Asymptotic inference for a stochastic differential equation with uniformly distributed time delay

For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local asymptotic mixed normality or local asymptotic quadraticity is proved for different values of the parameter. Applications to the asymptotic behaviour of the maximum likelihood estimator of the parameter based on continuous sample are given

Asymptotic Normality of Quadratic Estimators

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations

Asymptotics for random effects models with serial correlation

This paper considers the large sample behavior of the maximum likelihood estimator of random effects models. Consistent estimation and asymptotic normality as N and/or T grows large is established for a comprehensive specification which allows for serial correlation in the form of AR(1) for the idiosyncratic or time-specific error component. The consistency and asymptotic normality properties of all commonly used random effects models are obtained as special cases of the comprehensive model. When N or T \rightarrow \infty only a subset of the parameters are consistent and asymptotic normality is established for the consistent subsets.Panel data; error components; consistency; asymptotic normality; maximum likelihood.

Confidence sets in nonparametric calibration of exponential Lévy models

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy density at nitely many points in the spectral calibration method. Furthermore, the asymptotic normality result leads to a test on the value of the volatility in exponential Lévy models.European option, Jump diffusion, Confidence sets, Asymptotic normality, Nonlinear inverse problem