tail behavior of a threshold autoregressive stochastic volatility model

We consider a threshold autoregressive stochastic volatility model where the driving noises are sequences of iid regurlarly random vatiables. We prove that both the right and the left tails of the marginal distribution of the log-volatility process are regularly varying with tail exponent. We also determine the exact values of the coefficients in the tail of the considered process.Stochastic volatility processes – Threshold – Tail distribution

Asymptotic Behavior for the Extreme Values of a Linear Regression Model

We consider a class of linear regression model with extreme distribution noise. We show by a mean of point process technique that the asymptotic distribution of the maximum is the same as the one of the max of the noise process, under specific conditions.Extreme value theory – Poisson random process – Point process – regression model.

tail behavior of a threshold autoregressive stochastic volatility model

International audienceWe consider a threshold autoregressive stochastic volatility model where the driving noises are sequences of iid regurlarly random vatiables. We prove that both the right and the left tails of the marginal distribution of the log-volatility process are regularly varying with tail exponent. We also determine the exact values of the coefficients in the tail of the considered process

Extreme Distribution of a Generalized Stochastic Volatility Model,

International audienceWe study the asymptotic behaviour of the extreme values of a stochastic volatility model when the noise follows a generalized error distribution extreme. We provide a Monte Carlo experiment to illustrate th choice of the assumptions. We deal also with the finite sample behaviour of the normalized maxima

Maximum likelihood estimation in the logistic regression model with a cure fraction

International audienceLogistic regression is widely used in medical studies to investigate the relationship between a binary response variable Y and a set of potential predictors X. The binary response may represent, for example, the occurrence of some outcome of interest (Y=1 if the outcome occurred and Y=0 otherwise). In this paper, we consider the problem of estimating the logistic regression model with a cure fraction. A sample of observations is said to contain a cure fraction when a proportion of the study subjects (the so-called cured individuals, as opposed to the susceptibles) cannot experience the outcome of interest. One problem arising then is that it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In this setting, a logistic regression analysis of the relationship between X and Y among the susceptibles is no more straightforward. We develop a maximum likelihood estimation procedure for this problem. We establish the consistency and asymptotic normality of the resulting estimator, and we conduct a simulation study to investigate its finite-sample behavior

A simulation study of maximum likelihood estimation in logistic regression with cured individuals

The logistic regression model is widely used to investigate the relationship between a binary outcome Y and a set of potential predictors X. Diop et al. (2011) present some conditions under which the maximum likelihood estimator is consistent and asymptotically normal in the logistic regression model with a cure fraction. So far, however, only limited simulation results are available to judge the quality of this estimator in finite samples. Therefore in this paper, we conduct a detailed simulation study of its numerical properties. We evaluate its accuracy and the quality of the normal approximation of its asymptotic distribution. We also study the quality of the approximation for constructing asymptotic Wald-type tests of hypothesis. Finally, we consider the problem of estimating the conditional probability of the outcome. Our results indicate that when the proportion of cured individuals is moderate to moderately large, and the sample size is large enough, reliable statistical inferences can be obtained for the regression effects and the probability of the outcome. Our results also indicate that the approximations can be problematic when the cure fraction is very large

Extreme Distribution of a Generalized Stochastic Volatility Model,

We study the asymptotic behaviour of the extreme values of a stochastic volatility model when the noise follows a generalized error distribution extreme. We provide a Monte Carlo experiment to illustrate th choice of the assumptions. We deal also with the finite sample behaviour of the normalized maxima.Extreme value theory – Generalized error distribution – Asymptotic theory

Minimum Hellinger distance estimation for locally stationary processes

In this paper, we are interested in the estimation of locally stationary processes by the minimum Hellinger distance estimator (Beran, 1977) in spectral framework. This distance is originally applied to probability distributions. Here we apply this distance to spectral density functions belonging to a specified parametric spectral family. We generalize the minimum Hellinger distance estimation method to processes that only show a locally stationary behaviour. Asymptotic properties of the estimator are shown. The robustness of the estimator is investigated through a simulation study. An application on real data is carried out