Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions

In this paper, we analyze the risk ratios of several shrinkage estimators using a balanced loss function. The James–Stein estimator is one of a group of shrinkage estimators that has been proposed in the existing literature. For these estimators, sufficient criteria for minimaxity have been established, and the James–Stein estimator’s minimaxity has been derived. We demonstrate that the James–Stein estimator’s minimaxity is still valid even when the parameter space has infinite dimension. It is shown that the positive-part version of the James–Stein estimator is substantially superior to the James–Stein estimator, and we address the asymptotic behavior of their risk ratios to the maximum likelihood estimator (MLE) when the dimensions of the parameter space are infinite. Finally, a simulation study is carried out to verify the performance evaluation of the considered estimators.

Study on the Electrical Conductivity of Inorganic Conductive Network in Sediments

The inorganic conductive network provides an essential channel for electron transport and supports the biogeochemical process in sediments, but the conductive mechanism of conductive network is not well understood. In this work, theory of circuit and electronics was applied to build a three-dimensional (3D) resistivity network simulation model for exploring the conductive mechanism and analysing the effect of the particle size on the conductive characteristic of inorganic conductive network. In order to simulate the real sediment environment, inorganic composites with silica (SiO2) particles as matrix using magnetite (Fe3O4) particles as fillers are constructed. The simulation results reveal that the electrical conductivity of these composites rises nonlinearly with the increasing volume fraction of conductive fillers, which is consistent with the percolation theory. Moreover, small-sized conductive particles or large-sized matrix particles are confirmed to exert a positive part in enhancing electrical conductivity of composites.

On the Green function of the killed fractional Laplacian on the periodic domain

We give a very simple proof of the positivity and unimodality of the Green function for the killed fractional Laplacian on the periodic domain. The argument relies on the Jacobi triple product and a probabilistic representation of the Green function. We also show by a contour integration that the Green function is completely monotone on the positive part of the periodic domain.

INSTITUTE OF OWNERSHIP IN THE POST-COMMUNIST REPUBLIC OF ALBANIA

Ownership as a genuine institute of civil rights in the Republic of Albania began to be considered complete only after the change of political systems. Until this period, ownership was a fragmented and incomplete institute due to the fact of the existence of public property, which was one of the principles of the ideology of the monist system. With the change of the corpus of domestic legislation and the signing of international agreements ratified in civil law, the concept of private property will undergo a fundamental change. Building a civil code totally different from the existing one would bring about a different treatment of private property. In the new code, private ownership would be of paramount importance both from a doctrinal and practical point of view. The implementation of the legislation would be a challenge in itself which, in addition to the positive part, will also face issues that are still part of the law practices. The focus would be on restitution and compensation of property to former owners but at the same time the private property institute would address in itself the new ways of acquiring probationary property, property protection and everything else related to this institute of which is considered a fundamental right by the Constitution of the Republic of Albania and the European Convention on Human Rights.

Interrater Reliability of the Prone Apprehension Relocation Test

Background: The Prone Apprehension Relocation Test (PART) augments existing radiographic measures and clinical provocative maneuvers in diagnosing hip instability. One measure of the potential clinical utility of the PART depends on the reproducibility of test results by evaluating providers including physicians, licensed athletic trainers, and physical therapists. Purpose: To determine the interrater reliability of the PART among health care providers. Study Design: Cohort study (diagnosis); Level of evidence, 3. Methods: We retrospectively identified patients in our institution’s hip preservation registry who presented between September 2017 and June 2019 for evaluation of hip pain. Patients included in the study had the PART performed by a single physician as well as 1 of 12 physician extenders (a licensed athletic trainer or a physical therapist). The providers were blinded to the findings of the other examining professional. Interrater reliability was assessed using the Cohen κ (≥0.75 was considered excellent; between 0.75 and 0.40, moderate; and ≤0.40, poor). Results: A total of 96 patients (190 hips) were included in this study (61 women and 35 men, average age 32 ± 12.1 years). A total of 23 hips had a positive PART from both examiners. Interrater reliability was excellent between health care professionals for the PART when evaluating the right hip (κ = 0.80), left hip (κ = 0.82), and when combining the results for left and right (κ = 0.81). A subanalysis of patients with a positive PART from both raters demonstrated that 19 of the 23 hips had a lateral center-edge angle >25°. Conclusion: Our study demonstrated excellent interrater reliability of the PART, supporting its use in the physical evaluation of painful hips.

Bayesian Analysis of Nonnegative Data Using Dependency-Extended Two-Part Models

This article is motivated by the challenge of analysing an agricultural field experiment with observations that are positive on a continuous scale or zero. Such data can be analysed using two-part models, where the distribution is a mixture of a positive distribution and a Bernoulli distribution. However, traditional two-part models do not include any dependencies between the two parts of the model. Since the probability of zero is anticipated to be high when the expected value of the positive part is low, and the other way around, this article introduces dependency-extended two-part models. In addition, these extensions allow for modelling the median instead of the mean, which has advantages when distributions are skewed. The motivating example is an incomplete block trial comparing ten treatments against weed. Gamma and lognormal distributions were used for the positive response, although any density on the support of real numbers can be accommodated. In a cross-validation study, the proposed new models were compared with each other and with a baseline model without dependencies. Model performance and sensitivity to choice of priors were investigated through simulation. A dependency-extended two-part model for the median of the lognormal distribution performed best with regard to mean square error in prediction. Supplementary materials accompanying this paper appear online.