On local asymptotic normality for functional autoregressive processes

On asymptotic normality of sequential LS-estimates of unstable autoregressive processes

For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contr...

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...

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 ...

On the Preservation of Local Asymptotic Normality Under Information Loss

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...