On the convergence rates of kernel estimator and hazard estimator for widely dependent samples
In this paper, we establish a Bernstein-type inequality for widely orthant dependent random variables, and obtain the rates of strong convergence for kernel estimators of density and hazard functions, under some suitable conditions.
Kernel Density and Hazard Rate Estimation for Censored Dependent Data
In some long term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common marginal distribution function having a density, and the nonparametric estimation of density and hazard rate under random censorship is of our interest. In this paper, we establish the asymptotic normality and the uniform consistency (with rates) of the kernel estimators for density and hazard function under a censored dependent model. A numerical study elucidates the behavior of the estimators for moderately large sample sizes.
Spin label motion in fatty acids.
Spin labels dissolved in highly purified fatty acid systems exhibit nearly identical tumbling rates in liquid and solid phases. Even though the spin labels do not have the same molecular geometry as the lipid matrix the melting point of the matrix can be inferred by measurements of the temperature dependency of molecular motion.