ABSTRACT
In recent years, numerous feature screening schemes have been developed for ultra-high dimensional standard survival data with only one failure event. Nevertheless, existing literature pays little attention to related investigations for competing risks data, in which subjects suffer from multiple mutually exclusive failures. In this article, we develop a new marginal feature screening for ultra-high dimensional time-to-event data to allow for competing risks. The proposed procedure is model-free, and robust against heavy-tailed distributions and potential outliers for time to the type of failure of interest. Apart from this, it is invariant to any monotone transformation of event time of interest. Under rather mild assumptions, it is shown that the newly suggested approach possesses the ranking consistency and sure independence screening properties. Some numerical studies are conducted to evaluate the finite-sample performance of our method and make a comparison with its competitor, while an application to a real data set is provided to serve as an illustration.
ABSTRACT
We study the minimum Skorohod distance estimation θ ε ∗ and minimum L 1 -norm estimation θ ε Ë of the drift parameter θ of a stochastic differential equation d X t = θ X t d t + ε d L t d , X 0 = x 0 , where { L t d , 0 ≤ t ≤ T } is a fractional Lévy process, ε ∈ ( 0 , 1 ] . We obtain their consistency and limit distribution for fixed T, when ε â 0 . Moreover, we also study the asymptotic laws of their limit distributions for T â ∞ .
ABSTRACT
An efficient and concise protocol for the highly regio- and stereoselective synthesis of ferrocene-containing disubstituted E-allylic ester derivatives via a palladium-catalyzed intermolecular arylesterification reaction of ferrocenylallene with aryl iodides and carboxylic acids has been developed. The regio- and stereoselectivities of this reaction may be controlled by the steric effect of the bulky ferrocene group.
