Mean Empirical Likelihood

Empirical likelihood methods are widely used in different settings to construct the confidence regions for parameters which satisfy the moment constraints. However, the empirical likelihood ratio confidence regions may have poor accuracy, especially for small sample sizes and multi-dimensional situations. A novel Mean Empirical Likelihood (MEL) method is proposed. A new pseudo dataset using the means of observation values is constructed to define the empirical likelihood ratio and it is proved that this MEL ratio satisfies Wilks’ theorem. Simulations with different examples are given to assess its finite sample performance, which shows that the confidence regions constructed by Mean Empirical Likelihood are much more accurate than that of the other Empirical Likelihood methods

Efficient Empirical Likelihood Inference for recovery rate of COVID-19 under Double-Censoring

Doubly censored data are very common in epidemiology studies. Ignoring censorship in the analysis may lead to biased parameter estimation. In this paper, we highlight that the publicly available COVID19 data may involve high percentage of double-censoring and point out the importance of dealing with such missing information in order to achieve better forecasting results. Existing statistical methods for doubly censored data may suffer from the convergence problems of the EM algorithms or may not be good enough for small sample sizes. This paper develops a new empirical likelihood method to analyse the recovery rate of COVID19 based on a doubly censored dataset. The efficient influence function of the parameter of interest is used to define the empirical likelihood (EL) ratio. We prove that $-2\log$(EL-ratio) asymptotically follows a standard $\chi^2$ distribution. This new method does not require any scale parameter adjustment for the log-likelihood ratio and thus does not suffer from the convergence problems involved in traditional EM-type algorithms. Finite sample simulation results show that this method provides much less biased estimate than existing methods, when censoring percentage is large. The method application to the COVID19 data will help researchers in other field to achieve better estimates and forecasting results

Formation Mechanism of Guided Resonances and Bound States in the Continuum in Photonic Crystal Slabs

We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry-P\'erot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. We show BICs at the center and on the edge of the Brillouin zone protected by symmetry, as well as BICs at generic wave vectors not protected by symmetry.Comment: 12 pages, 3 figure

Empirical Likelihood Based on Synthetic Right Censored Data

In this paper, we develop a Mean Empirical Likelihood (MeanEL) method for right censored data. This MeanEL approach is based on traditional empirical likelihood methods but uses synthetic data to construct an EL ratio statistics, which is shown to have a $\chi^2$ limiting distribution. Different simulation studies show that the MeanEL confidence intervals tend to have more accurate coverage probabilities than other existing Empirical Likelihood methods. Theoretical comparisons of different EL methods are also provided under a general framework

Osmotic characteristics and fertility of murine spermatozoa collected in different solutions

Osmotic stress is an important factor that can result in cell damage during cryopreservation. Before ejaculation or collection for cryopreservation, murine spermatozoa are stored in epididymal fluid, a physiologically hyperosmotic environment (w415 mmol/kg). The objectives of this study were to determine the osmotic tolerance limits of sperm motion parameters of ICR and C57BL/6 mouse spermatozoa collected in isosmotic (290 mmol/kg) and hyperosmotic (415 mmol/kg) media, and the effect of the osmolality of sperm collection media on sperm fertility after cryopreservation. Our results indicate that murine spermatozoa collected in media with different osmolalities (290 and 415 mmol/kg Dulbecco’s phosphate buffered saline (DPBS)) appeared to have different osmotic tolerances for the maintenance of sperm motility and other motion parameters in both mouse strains. The hypo- and hyperosmotic treatments decreased motility and affected other motion parameters of spermatozoa collected in 290 mmol/kg DPBS. The extent of the change of motion parameters after treatments corresponded with the levels of osmotic stress. However, for spermatozoa collected in 415 mmol/kg DPBS, exposure to 290 mmol/kg DPBS tended to increase sperm motility and the quality of their motion parameters. The osmolality of sperm collection medium can affect murine sperm fertility. Spermatozoa collected in 415 mmol/kg medium showed higher fertility compared with spermatozoa collected in 290 mmol/kg as assessed by IVF. Results characterizing murine sperm osmotic tolerance collected in media with different osmolalities from different strains and the effect of collection media osmolality on sperm fertility after cryopreservation will be useful in designing cryopreservation protocols