Local asymptotic normality property for fractional Gaussian noise under high-frequency observations

Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling

We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Lévy process X, when we observe high-frequency data X∆n , X2∆n , . . . , Xn∆n with sampling mesh ∆n → 0 and the terminal sampling time n∆n → ∞. The rate of convergence turns out to be ( √ n∆n, √ n∆n, √ n, √ n) for the dominating parameter (α, β, δ, μ), where α stands for the heaviness of the tails, β ...

Local Asymptotic Normality Property for Lacunar Wavelet Series Multifractal Model

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. T...

On the Preservation of Local Asymptotic Normality Under Information Loss

Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable Lévy processes

We prove the Local Asymptotic Mixed Normality property from high frequency observations, of a continuous time process solution of a stochastic differential equation driven by a pure jump Lévy process. The process is observed on the fixed time interval [0, 1] and the parameter appears in the drift coefficient only. We compute the asymptotic Fisher information and find that the rate in the LAMN p...

Asymptotic Normality under Two-Phase Sampling Designs

Large sample properties of statistical inferences in the context of finite populations are harder to determine than in the iid case due to their dependence jointly on the characteristics of the finite population and the sampling design employed. There have been many discussions on special inference procedures under special sampling designs in the literature. General and comprehensive results ar...