Orthogonal Equivariant Minimax Estimatorsof Bivariate Normal Covariance Matrix and Precision Matrix

1983 ◽  
Vol 32 (1-2) ◽  
pp. 23-46 ◽  
Author(s):  
Divakar Sharma ◽  
K. Krishnamoorthy
Keyword(s):  
Covariance Matrix ◽  
Loss Function ◽  
Unbiased Estimator ◽  
Wishart Distribution ◽  
Loss Functions ◽  
Precision Matrix ◽  
Bivariate Normal ◽  
Minimax Estimators ◽  
Simulation Results ◽  
Better Than

The scale and orthogonal equivariant minimax estimators are obtained for the bivariate normal covariance matrix and precision matrix under Selliah's (1964} and Stein's (1961) loss functions. These new estimators are better than Selliah's and Stein's minimax estimators. An unbiased estimator of the risk of the new estimator is obtained under Selliah's loss function using Haff's (1979) identity for the Wishart distribution. Simulation results seem to indicate that the new estimators dominate the corresponding Hatf's [(1979), (1980)] estimators. We also prove that, for p-2, Haff's estimators are not minimax.

scholarly journals COVRATIO Statistic as a Discrimination Method for Multivariate Normal Distribution

2021 ◽  
Vol 50 (7) ◽  
pp. 2079-2084
Author(s):  
Norli Anida Abdullah ◽  
Afera Mohamad Apandi ◽  
Mohd Iqbal Shamsudheen ◽  
Yong Zulina Zubairi
Keyword(s):  
Normal Distribution ◽  
Covariance Matrix ◽  
Multivariate Normal Distribution ◽  
Discrimination Function ◽  
Multivariate Normal ◽  
Full Dataset ◽  
Linear Discrimination ◽  
Simulation Results ◽  
Better Than ◽  
Discrimination Method

The COVRATIO statistic has been used to identify the presence of outlier in data, which is based on deletion approach, where the determinant of covariance matrix for the full dataset excludes i-th row. This study proposes a novel discrimination method for the multivariate normal (MVN) distribution using the idea of COVRATIO statistic, denoted as . The linear discrimination function (LDF) for MVN distribution will be compared to the statistic. Simulation results showed that the as discrimination method performs better than the LDF with lower misclassification probabilities in all cases considered. The interest in the discrimination method arose in connection with the study of an application to discriminate the shape of the human maxillary dental arches, thus statistic may be considered as an alternative.

scholarly journals Estimation of AR (2) Model with Dependent Errors for Unbounded Stationary and Nonstationary Time Series

2021 ◽  
Vol 23 (12) ◽  
pp. 417-422
Author(s):  
Prof. Ahmed Amin EL- Sheikh ◽  
◽  
Mohammed Ahmed Farouk Ahmed ◽  
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Covariance Matrix ◽  
Nonstationary Time Series ◽  
Stationary Time Series ◽  
Times Series ◽  
The Third ◽  
Stationary Conditions ◽  
Simulation Results ◽  
Better Than

In this paper the GLS and the ML estimators, the variance-covariance matrix, the unbiased for the GLS and the ML estimators of parameters of AR (2) model with constant in case of dependent errors have been derived, the simulation results shown that the values of MSE and Thiel’s U in case of unbounded stationary time series for all sample size T are less than the values of MSE and Thiel’s U in case of unbounded nonstationary time series which approved that the results for unbounded stationary times series are better than the results for unbounded nonstationary times series, and the simulation results for unbounded nonstationary time series shown that by using the measurement of MSE the best case among of all cases of nonstationary which gives the smallest values of MSE is case four when the first and the second conditions of stationary conditions for AR (2) model are exists, while by using the measurement of Thiel’s U the best case among of all cases of nonstationary which gives the smallest values of Thiel’s U is case six when the second and the third conditions of stationary conditions for AR (2) model are exists.

An Estimator of Normal Covariance Matrix

1980 ◽  
Vol 29 (3-4) ◽  
pp. 161-168 ◽  
Author(s):  
Divakar Sharma
Keyword(s):  
Covariance Matrix ◽  
Loss Function ◽  
Triangular Matrices ◽  
The Mean ◽  
Lower Triangular ◽  
Lower Triangular Matrices ◽  
Mean Vector ◽  
Better Than

Solliah (1964), by considering the group of lower triangular matrices, suggested an estimator of the normal covariance matrix Σ when the mean vector is known and the loss function is tr [Formula: see text] His estimator besides being minimax is better than the MLB of Σ. In this paper, we improve upon his estimator and calculate the reduction in the risk when Σ is 2×2.

Valence electron spectroscopy of inhomogeneous media

1992 ◽  
Vol 50 (2) ◽  
pp. 1150-1151
Author(s):  
A. Howie ◽  
D.W. McComb
Keyword(s):  
Specific Gravity ◽  
Loss Function ◽  
Electron Spectroscopy ◽  
Valence Electron ◽  
Peak Height ◽  
Loss Functions ◽  
Loss Peak ◽  
High Energies ◽  
Valence Electron Density ◽  
Electron Microscopist

The bulk loss function Im(-l/ε (ω)), a well established tool for the interpretation of valence loss spectra, is being progressively adapted to the wide variety of inhomogeneous samples of interest to the electron microscopist. Proportionality between n, the local valence electron density, and ε-1 (Sellmeyer's equation) has sometimes been assumed but may not be valid even in homogeneous samples. Figs. 1 and 2 show the experimentally measured bulk loss functions for three pure silicates of different specific gravity ρ - quartz (ρ = 2.66), coesite (ρ = 2.93) and a zeolite (ρ = 1.79). Clearly, despite the substantial differences in density, the shift of the prominent loss peak is very small and far less than that predicted by scaling e for quartz with Sellmeyer's equation or even the somewhat smaller shift given by the Clausius-Mossotti (CM) relation which assumes proportionality between n (or ρ in this case) and (ε - 1)/(ε + 2). Both theories overestimate the rise in the peak height for coesite and underestimate the increase at high energies.

scholarly journals Simulation and Nonlinearity Optimization of a High-Pressure Sensor

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4419
Author(s):  
Ting Li ◽  
Haiping Shang ◽  
Weibing Wang
Keyword(s):  
High Pressure ◽  
Pressure Sensor ◽  
Pressure Sensors ◽  
Original Model ◽  
Ansys Software ◽  
Nonlinear Error ◽  
Sensor Model ◽  
Optimized Model ◽  
Simulation Results ◽  
Better Than

A pressure sensor in the range of 0–120 MPa with a square diaphragm was designed and fabricated, which was isolated by the oil-filled package. The nonlinearity of the device without circuit compensation is better than 0.4%, and the accuracy is 0.43%. This sensor model was simulated by ANSYS software. Based on this model, we simulated the output voltage and nonlinearity when piezoresistors locations change. The simulation results showed that as the stress of the longitudinal resistor (RL) was increased compared to the transverse resistor (RT), the nonlinear error of the pressure sensor would first decrease to about 0 and then increase. The theoretical calculation and mathematical fitting were given to this phenomenon. Based on this discovery, a method for optimizing the nonlinearity of high-pressure sensors while ensuring the maximum sensitivity was proposed. In the simulation, the output of the optimized model had a significant improvement over the original model, and the nonlinear error significantly decreased from 0.106% to 0.0000713%.

scholarly journals Study on Radar Echo-Filling in an Occlusion Area by a Deep Learning Algorithm

2021 ◽  
Vol 13 (9) ◽  
pp. 1779
Author(s):  
Xiaoyan Yin ◽  
Zhiqun Hu ◽  
Jiafeng Zheng ◽  
Boyong Li ◽  
Yuanyuan Zuo
Keyword(s):  
Deep Learning ◽  
Loss Function ◽  
Learning Algorithm ◽  
Weather Radar ◽  
Loss Functions ◽  
Training Dataset ◽  
Echo Intensity ◽  
Common Mean ◽  
Deep Learning Algorithm ◽  
Radar Beam

Radar beam blockage is an important error source that affects the quality of weather radar data. An echo-filling network (EFnet) is proposed based on a deep learning algorithm to correct the echo intensity under the occlusion area in the Nanjing S-band new-generation weather radar (CINRAD/SA). The training dataset is constructed by the labels, which are the echo intensity at the 0.5° elevation in the unblocked area, and by the input features, which are the intensity in the cube including multiple elevations and gates corresponding to the location of bottom labels. Two loss functions are applied to compile the network: one is the common mean square error (MSE), and the other is a self-defined loss function that increases the weight of strong echoes. Considering that the radar beam broadens with distance and height, the 0.5° elevation scan is divided into six range bands every 25 km to train different models. The models are evaluated by three indicators: explained variance (EVar), mean absolute error (MAE), and correlation coefficient (CC). Two cases are demonstrated to compare the effect of the echo-filling model by different loss functions. The results suggest that EFnet can effectively correct the echo reflectivity and improve the data quality in the occlusion area, and there are better results for strong echoes when the self-defined loss function is used.

scholarly journals Injection-rolling nozzle in an imprint system with continuous injection direct rolling for ultra-thin microstructure guide light plate

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110112
Author(s):  
Yan Lou ◽  
Kewei Chen ◽  
Xiangwei Zhou ◽  
Yanfeng Feng
Keyword(s):  
Flow Velocity ◽  
Superior Performance ◽  
Light Transmittance ◽  
Velocity Difference ◽  
Orthogonal Experiments ◽  
Width Direction ◽  
Direct Rolling ◽  
Simulation Results ◽  
Continuous Injection ◽  
Better Than

A novel Injection-rolling Nozzle (IRN) in an imprint system with continuous injection direct rolling (CIDR) for ultra-thin microstructure polymer guide light plates was developed to achieve uniform flow velocity and temperature at the width direction of the cavity exit. A novel IRN cavity was designed. There are eight of feature parameters of cavity were optimized by orthogonal experiments and numerical simulation. Results show that the flow velocity at the width direction of the IRN outlet can reach uniformity, which is far better than that of traditional cavity. The smallest flow velocity difference and temperature difference was 0.6 mm/s and 0.24 K, respectively. The superior performance of the IRN was verified through a CIDR experiment. Several 0.35-mm thick, 340-mm wide, and 10-m long microstructural Polymethyl Methacrylate (PMMA) guide light plates were manufactured. The average filling rates of the microgrooves with the aspect ratio 1:3 reached above 93%. The average light transmittance is 88%.

A Densely Connected Network Based on U-Net for Medical Image Segmentation

2021 ◽  
Vol 17 (3) ◽  
pp. 1-14
Author(s):  
Zhenzhen Yang ◽  
Pengfei Xu ◽  
Yongpeng Yang ◽  
Bing-Kun Bao
Keyword(s):  
Feature Extraction ◽  
Image Segmentation ◽  
Loss Function ◽  
Network Architecture ◽  
Medical Image ◽  
Medical Image Segmentation ◽  
Cross Entropy ◽  
Loss Functions ◽  
Feature Maps ◽  
Different Levels

The U-Net has become the most popular structure in medical image segmentation in recent years. Although its performance for medical image segmentation is outstanding, a large number of experiments demonstrate that the classical U-Net network architecture seems to be insufficient when the size of segmentation targets changes and the imbalance happens between target and background in different forms of segmentation. To improve the U-Net network architecture, we develop a new architecture named densely connected U-Net (DenseUNet) network in this article. The proposed DenseUNet network adopts a dense block to improve the feature extraction capability and employs a multi-feature fuse block fusing feature maps of different levels to increase the accuracy of feature extraction. In addition, in view of the advantages of the cross entropy and the dice loss functions, a new loss function for the DenseUNet network is proposed to deal with the imbalance between target and background. Finally, we test the proposed DenseUNet network and compared it with the multi-resolutional U-Net (MultiResUNet) and the classic U-Net networks on three different datasets. The experimental results show that the DenseUNet network has significantly performances compared with the MultiResUNet and the classic U-Net networks.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

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