No description available.

Inaug. Diss.--Göteborg. / On t.p. p̳ is subscript.

No description available.

We use the methods of exponential asymptotics to study the solutions of a one dimensional wave equation with a non-constant wave speed c(x,t) modelling, for example, a slowly varying spatio-temporal topography. The equation reads htt(x,t) = (c2(x,t)hx(x,t))x' (1) where the subscripts denote differentiation w.r.t. the parameters x and t respectively. We focus on the exponentially small reflected wave that appears as a result of a Stokes phenomenon associated with the complex singularities of the speed. This part of the solution is not captured by the standard WKBJ (geometric optics) approach. We first revisit the time-independent propagation problem using resurgent analysis. Our results recover those obtained using Meyers integral-equation approach or the Kruskal-Segur (K-S) method. We then consider the time-dependent propagation of a wavepacket, assuming increasingly general models for the wave speed: time independent, c(x), and separable, c1(x)c2(t). We also discuss the situation when the wave speed is an arbitrary function, c(x,t), with the caveat that the analysis of this setup has yet to be completed. We propose several methods for the computation of the reflected wavepacket. An integral transform method, using the Dunford integral, provides the solution in the time independent case. A second method exploits resurgence: we calculate the Stokes multiplier by inspecting the late terms of the dominant asymptotic expansion. In addition, we explore the benefits of an integral transform that relates the coefficients of the dominant solution in the time-dependent problem to the coefficients of the dominant solution in the time-independent problem. A third method is a partial differential equation extension of the K-S complex matching approach, containing details of resurgent analysis. We confirm our asymptotic predictions against results obtained from numerical integration.

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

O objetivo deste trabalho é fazer uma revisão dos modelos não lineares de família exponencial (Cordeiro & Paula (1989); Wei (1998)) para respostas independentes e apresentar possíveis extensões para o caso de dados correlacionados. Inicialmente são apresentados exemplos ilustrativos, alguns dos quais são reanalizados ao longo do texto. Em seguida são discutidos procedimentos de estimação e testes de hipóteses, tais como apresentação de um processo de estimação que pode ser adaptado ao processo iterativo usado na classe dos modelos lineares generalizados, e alguns resultados assintóticos. Técnicas usuais de diagnóstico, como pontos de alavanca, análise de resíduos e diagnóstico de influência são adaptados para a classe dos modelos não lineares de família exponencial. Extensões para a classe dos modelos não lineares com resposta binomial negativa são também apresentadas. Finalmente, são consideradas duas possíveis extensões dos modelos não lineares de família exponencial para dados correlacionados, através de equações de estimação generalizadas e através de modelagem mista em que efeitos aleatórios em forma linear são adicionados ao componente não linear da parte sistemática do modelo conforme sugerido recentemente por Tang et al. (2006a). / The aim of this work is to present a review of the exponential family nonlinear models (Cordeiro & Paula (1989); Wei (1998)) for independent responses and to present possible extensions for the case of correlated data. Firstly, ilustrative examples are presented with some of them being reanalyzed along the text. Then, estimation and hypothesis testing procedures, such as the presentation of an iterative process adapted from the one of generalized linear models, and some asymptotic results are discussed. Useful diagnostic techniques, as calculation of leverage measures, residual analysis and influence diagnostics are adapted for the class of exponential family nonlinear models. Extensions to nonlinear negative binomial models are also presented. Finally, two possible extensions for correlated data are considered, by using generalized estimating equations and mixed modeling in which linear random effects are added into the systematic component together with the nonlinear function, as suggested by Tang et al. (2006a).

The exponential model of Bloomfield (1973) is becoming increasingly important due to its recent applications to long memory time series. However, this model has received little consideration in the context of short memory time series. Furthermore, there has been very little attempt at using the EXP model as a model to analyze observed time series data. This dissertation research is largely focused on developing new methods to improve the utility and robustness of the EXP model. Specifically, a new nonparametric method of parameter estimation is developed using wavelets. The advantage of this method is that, for many spectra, the resulting parameter estimates are less susceptible to biases associated with methods of parameter estimation based directly on the raw periodogram. Additionally, several methods are developed for the validation of spectral models. These methods test the hypothesis that the estimated model provides a whitening transformation of the spectrum; this is equivalent to the time domain notion of producing a model whose residuals behave like the residuals of white noise. The results of simulation and real data analysis are presented to illustrate these methods.

This dissertation contains three essays. They are related to the exponential series estimation of copulas and the application of parametric copulas in financial econometrics. Chapter II proposes a multivariate exponential series estimator (ESE) to estimate copula density nonparametrically. The ESE attains the optimal rate of convergence for nonparametric density. More importantly, it overcomes the boundary bias of copula estimation. Extensive Monte Carlo studies show the proposed estimator outperforms kernel and log-spline estimators in copula estimation. Discussion is provided regarding application of the ESE copula to Asian stock returns during the Asian financial crisis. The ESE copula complements the existing nonparametric copula studies by providing an alternative dedicated to the tail dependence measure. Chapter III proposes a likelihood ratio statistic using a nonparametric exponential series approach. The order of the series is selected by Bayesian Information Criterion (BIC). I propose three further modifications on my test statistic: 1) instead of putting equal weight on the individual term of the exponential series, I consider geometric and exponential BIC average weights; 2) rather than using a nested sequence, I consider all subsets to select the optimal terms in the exponential series; 3) I estimate the likelihood ratio statistic using the likelihood cross-validation. The extensive Monte Carlo simulations show that the proposed tests enjoy good finite sample performances compared to the traditional methods such as the Anderson-Darling test. In addition, this data-driven method improves upon Neyman’s score test. I conclude that the exponential series likelihood ratio test can complement the Neyman’s score test. Chapter IV models and forecasts S&P500 index returns using the Copula-VAR approach. I compare the forecast performance of the Copula-VAR model with a classical VAR model and a univariate time series model. I use this approach to forecast S&P500 index returns. I apply a modified Diebold-Mariano test to test the equality of mean squared forecast errors and utilize a forecast encompassing test to evaluate forecasts. The findings suggest that allowing a more flexible specification in the error terms using copula tends improve the forecast accuracy. I also demonstrate combined forecasts improved forecasts accuracy over individual models.

Two novel ultra-low-voltage (ULV) low-power (LP) variable gain amplifiers (VGA) are presented in this paper. These amplifiers based on complementary MOS transistors operating in weak inversion region are composed of pseudo-exponential current-to-current converters and analog multipliers. The gain of the amplifiers can be controlled by an exponential function circuit. The proposed circuits have been verified with the 0.25£gm CMOS technology by HSPICE simulations. The simulation results confirm the feasibility of the proposed VGAs.