative to traditional digital filtering methods ssa is a novel non parametric technique based on principles of multivariate statistics the original time series is decomposed into a number of additive time series each of which can be easily identified as being part of the modulated signal or as being part of the random noise several examples that demonstrate the superiority of this technique over other methods used in biomechanical analysis are presented in this paper

group sequential tests for delayed responses with discussion summary group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect a lack of an effect or concerns about patient safety in many studies the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond we formulate a new form of group sequential test which gives a proper treatment of these pipeline subjects these tests can be applied even when the continued accrual of data after the decision to stop the trial is unexpected we illustrate our methods through a series of examples we define error spending versions of these new designs which handle unpredictable group sizes and provide an information monitoring framework that can accommodate nuisance parameters such as an unknown response variance by studying optimal versions of our new designs we show how the benefits of lower expected sample size that are normally achieved by a group sequential test are reduced when there is a delay in response the loss of efficiency for larger delays can be ameliorated by incorporating data on a correlated short term end point fitting a joint model for the two end points but still making inferences on the original longer term end point we derive p values and confidence intervals on termination of our new tests

application of he s variational iteration method for solving the reaction diffusion equation with ecological parameters he s variational iteration method is applied to the search for the solution of the reaction diffusion problem with ecological parameters the method is extremely simple and concise and comparison with the adomian method reveals that the present method is an attracting mathematical tool

evaluation of the power of rerandomization tests with application to weather modification experiments abstract computations of power of rerandomization tests by exact methods are known to be computationally exorbitant we introduce a much cheaper naive method of evaluating power and show both by simulation and analytically for a special case that it very mildly overestimates true power we further derive a normal approximation to re randomization distributions of linear statistics and illustrate its closeness to the true distributions this yields analytical formulas for calculating power approximately at negligible computational cost the proposed methods therefore eliminate the previously prohibitive cost of calculating power for rerandomization tests and make it practical to evaluate the sample sizes needed for a randomized experiment to be analyzed by rerandomization see also gabriel and hall 1983 its application to weather modification experiments is illustrated

allocation of effort in monte carlo simulation for power of permutation tests abstract consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample if the power of such a test is investigated by simulation the computer code must have two main loops in the outer loop which has o iterations data are generated under a specific alternative hypothesis for each outer iteration there are i inner iterations in each of which the data are permuted and the statistic calculated assume that the costs of inner and outer iterations are known and the total cost of the study is fixed so that i and o are constrained by o io for fixed this article considers what the optimal choice for i is in a mean squared sense a general expression is derived for the mean squared error of the distribution of p values if the alternative hypothesis is close to the null the optimal c

robust permutation tests for matched pairs designs abstract a branch and bound algorithm is described for finding the permutation randomization p value in matched pairs designs without enumeration of the entire reference distribution it is not restricted to test statistics that are linear in functions of the observations and permutation tests based on trimmed means are investigated we apply the algorithm to six examples demonstrating that the use of a moderately trimmed instead of an untrimmed mean can sometimes lead to substantially smaller p values and shorter confidence intervals confidence intervals are obtained by trial and error inversion of the p value permutation tests arise in randomization inference though they can be applied to nonrandomized studies under the randomization model permutation tests are exact giving the correct probability of a type i error without distributional assumptions the observed test statistic is compared with the reference set of test statistics that would occur under all possible randomizations thus inf

time varying filtering and signal estimation using wigner distribution synthesis techniques the short time fourier transform stft the ambiguity function af and the wigner distribution wd are mixed time frequency signal representations that use fourier transform techniques to map a one dimensional function of time into a two dimensional function of time and frequency these mixed time frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems although much work has also been done to develop stft and af synthesis algorithms that can be used to implement a variety of time varying signal processing operations no such synthesis techniques have thus far been developed for the wd in this paper a signal synthesis algorithm that works directly with the real valued high resolution wd will be derived examples of how this wd synthesis procedure can be used to perform time varying filtering operations or signal separation will be given

an adaptive mantel haenszel test for sensitivity analysis in observational studies in a sensitivity analysis in an observational study with a binary outcome is it better to use all of the data or to focus on subgroups that are expected to experience the largest treatment effects the answer depends on features of the data that may be difficult to anticipate a trade off between unknown effect sizes and known sample sizes we propose a sensitivity analysis for an adaptive test similar to the mantel haenszel test the adaptive test performs two highly correlated analyses one focused analysis using a subgroup one combined analysis using all of the data correcting for multiple testing using the joint distribution of the two test statistics because the two component tests are highly correlated this correction for multiple testing is small compared with for instance the bonferroni inequality the test has the maximum design sensitivity of two component tests a simulation evaluates the power of a sensitivity analysis using the adaptive test two examples are presented an r package sensitivity2x2xk implements the procedure

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

time frequency analysis of postural sway postural sway during quiet stance has been used to characterize the postural control system most studies have used center of pressure cop measurements and have assumed stationarity however recent research has indicated that cop is not stationary the purpose of this study is to introduce and demonstrate a nonstationary spectral estimation technique to examine the time varying nature of postural sway data from two experiments were used to verify the usefulness of the spectral estimator for the analysis of cop the first data set contains cop recorded from normal subjects swaying about their ankles in response to a metronome as it was gradually changed from 2 to 1 hz the time frequency distribution reveals time varying spectral changes corresponding to frequency changes made by the subjects the second set consists of cop from normal subjects and vestibularly impaired patients standing quietly on a force plate with eyes closed for 100 s the time frequency distributions for the cop were estimated for both sets of data the cop s appear to be nonstationary with the energies at a given frequency modulating through time

improved accuracy of biomechanical motion data obtained during impacts using a time frequency low pass filter biomechanical motion data involving impacts are not adequately represented using 31 conventional low pass filters cf time frequency filters tff are a viable alternative but 32 have been largely overlooked by movement scientists we modified georgakis and 33 subramaniam s 2009 fractional fourier filter mfrff and demonstrated it performed better 34 than cfs for obtaining lower leg accelerations during football instep kicking the mfrff 35 displayed peak marker accelerations comparable to a reference accelerometer during foot to 36 ball impact peak error 5 0 11 4 whereas cfs severely underestimated these peaks 37 30 70 error during the non impact phases the mfrff performed comparably to cfs 38 using an appropriate 12 20hz cut off frequency rmse 37 3 7 6 m s2 vs 42 1 11 4 39 m s2 respectively since accuracy of segmental kinematics is fundamental for understanding 40 human movement the mfrff should be applied to a range of biomechanical impact scenarios 41 e g locomotion landing and striking motions to enhance the efficacy of study in these areas

efficient calculation of the permutation distribution of trimmed means abstract the permutation distribution of the trimmed mean in matched pairs designs is studied this statistic is important since it is robust to both outliers and distributional assumptions a polynomial time algorithm for this inherently exponential time problem is presented the characteristic function of the distribution provides both the basis for the algorithm and a vehicle for calculating the asymptotic permutation distribution

the use of optimally regularized fourier series for estimating higher order derivatives of noisy biomechanical data abstract optimally regularized filtered fourier series can be used most effectively for estimating higher order derivatives of noisy data sequences such as occur in biomechanical investigations as the optimal filtering process takes place in the derivative domain use being made of the statistical information contained in the periodogram of the data sequence no numerical differentiation as such takes place and all the problems known to be associated with such a procedure are avoided the optimally filtered approximation to the function itself is obtained by the same technique the algorithm is based on known results from time series and approximation theory and offers several advantages when compared with other techniques the optimally filtered approximations of the function and all its required derivatives are obtained in a single run compact analytical fourier representations of the filtered function and the derivatives are available allowing interpolation between data points and further analytical treatment of the function all the desirable properties of fourier approximations such as periodicity end point continuity etc can be utilized if fast fourier transforms are used the algorithm is computationally far more efficient than other techniques

variational iteration method for unsteady flow of gas through a porous medium using he s polynomials and pade approximants in this paper we apply the variational iteration method using he s polynomials for finding the analytical solution of unsteady flow of gas through a porous medium the proposed method is an elegant combination of he s variational iteration and the homotopy perturbation methods the suggested algorithm is quite efficient and is practically well suited for use in such problems the proposed iterative scheme finds the solution without any discretization linearization or restrictive assumptions the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution and to determine the initial slope a clear advantage of this technique over the decomposition method is that no calculation of adomian s polynomials is needed

symmetry based inference in an instrumental variable setting we describe exact inference based on group invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model it is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form when applied to the linear model this exact inference provides a unified approach to a variety of parametric and distribution free tests in particular we consider exact instrumental variable inference based on symmetry assumptions the unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification in a multivariate instrumental variables context generalizations of anderson rubin confidence sets are considered

a closed form approximation for the fractional black scholes model with transaction costs abstract in this paper we investigate option valuation problems under the fractional black scholes model the aim is to propose a pricing formula for the european option with transaction costs where the costs structure contains fixed costs a cost propositional to the volume traded and a cost proportional to the value traded precisely we provide an approximate solution of the nonlinear hoggard whalley wilmott equation the comparison results reveal that our approximate solutions are close to the numerical computations moreover the comparison results demonstrate that the price of the european option decreases as the hurst exponent increases

computational tools for exact conditional logistic regression logistic regression analyses are often challenged by the inability of unconditional likelihood based approximations to yield consistent valid estimates and p values for model parameters this can be due to sparseness or separability in the data conditional logistic regression though useful in such situations can also be computationally unfeasible when the sample size or number of explanatory covariates is large we review recent developments that allow efficient approximate conditional inference including monte carlo sampling and saddlepoint approximations we demonstrate through real examples that these methods enable the analysis of significantly larger and more complex data sets we find in this investigation that for these moderately large data sets monte carlo seems a better alternative as it provides unbiased estimates of the exact results and can be executed in less cpu time than can the single saddlepoint approximation moreover the double saddlepoint approximation while computationally the easiest to obtain offers little practical advantage it produces unreliable results and cannot be computed when a maximum likelihood solution does not exist

a comparison of automatic filtering techniques applied to biomechanical walking data abstract the purpose of this study was to compare and evaluate six automatic filtering techniques commonly used in biomechanics for filtering gait analysis kinematic signals namely 1 power spectrum signal to noise ratio assessment 2 generalised cross validation spline 3 least squares cubic splines 4 regularisation of fourier series 5 regression model and 6 residual analysis a battery of 1440 signals representing the displacements of seven markers attached upon the surface of the right lower limbs and one marker attached upon the surface of the sacrum during walking were used their original signal and added noise characteristics were known a priori the signals were filtered with every technique and the root mean square error between the filtered and reference signal was calculated for each derivative domain results indicated that among the investigated techniques there is not one that performs best in all the cases studied generally the techniques of power spectrum estimation least squares cubic splines and generalised cross validation produced the most acceptable results

amplification of sensitivity analysis in matched observational studies a sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed in matched observational studies of treatment effects a key assumption in some analyses is that subjects matched for observed covariates are comparable and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching what properties would such an unobserved covariate need to have to materially alter the inference about treatment effects for ease of calculation and reporting it is convenient that the sensitivity analysis be of low dimension perhaps indexed by a scalar sensitivity parameter but for interpretation in specific contexts a higher dimensional analysis may be of greater relevance an amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points perhaps a curve in a higher dimensional sensitivity analysis such that the possible inferences are

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

qualitative robustness of tests abstract a test is qualitatively robust by definition if its sequence of n 1 log transformed p values n being a measure of the sample size is continuous as a point function of the observations and weakly equicontinuous as a function of discrete probability measures this definition is applitable both to unconditional and to conditional tests under weak regularity conditions an unconditional test is qualitatively robust if and only if its test statistic is continuous a counterexample shows that conditional tests do not share this property the sample mean student s t and ybar xbar permutation tests are not qualitatively robust the sign wilcoxon huber censored likelihood and normal scores tests are qualitatively robust

rerandomization inference on regression and shift effects computationally feasible methods abstract an idea due to quade 1973 is used to develop a method that reduces the computational load for rerandomization inferences in certain situations and for experiments carried out with a sufficiently small reference set of randomizations makes computations entirely feasible consider an experimental design for n units for which an experimental plan e is to be chosen randomly from a set of k plans plan e will assign treatment dosage de u to unit u with postulated additive effect de u reflected in the observation zu rerandomization inferences are to be carried out by means of pivotal statistics te e z be z be z 1 be d e where z and d e are observation and dosage vectors and be mdot is the regression slope onto d e the dosages under plan e a the p value of a test of the hypotheses versus is essentially the proportion of te e z values e that are at most b if t l e z is the lth largest of the te e z s e then a l l k confi

time frequency analysis and filtering of kinematic signals with impacts using the wigner function accurate estimation of the second derivative biomechanical signals are represented in the time frequency domain using the wigner distribution function filtering of this representation for the case of a non stationary displacement signal with impact is studied smoothed displacement data are then double differentiated and compared with references accelerometer data it is shown that this technique is able to remove noise from these signals in a better way than conventional filtering techniques currently used in biomechanics

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation