Simulation-Based Finite-Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing

Statistical tests in vector autoregressive (VAR) models are typically based on large-sample approximations, involving the use of asymptotic distributions or bootstrap techniques. After documenting that such methods can be very misleading even with fairly large samples, especially when the number of lags or the number of equations is not small, we propose a general simulation-based technique that allows one to control completely the level of tests in parametric VAR models. In particular, we show that maximized Monte Carlo tests [Dufour (2002)] can provide provably exact tests for such models, whether they are stationary or integrated. Applications to order selection and causality testing are considered as special cases. The technique developed is applied to quarterly and monthly VAR models of the U.S. economy, comprising income, money, interest rates and prices, over the period 1965-1996.

New simulation schemes for the Heston model

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma.

Simulation de profils de gravure et de dépôt à l’échelle du motif pour l’étude des procédés de microfabrication utilisant une source plasma de haute densité à basse pression

En lien avec l’avancée rapide de la réduction de la taille des motifs en microfabrication, des processus physiques négligeables à plus grande échelle deviennent dominants lorsque cette taille s’approche de l’échelle nanométrique. L’identification et une meilleure compréhension de ces différents processus sont essentielles pour améliorer le contrôle des procédés et poursuivre la «nanométrisation» des composantes électroniques. Un simulateur cellulaire à l’échelle du motif en deux dimensions s’appuyant sur les méthodes Monte-Carlo a été développé pour étudier l’évolution du profil lors de procédés de microfabrication. Le domaine de gravure est discrétisé en cellules carrées représentant la géométrie initiale du système masque-substrat. On insère les particules neutres et ioniques à l’interface du domaine de simulation en prenant compte des fonctions de distribution en énergie et en angle respectives de chacune des espèces. Le transport des particules est effectué jusqu’à la surface en tenant compte des probabilités de réflexion des ions énergétiques sur les parois ou de la réémission des particules neutres. Le modèle d’interaction particule-surface tient compte des différents mécanismes de gravure sèche telle que la pulvérisation, la gravure chimique réactive et la gravure réactive ionique. Le transport des produits de gravure est pris en compte ainsi que le dépôt menant à la croissance d’une couche mince. La validité du simulateur est vérifiée par comparaison entre les profils simulés et les observations expérimentales issues de la gravure par pulvérisation du platine par une source de plasma d’argon.

New insights on growth mechanisms of protein clusters at surfaces: an AFM and simulation study

Despite its relevance to a wide range of technological and fundamental areas, a quantitative understanding of protein surface clustering dynamics is often lacking. In inorganic crystal growth, surface clustering of adatoms is well described by diffusion-aggregation models. In such models, the statistical properties of the aggregate arrays often reveal the molecular scale aggregation processes. We investigate the potential of these theories to reveal hitherto hidden facets of protein clustering by carrying out concomitant observations of lysozyme adsorption onto mica surfaces, using atomic force microscopy. and Monte Carlo simulations of cluster nucleation and growth. We find that lysozyme clusters diffuse across the substrate at a rate that varies inversely with size. This result suggests which molecular scale mechanisms are responsible for the mobility of the proteins on the substrate. In addition the surface diffusion coefficient of the monomer can also be extracted from the comparison between experiments and simulations. While concentrating on a model system of lysozyme-on-mica, this 'proof of concept' study successfully demonstrates the potential of our approach to understand and influence more biomedically applicable protein-substrate couples.

Ordering on multiple lengthscales in a series of side group liquid crystal block copolymers containing a cholesteryl-based mesogen

Hierarchical ordering in a side group liquid crystal block copolymer is investigated by differential scanning calorimetry, polarized optical microscopy, small-angle X-ray and neutron scattering (SAXS and SANS) and transmission electron microscopy (TEM). A series of block copolymers with a range of compositions was prepared by atom transfer radical polymerization, comprising a polystyrene block and a poly(methyl methacrylate) block bearing chiral cholesteryl mesogens. Smectic ordering is observed as well as microphase separation of the block copolymer. Lamellar structures were observed for far larger volume fractions than for coil-coil copolymers (up to a volume fraction of liquid crystal block, f(LC) = 0.8). A sample with f(LC) = 0.86 exhibited a hexagonal-packed cylinder morphology, as confirmed by SAXS and TEM. The matrix comprised the liquid crystal block, with the mesogens forming smectic layers. For the liquid crystal homopolymer and samples with high f(LC), a smectic-smectic phase transition was observed below the clearing point. At low temperature, the smectic phase comprises coexisting domains with monolayer S-A,S-1 coexisting with interdigitated S-A,S-d domains. At high temperature a SA,1 phase is observed. This is the only structure observed for samples with lower f(LC). These unprecedented results point to the influence of block copolymer microphase separation on the smectic ordering.

Double-gyroid morphology of a polystyrene-block-poly(ferrocenylethylmethylsilane) diblock copolymer: a route to ordered bicontinuous nanoscale architectures

A polystyrene-block-poly(ferrocenylethylmethylsilane) diblock copolymer, displaying a double-gyroid morphology when self-assembled in the solid state, has been prepared with a PFEMS volume fraction phi(PFMS)=0.39 and a total molecular weight of 64 000 Da by sequential living anionic polymerisation. A block copolymer with a metal-containing block with iron and silicon in the main chain was selected due to its plasma etch resistance compared to the organic block. Self-assembly of the diblock copolymer in the bulk showed a stable, double-gyroid morphology as characterised by TEM. SAXS confirmed that the structure belonged to the Ia3d space group.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using latticebased Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.

Analysis and compensation of power amplifier nonlinearity in MIMO transmit diversity systems

The nonlinearity of high-power amplifiers (HPAs) has a crucial effect on the performance of multiple-input-multiple-output (MIMO) systems. In this paper, we investigate the performance of MIMO orthogonal space-time block coding (OSTBC) systems in the presence of nonlinear HPAs. Specifically, we propose a constellation-based compensation method for HPA nonlinearity in the case with knowledge of the HPA parameters at the transmitter and receiver, where the constellation and decision regions of the distorted transmitted signal are derived in advance. Furthermore, in the scenario without knowledge of the HPA parameters, a sequential Monte Carlo (SMC)-based compensation method for the HPA nonlinearity is proposed, which first estimates the channel-gain matrix by means of the SMC method and then uses the SMC-based algorithm to detect the desired signal. The performance of the MIMO-OSTBC system under study is evaluated in terms of average symbol error probability (SEP), total degradation (TD) and system capacity, in uncorrelated Nakagami-m fading channels. Numerical and simulation results are provided and show the effects on performance of several system parameters, such as the parameters of the HPA model, output back-off (OBO) of nonlinear HPA, numbers of transmit and receive antennas, modulation order of quadrature amplitude modulation (QAM), and number of SMC samples. In particular, it is shown that the constellation-based compensation method can efficiently mitigate the effect of HPA nonlinearity with low complexity and that the SMC-based detection scheme is efficient to compensate for HPA nonlinearity in the case without knowledge of the HPA parameters.

GSHMC: an efficient method for molecular simulation

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

A Time Efficient Optical Model for GATE Simulation of a LYSO Scintillation Matrix Used in PET Applications

A time efficient optical model is proposed for GATE simulation of a LYSO scintillation matrix coupled to a photomultiplier. The purpose is to avoid the excessively long computation time when activating the optical processes in GATE. The usefulness of the model is demonstrated by comparing the simulated and experimental energy spectra obtained with the dual planar head equipment for dosimetry with a positron emission tomograph ( DoPET). The procedure to apply the model is divided in two steps. Firstly, a simplified simulation of a single crystal element of DoPET is used to fit an analytic function that models the optical attenuation inside the crystal. In a second step, the model is employed to calculate the influence of this attenuation in the energy registered by the tomograph. The use of the proposed optical model is around three orders of magnitude faster than a GATE simulation with optical processes enabled. A good agreement was found between the experimental and simulated data using the optical model. The results indicate that optical interactions inside the crystal elements play an important role on the energy resolution and induce a considerable degradation of the spectra information acquired by DoPET. Finally, the same approach employed by the proposed optical model could be useful to simulate a scintillation matrix coupled to a photomultiplier using single or dual readout scheme.