One Parameter A (α) Distribution: Different Methods of Estimation

This paper addresses the different methods of estimation of the unknown parameter of one parameter A(α) distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimator, least square and weighted least square estimators, maximum product spacing estimators, Cram´er-von Mises estimator and compare those using extensive numerical simulations. Next, we obtain parametric bootstrap confidence interval of the parameter using frequentist approaches. Finally, one real data set has been analysed for illustrative purposes.

Parametric Estimation in the Vasicek-Type Model Driven by Sub-Fractional Brownian Motion

In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion: d X t = ( μ + θ X t ) d t + d S t H , t ≥ 0 with X 0 = 0 , where S H is a sub-fractional Brownian motion whose Hurst index H is greater than 1 2 , and μ ∈ R , θ ∈ R + are two unknown parameters. Based on the so-called continuous observations, we suggest the least square estimators of μ and θ and discuss the consistency and asymptotic distributions of the two estimators.