pricing geometric asian rainbow options under the mixed fractional brownian motion abstract we deal with the pricing of geometric asian rainbow options under the mixed fractional brownian motion based on standard no arbitrage arguments we obtain a partial differential problem in several independent variables which we solve by employing suitable changes of variables and analytical results derived in bos and ware 2001 and stulz 1982b numerical test cases are presented in which the pricing formula obtained is applied to geometric asian rainbow options on two and three underlying assets monte carlo simulations are also performed which confirm the correctness of the proposed closed form solution

fisher information in quantum statistics braunstein and caves braunstein s l and caves c m 1994 phys rev lett 72 3439 43 proposed to use helstrom s quantum information number to define meaningfully a metric on the set of all possible states of a given quantum system they showed that the quantum information is nothing other than the maximal fisher information in a measurement of the quantum system maximized over all possible measurements combining this fact with classical statistical results they argued that the quantum information determines the asymptotically optimal rate at which neighbouring states on some smooth curve can be distinguished based on arbitrary measurements on n identical copies of the given quantum system we show that the measurement which maximizes the fisher information typically depends on the true unknown state of the quantum system we close the resulting loophole in the argument by showing that one can still achieve the same optimal rate of distinguishability by a two stage adaptive measurement procedure when we consider states lying not on a smooth curve but on a manifold of higher dimension the situation becomes much more complex we show that the notion of distinguishability of close by states depends strongly on the measurement resources one allows oneself and on a further specification of the task at hand the quantum information matrix no longer seems to play a central role

detecting a major gene in an f2 population the aim of this paper is to study the behavior of the likelihood ratio test for the detection of a major gene in an f2 population the model is a mixture of three normal distributions where the proportions are known the information matrix is not positive definite and therefore classical results cannot be used an example concerning beans is given

quantum estimation for non differentiable models state estimation is a classical problem in quantum information in optimization of an estimation scheme to find a lower bound to the error of the estimator is a very important step so far all the proposed tractable lower bounds use a derivative of the density matrix however sometimes we are interested in quantities with singularity e g concurrence etc in this paper lower bounds to a mean square error of an estimator are derived for a quantum estimation problem without smoothness assumptions our main idea is to replace the derivative by difference as is done in classical estimation theory we applied the inequalities to several examples and derived an optimal estimator for some of them

exponential decay for binary time varying covariates in cox models cox models are commonly used in the analysis of time to event data one advantage of cox models is the ability to include time varying covariates often a binary covariate that codes for the occurrence of an event that affects an individual subject a common assumption in this case is that the effect of the event on the outcome of interest is constant and permanent for each subject in this paper we propose a modification to the cox model to allow the influence of an event to exponentially decay over time methods for generating data using the inverse cumulative density function for the proposed model are developed likelihood ratio tests and aic are investigated as methods for comparing the proposed model to the commonly used permanent exposure model a simulation study is performed and 3 different data sets are presented as examples

strong consistency and asymptotic efficiency for adaptive quantum estimation problems it is shown that for an adaptive quantum estimation scheme based on locally unbiased measurements the sequence of maximum likelihood estimators is strongly consistent and asymptotically efficient

the statistical performance of an mcf 7 cell culture assay evaluated using generalized linear mixed models and a score test biological assays often utilize experimental designs where observations are replicated at multiple levels and where each level represents a separate component of the assay s overall variance statistical analysis of such data usually ignores these design effects whereas more sophisticated methods would improve the statistical power of assays this report evaluates the statistical performance of an in vitro mcf 7 cell proliferation assay e screen by identifying the optimal generalized linear mixed model glmm that accurately represents the assay s experimental design and variance components our statistical assessment found that 17 oestradiol cell culture assay data were best modelled with a glmm configured with a reciprocal link function a gamma error distribution and three sources of design variation plate to plate well to well and the interaction between plate to plate variation and dose the gamma distributed random error of the assay was estimated to have a coefficient of variation cov 3 2 per cent and a variance component score test described by x lin found that each of the three variance components were statistically significant the optimal glmm also confirmed the estrogenicity of five weakly oestrogenic polychlorinated biphenyls pcbs 17 49 66 74 and 128 based on information criteria the optimal gamma glmm consistently out performed equivalent naive normal and log normal linear models both with and without random effects terms because the gamma glmm was by far the best model on conceptual and empirical grounds and requires only trivially more effort to use we encourage its use and suggest that naive models be avoided when possible copyright 2006 john wiley sons ltd

repeated spatial extrapolation an extraordinarily efficient approach for option pricing various finite difference methods for option pricing have been proposed in this paper we demonstrate how a very simple approach namely the repeated spatial extrapolation can perform extremely better than the finite difference schemes that have been developed so far in particular we consider the problem of pricing vanilla and digital options under the black scholes model and show that if the payoff functions are dealt with properly then errors close to the machine precision are obtained in only some hundredths of a second

testing the correlation for clustered categorical and censored discrete time to event data when covariates are measured without with errors summary in the analysis of clustered categorical data it is of common interest to test for the correlation within clusters and the heterogeneity across different clusters we address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models for clustered nominal and ordinal categorical responses we extend the results to accommodate clustered censored discrete time to event data we next consider such tests in the situation where covariates are measured with errors we propose using the simex method to construct the score tests for the null hypothesis that the variance components are zero key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates the asymptotic properties of the proposed tests are studied we illustrate these tests by analyzing two data sets and evaluate their performance with simulations

on some nonregular tests for a modified weibull model summary certain tests on the parameters of a modified weibull distribution are considered nonregular asymptotic behaviour of likelihood based test statistics is observed competing tests based on extreme order statistics are investigated and comparisons are made of power functions

inference and testing on the boundary in extended constant conditional correlation garch models we consider inference and testing in extended constant conditional correlation garch models in the case where the true parameter vector is a boundary point of the parameter space this is of particular importance when testing for volatility spillovers in the model the large sample properties of the qmle are derived together with the limiting distributions of the related lr wald and lm statistics due to the boundary problem these large sample properties become nonstandard the size and power properties of the tests are investigated in a simulation study as an empirical illustration we test for no volatility spillovers between foreign exchange rates

attaining the ultimate precision limit in quantum state estimation we derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non degenerate our results hold under an assumption called local asymptotic covariance which is weaker than unbiasedness or local unbiasedness the derivation is based on an analysis of the limiting distribution of the estimator s deviation from the true value of the parameter and takes advantage of quantum local asymptotic normality a useful asymptotic characterization of identically prepared states in terms of gaussian states we first prove our results for the mean square error of a special class of models called d invariant and then extend the results to arbitrary models generic cost functions and global state estimation where the unknown parameter is not restricted to a local neighbourhood of the true value the extension includes a treatment of nuisance parameters i e parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation as an illustration of the general approach we provide the optimal estimation strategies for the joint measurement of two qubit observables for the estimation of qubit states in the presence of amplitude damping noise and for noisy multiphase estimation

a bridging domain method for coupling continua with molecular dynamics abstract a bridging domain method for coupling continuum models with molecular models is described in this method the continuum and molecular domains are overlapped in a bridging subdomain where the hamiltonian is taken to be a linear combination of the continuum and molecular hamiltonians we enforce the compatibility in the bridging domain by lagrange multipliers or by the augmented lagrangian method an explicit algorithm for dynamic solutions is developed results show that this multiscale method can avoid spurious wave reflections at the molecular continuum interface without any additional filtering procedures even for problems with significant nonlinearities the method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain a multiple time step algorithm is also developed within this framework

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

a fast high order finite difference algorithm for pricing american options we describe an improvement of han and wu s algorithm h han x wu a fast numerical method for the black scholes equation of american options siam j numer anal 41 6 2003 2081 2095 for american options a high order optimal compact scheme is used to discretise the transformed black scholes pde under a singularity separating framework a more accurate free boundary location based on the smooth pasting condition and the use of a non uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained comparisons with some recently proposed methods for the american options problem are carried out to show the advantage of our numerical method

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

miscellanea random coefficient autoregressive models for longitudinal data summary stable autoregressive models with exogenous covariates can be used to mimic nonstationary stabilising growth profiles in longitudinal data if different individuals have very different trajectories the autoregressive parameters can be interpreted as random variables varying from one individual to the next if all random effects are assumed gaussian the model will be quite easy to estimate although the marginal distributions of the observations will no longer be gaussian however this kind of model can only be used when the observations are equally spaced

replica time integrators this paper is concerned with the classical problem of wave propagation in discrete models of nonuniform spatial resolution we develop a new class of replica time integrators rtis that permit the two way transmission of thermal phonons across mesh interfaces this two way transmissibility is accomplished by representing the state of the coarse regions by means of replica ensembles consisting of collections of identical copies of the coarse regions in dimension d rtis afford an o n d speed up factor in sequential mode and o n d 1 in parallel over regions that are coarsened n fold in this work we restrict ourselves to the solution of the 3d continuous wave equation for both linear and non linear materials by a combination of phase error analysis and numerical testing we show that rtis are convergent and result in exact two way transmissibility at the courant friedrichs lewy limit for any angle of incidence in this limit rtis allow step waves and high frequency harmonics to cross mesh interfaces in both directions without internal reflections or appreciable loss or addition of energy the possible connections of rtis with discrete to continuum approaches and in particular with the transition between molecular dynamics and continuum thermodynamics are also pointed to by way of future outlook

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

censored survival data with misclassified covariates a case study of breast cancer mortality abstract from a cancer registry in the san francisco bay area we obtained survival data for 2 495 women diagnosed with breast cancer at ages 55 64 we relate mortality among these women to the time since diagnosis and to the stage of the disease at diagnosis we divide the study period extending through 10 years into five two year periods and for each stage we assume a constant hazard rate during each of these periods let jk be the j k matrix of hazard rates for the j 5 periods and k 5 stages the most general model allows jk to vary freely a plot of maximum likelihood estimates of the hazard rates shows some tendency for increase with stage but no simple patterns or parallelism across stage we seek more restrictive models to get simpler interpretations the exponential model assumes that although jk may vary with stage it is constant over the five periods for each stage this model which assumes no dependence of hazard rate on time since diagnosis is quite restrictive and i

joint estimation of location dispersion and random effects in robust design this article presents a methodology for simultaneously modeling three components of a general mixed model approach to robust design location fixed effects dispersion effects and random effects control noise and random factors can be accommodated with this approach parameters associated with all three are estimated jointly using residual maximum likelihood and assuming normality simulated and real datasets illustrate the key concepts and advantages over previously proposed approaches

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

inference from grouped data in three parameter weibull models with applications to breakdown voltage experiments an important objective of breakdown voltage experiments is to estimate either the threshold below which no breakdown occurs or other voltage levels below which breakdown occurs with a small probability a commonly used statistical technique in these studies is to fit a three parameter weibull distribution to the experimental data difficulties in applying the method of maximum likelihood to three parameter weibull models due to nonregularity have led to a variety of alternative approaches in the literature in practice however voltage breakdown and other failure time data are usually discretized or rounded off for grouped data from the weibull model there are still difficulties in applying likelihood methods when the sample size is moderate because of the so called embedded model problem after a brief review of this problem and related likelihood theory we show how the difficulties can be resolved and how likelihood based confidence intervals for the weibull parameters and quantiles can be constru

conservation properties of the bridging domain method for coupled molecular continuum dynamics an overlaid domain decomposition method called the bridging domain method for the coupled simulation of molecular continuum systems is analyzed in this method compatibility between the atomistic and the continuum subdomains is enforced by lagrange multipliers two forms are considered 1 a consistent constraint form which employs the exact non diagonal lagrange multiplier equations and thus enforces compatibility exactly but is computationally demanding and 2 a diagonalized constraint form which is computationally more efficient it is shown that the consistent constraint form conserves linear momentum angular momentum and energy the diagonalized constraint form dissipates energy the diagonalized form is shown to be more effective in suppressing spurious reflections at the interface copyright 2008 john wiley sons ltd

permutation tests for random effects in linear mixed models summary inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis as a result the asymptotic null distribution of the wald score and likelihood ratio tests will not have the typical 2 distribution although it has been proved that the correct asymptotic distribution is a mixture of 2 distributions the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect as alternatives we present two permutation tests one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic both methods involve weighted residuals with the weights determined by the among and within subject variance components the null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples we examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients

pricing options in jump diffusion models an extrapolation approach we propose a new computational method for the valuation of options in jump diffusion models the option value function for european and barrier options satisfies a partial integrodifferential equation pide this pide is commonly integrated in time by implicit explicit imex time discretization schemes where the differential diffusion term is treated implicitly while the integral jump term is treated explicitly in particular the popular imex euler scheme is first order accurate in time second order accuracy in time can be achieved by using the imex midpoint scheme in contrast to the above approaches we propose a new high order time discretization scheme for the pide based on the extrapolation approach to the solution of odes that also treats the diffusion term implicitly and the jump term explicitly the scheme is simple to implement can be added to any pide solver based on the imex euler scheme and is remarkably fast and accurate we demonstrate our approach on the examples of merton s and kou s jump diffusion models the diffusion extended variance gamma model as well as the two dimensional duffie pan singleton model with correlated and contemporaneous jumps in the stock price and its volatility by way of example pricing a one year double barrier option in kou s jump diffusion model our scheme attains accuracy of 10 5 in 72 time steps in 0 05 seconds in contrast it takes the first order imex euler scheme more than 1 3 million time steps in 873 seconds and the second order imex midpoint scheme 768 time steps in 0 49 seconds to attain the same accuracy our scheme is also well suited for bermudan options combining simplicity of implementation and remarkable gains in computational efficiency we expect this method to be very attractive to financial engineering modelers

three dimensional perfectly matched layer for the absorption of electromagnetic waves the perfectly matched layer is a technique of free space simulation developed for solving unbounded electromagnetic problems with the finite difference time domain method referred to as pml this technique has been described in a previous paper for two dimensional problems the present paper is devoted to the three dimensional case the theory of the perfectly matched layer is generalized to three dimensions and some numerical experiments are shown to illustrate the efficiency of this new method of free space simulation

numerical pricing of options using high order compact finite difference schemes we consider high order compact hoc schemes for quasilinear parabolic partial differential equations to discretise the black scholes pde for the numerical pricing of european and american options we show that for the heat equation with smooth initial conditions the hoc schemes attain clear fourth order convergence but fail if non smooth payoff conditions are used to restore the fourth order convergence we use a grid stretching that concentrates grid nodes at the strike price for european options for an american option an efficient procedure is also described to compute the option price greeks and the optimal exercise curve comparisons with a fourth order non compact scheme are also done however fourth order convergence is not experienced with this strategy to improve the convergence rate for american options we discuss the use of a front fixing transformation with the hoc scheme we also show that the hoc scheme with grid stretching along the asset price dimension gives accurate numerical solutions for european options under stochastic volatility

characterizing additively closed discrete models by a property of their maximum likelihood estimators with an application to generalized hermite distributions this article reports on two parameter count distributions satisfying very general conditions that are closed under addition so that their maximum likelihood estimator mle of the population mean is the sample mean the most important of these in practice the generalized hermite distribution is analyzed and a necessary and sufficient condition is given to ensure that the mle is the solution of likelihood equations score test to contrast the poisson assumption is studied and two examples of applications are given

autoregressive generalized linear mixed effect models with crossed random effects an application to intensive binary time series eye tracking data as a method to ascertain person and item effects in psycholinguistics a generalized linear mixed effect model glmm with crossed random effects has met limitations in handing serial dependence across persons and items this paper presents an autoregressive glmm with crossed random effects that accounts for variability in lag effects across persons and items the model is shown to be applicable to intensive binary time series eye tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses in addition a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects

on dependent repeated screening tests a screening test is applied n times to a person with known true status if more than k tests have positive outcomes then the person is assigned to be screen positive otherwise the person is assigned to be screen negative assuming that the tests are exchangeable we can characterize the possible dependence among tests by at most n parameters called canonical moments which can be estimated from the data the performance characteristics of the composite test such as likelihood ratios sensitivity and specificity can be computed based on these estimates thus we can choose n and k so that the desired levels of likelihood ratios sensitivity and specificity can be achieved we study the cases n 2 and n 3 in detail

a high order finite difference method for option valuation in this paper we propose the use of an efficient high order finite difference algorithm to price options under several pricing models including the blackscholes model the mertons jumpdiffusion model the hestons stochastic volatility model and the nonlinear transaction costs or illiquidity models we apply a local mesh refinement strategy at the points of singularity usually found in the payoff of most financial derivatives to improve the accuracy and restore the rate of convergence of a non uniform high order five point stencil finite difference scheme for linear models the time stepping is dealt with by using an exponential time integration scheme with carathodoryfejr approximations to efficiently evaluate the product of a matrix exponential with a vector of option prices nonlinear blackscholes equations are solved using an efficient iterative scheme coupled with a richardson extrapolation our numerical experiments clearly demonstrate the high order accuracy of the proposed finite difference method making the latter a method of choice for solving both linear and nonlinear partial differential equations in financial engineering problems

estimation of incubation period and generation time based on observed length biased epidemic cohort with censoring for covid 19 outbreak in china the incubation period and generation time are key characteristics in the analysis of infectious diseases the commonly used contact tracing based estimation of incubation distribution is highly influenced by the individuals judgment on the possible date of exposure and might lead to significant errors on the other hand interval censoring based methods are able to utilize a much larger set of traveling data but may encounter biased sampling problems the distribution of generation time is usually approximated by observed serial intervals however it may result in a biased estimation of generation time especially when the disease is infectious during incubation in this paper the theory from renewal process is partially adopted by considering the incubation period as the interarrival time and the duration between departure from wuhan and onset of symptoms as the mixture of forward time and interarrival time with censored intervals in addition a consistent estimator for the distribution of generation time based on incubation period and serial interval is proposed for incubation infectious diseases a real case application to the current outbreak of covid 19 is implemented we find that the incubation period has a median of 8 50 days 95 confidence interval ci 7 22 9 15 the basic reproduction number in the early phase of covid 19 outbreak based on the proposed generation time estimation is estimated to be 2 96 95 ci 2 15 3 86

a boundary element method to price time dependent double barrier options abstract in this paper we propose a new method for pricing double barrier options with moving barriers under the black scholes and the cev models first of all by applying a variational technique typical of the boundary element method we derive an integral representation of the double barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of volterra integral equations of the first kind second we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate even if the barriers are not differentiable functions moreover the numerical method presented in this paper performs significantly better than the finite difference approach

extrapolation of difference methods in option valuation in the present investigation the fully implicit and crank nicolson difference schemes for solving option prices are analyzed it is proved that the error expansions for the difference methods have the correct form for applying richardson extrapolation to increase the order of accuracy of the approximations the difference methods are applied to european american and down and out knock out call options computational results indicate that richardson extrapolation significantly decreases the amount of computational work by as much as a factor of 16 in estimation of option prices

finite element solution of diffusion problems with irregular data diffusion problems occuring in practice often involve irregularities in the initial or boundary data resulting in a local break down of the solution s regularity this may drastically reduce the accuracy of discretization schemes over the whole interval of integration unless certain precautions are taken the diagonal pade schemes of order 2 combined with a standard finite element discretization usually require an unnatural step size restriction in order to achieve even locally optimal accuracy it is shown here that this restriction can be avoided by means of a sample damping procedure which preserves the order of the discretization and in the case 1 does not increase the costs

bridging multi scale method for localization problems abstract a bridging multi scale method is proposed for the analysis of a class of localization problems in which the micropolar continuum model is used to describe the localized deformation and the dynamic failure occurs only in a small number of localized regions it starts with a concurrent discretization of the entire domain with both coarse and fine scale finite element meshes the coarse scale mesh is employed to capture the nonlinear response with long wavelength outside the localized regions whereas the fine scale mesh captures the detailed physics of the localized deformation for both the coarse and fine scale meshes to coexist a bridging scale term is constructed so that the information common to both scales is correctly subtracted to achieve computational efficiency the localized regions are first identified by a preliminary calculation and the fine scale degrees of freedom dofs outside the localized regions are mathematically represented by the construction of dynamic interface conditions applied to the edges of these regions hence a large portion of the fine scale dofs are eliminated and the fine scale equations are reduced to a much smaller set with the added dynamic interface conditions the two way coupled coarse scale and reduced fine scale equations are then solved by a mixed time integration procedure applications to one dimensional and two dimensional dynamic shear localization problems are presented

asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints summary the analysis of moment structural models has become an important tool of investigation in behavioural educational and economic studies the chi squared largesample test is routinely employed to assess the goodness of fit of the model considered however in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met here we consider the case where the population value of the parameter vector is a boundary point of the feasible region we show that in this case the asymptotic distribution of test statistic is a mixture of chi squared distributions the problem of finding the corresponding weights is discussed

latent change classes in dichotomous data changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra the llra does not require observable criteria representing a single underlying latent trait but it postulates the generalizability of the treatment effects over criteria and subjects to test this latter crucial assumption the mixture llra was proposed that allows directly unobservable types of subjects to have different treatment effects as the earlier methods for estimating the parameters of the mixture llra have specific drawbacks a further method based on the conditional maximum likelihood principle will be presented here in contrast to the earlier conditional methods it uses all of the dichotomous change data while having fewer parameters further its goodness of fit tests become more sensitive to a falsely specified number of change types even though the treatment effects are biased for typically occurring small to moderate sample sizes however parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests finally three applications of the new method to empirical data are described first about the effect of the so called trager psychophysical integration second about the effect of autogenic therapy on patients with psychosomatic symptoms and third about the effect of religious education on the attitude towards sects

high order accurate implicit methods for barrier option pricing abstract this paper deals with a high order accurate implicit finite difference approach to the pricing of barrier options in this way various types of barrier options are priced including barrier options paying rebates and options on dividend paying stocks moreover the barriers may be monitored either continuously or discretely in addition to the high order accuracy of the scheme and the stretching effect of the coordinate transformation the main feature of this approach lies on a probability based optimal determination of boundary conditions this leads to much faster and accurate results when compared with similar pricing approaches the strength of the present scheme is particularly demonstrated in the valuation of discretely monitored barrier options where it yields values closest to those obtained from the only semi analytical valuation methods available the scheme is also applied to the analysis of greeks data such as delta and gamma

the analysis of asthma control under a markov assumption with use of covariates in studies of disease states and their relation to evolution data on the state are usually obtained at in frequent time points during follow up moreover in many applications there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution we developed a continuous time markov model with use of time dependent covariates and a markov model with piecewise constant intensities to model asthma evolution methods to estimate the effect of covariates on transition intensities to test the assumption of time homogeneity and to assess goodness of fit are proposed we apply these methods to asthma control we consider a three state model and we discuss in detail the analysis of asthma control evolution copyright 2003 john wiley sons ltd

testing the number of components in a normal mixture we demonstrate that under a theorem proposed by vuong the likelihood ratio statistic based on the kullback leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi squared random variables with one degree of freedom under general regularity conditions we report simulation studies of two cases where we are testing a single normal versus a two component normal mixture and a two component normal mixture versus a three component normal mixture an empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution

on smoothing of the crank nicolson scheme and higher order schemes for pricing barrier options most option pricing problems have nonsmooth payoffs or discontinuous derivatives at the exercise price discrete barrier options have not only nonsmooth payoffs but also time dependent discontinuities in pricing barrier options certain aspects are triggered if the asset price becomes too high or too low standard smoothing schemes used to solve problems with nonsmooth payoff do not work well for discrete barrier options because of discontinuities introduced in the time domain when each barrier is applied moreover these unwanted oscillations become worse when estimating the hedging parameters e g delta and gamma we have an improved smoothing strategy for the crank nicolson method which is unique in achieving optimal order convergence for barrier option problems numerical experiments are discussed for one asset and two asset problems time evolution graphs are obtained for one asset problems to show how option prices change with respect to time this smoothing strategy is then extended to higher order methods using diagonal m m pade main schemes under a smoothing strategy of using as damping schemes the 0 2m 1 subdiagonal pade schemes