Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the Real Elliptically Symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model where the parametric part is given by the mean vector and by the scatter matrix while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance. The first part of the paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. The second part of the paper, building on the mathematical tools previously introduced, the Constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced. The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust $M$-estimator of mean vector and scatter matrix when no a-priori information on the density generator is available. A closed form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix $M$-estimators with respect to the CSCRB.Comment: This paper has been accepted for publication in IEEE Transactions on Signal Processin

Alumina Thin film Coatings at Optimized Conditions using RF Magnetron Sputtering Process

This study deals with the extensive investigation of Alumina thin film coating deposited on glass, stainless steel, and polycarbonate substrates at 25oC. The transmittance, reflectance, and surface roughness were determined. Transmittance was observed from 88 to 91 % for alumina thin film coating on glass and polycarbonate substrates. The stiffness, hardness, and elastic modulus were 58, 52, and 47 μN/nm, 7.52, 7.14, 6.87, 103, 112, and 122 GPa thin-film coating on different substrates. An increase in surface roughness and transmittance was observed with sputtering power and the thickness of the coating

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Evaluation of outcome following paracervical infiltration with or without saline and adrenaline during vaginal hysterectomy

Background: Paracervical infiltration is used in vaginal hysterectomy to facilitate dissection. Use of paracervical infiltration however can be associated with local ischemia and infection. We did a study to find out its benefits during vaginal hysterectomy.Methods: It was a prospective case control study. Patients were divided into two groups. In the first group, no paracervical infiltration was given. In the second group paracervical infiltration was given before hysterectomy. The operating time, blood loss and postoperative infection were noted in each group.Results: The operating time was slightly higher in vaginal hysterectomy group without infiltration (p=0.025) The operating time in laparoscopic assisted vaginal hysterectomy group was not significant (p=0.0296). There was significant difference in Hemoglobin after surgery in both groups (p value 0.614 for vaginal hysterectomy and 0.173 for laparoscopic assisted vaginal hysterectomy). There was no case of infection in both groups.Conclusions: From our study, we concluded that paracervical infiltration offers no distinctive advantage during vaginal hysterectomy or laparoscopic assisted vaginal hysterectomy.