No abstract

This paper deals with the problem of estimating the parameters for fractional diffusion process from discrete observations when the Hurst parameter H is unknown. With combination of several methods, such as the Donsker type approximate formula of fractional Brownian motion, quadratic variation method, and the maximum likelihood approach, we give the parameter estimations of the Hurst index, diffusion coefficients, and volatility and then prove their strong consistency. Finally, an extension for generalized fractional diffusion process and further work are briefly discussed.

Everything is connected in the world. From small groups to global societies, the interactions among people, technology, and policies need sophisticated techniques to be perceived and forecasted. In social network, it has been concluded that the microblog users influence and microblog grade are nonlinearly dependent. However, to the best of our knowledge, the nonlinear influence predication of social network has not been explored in the existing literature. This article proposes a partial autoregression single index model to combine network structure (linear) and static covariates (nonparametric) flexibly. Compared with previous work, our model has fewer limits and more applications. The profile least squares estimation is employed to infer this semiparametric model, and variables selection is performed via the smoothly clipped absolute deviation penalty (SCAD). Simulations are conducted to demonstrate finite sample behaviors.

Simplicial depth (SD) plays an important role in discriminant analysis, hypothesis testing, machine learning, and engineering computations. However, the computation of simplicial depth is hugely challenging because the exact algorithm is an NP problem with dimension d and sample size n as input arguments. The approximate algorithm for simplicial depth computation has extremely low efficiency, especially in high-dimensional cases. In this study, we design an importance sampling algorithm for the computation of simplicial depth. As an advanced Monte Carlo method, the proposed algorithm outperforms other approximate and exact algorithms in accuracy and efficiency, as shown by simulated and real data experiments. Furthermore, we illustrate the robustness of simplicial depth in regression analysis through a concrete physical data experiment.