We show local asymptotic normality (LAN) for a statistical model of discretely observed ergodic jump-diffusion processes, where the drift coefficient, diffusion and jump structure are parametrized. Under LAN property, we can discuss efficiency regular estimators, quasi-maximum-likelihood Bayes-type estimators proposed in Shimizu Yoshida (Stat. Inference Stoch. Process. 9 (2006) 227–277) Ogihara...

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically distributed data. We do not need the law of large numbers (LLN) or the central limit theorem (CLT). We do not need sample size going to infinity or anything going t...

Petrovskaya and Leontovich (1982) proved a central limit theorem for sums of dependent random variables indexed by a graph. We apply this theorem to obtain asymptotic normality for the number of local maxima of a random function on certain graphs and for the number of edges having the same color at both endpoints in randomly colored graphs. We briefly motivate these problems, and conclude with ...

We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove its consistency and asymptotic normality under mild assumptions. We study the semiparametric likelihood process and prove local asymptotic normality of the ...

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically distributed data. We do not need the law of large numbers (LLN) or the central limit theorem (CLT). We do not need sample size going to infinity or anything going t...

The paper establishes the local asymptotic normality property for general conditionally heteroskedastic time series models of multiplicative form, $\epsilon _t=\sigma _t(\boldsymbol {\theta }_0)\eta _t$ , where volatility $\sigma }_0)$ is a parametric function $\{\epsilon _{s}, s< t\}$ and $(\eta _t)$ sequence i.i.d. random variables with common density $f_{\boldsymbol }_0}$ . In contrast ea...