In the present article, we investigate nonparametric estimation of the unknown drift function b in an integrated Lévy driven jump diffusion model. Our aim will be to estimate the drift on a compact set based on a high-frequency data sample. Instead of observing the jump diffusion process V itself, we observe a discrete and high-frequent sample of the integrated process
Vsds.Based on the available observations of Xt, we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function b. Under appropriate assumptions, we will bound the L 2 -risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.MSC 2010 Classification: 62M09, 62G08
In this article we propose two new Multiplicative Bias Correction (MBC) techniques for nonparametric multivariate density estimation. We deal with positively supported data but our results can easily be extended to the case of mixtures of bounded and unbounded supports. Both methods improve the optimal rate of convergence of the mean squared error up to O(n −8/(8+d) ), where d is the dimension of the underlying data set. Moreover, they overcome the boundary effect near the origin and their values are always non-negative. We investigate asymptotic properties like bias and variance as well as the performance of our estimators in Monte Carlo Simulations and in a real data example.
The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts.
The eligibility of poly(vinylidene fluoride-trifluoroethylene) films for microsystem integration has been investigated with respect to strongly strain-reliant device designs such as for example vibration-based piezoelectric energy harvesting devices. Due to their ability to withstand extraordinary elongations, the integration of polymeric materials into appropriately designed devices is exceptionally promising and has been accordingly assessed. However, polymeric films often suffer from an immense sensitivity to many of the processing steps used during microfabrication like lithography. This contribution will show that this is not necessarily so. Functional films have been prepared and comprehensively characterized providing a benchmark for processing induced material deterioration. Further, the damage potential emanating from consecutive processing and lithographical pattern transfer steps was focused on. The inferred course of action was finally applied to the fabrication and vibrational proof of concept of a microsystem based on the polymeric material system poly(vinylidene fluoride-trifluoroethylene).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.