scholarly journals An Estimator of Heavy Tail Index through the Generalized Jackknife Methodology

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Weiqi Liu ◽  
Hongwei Xing
Keyword(s):  
Mean Squared Error ◽  
Heavy Tail ◽  
Tail Index ◽  
Hill’S Estimator ◽  
Asymptotically Normal ◽  
Finite Samples ◽  
Minimum Mean Squared Error ◽  
Sample Paths ◽  
Wide Range ◽  
Class Of Estimators

In practice, sometimes the data can be divided into several blocks but only a few of the largest observations within each block are available to estimate the heavy tail index. To address this problem, we propose a new class of estimators through the Generalized Jackknife methodology based on Qi’s estimator (2010). These estimators are proved to be asymptotically normal under suitable conditions. Compared to Hill’s estimator and Qi’s estimator, our new estimator has better asymptotic efficiency in terms of the minimum mean squared error, for a wide range of the second order shape parameters. For the finite samples, our new estimator still compares favorably to Hill’s estimator and Qi’s estimator, providing stable sample paths as a function of the number of dividing the sample into blocks, smaller estimation bias, and MSE.

scholarly journals Best integer equivariant estimation for elliptically contoured distributions

2020 ◽  
Vol 94 (9) ◽  
Author(s):  
P. J. G. Teunissen
Keyword(s):  
Normal Distribution ◽  
Mean Squared Error ◽  
Multivariate Normal ◽  
Elliptically Contoured Distributions ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Wide Range ◽  
Equivariant Estimation ◽  
Elliptically Contoured ◽  
Carrier Phase Ambiguity

Abstract This contribution extends the theory of integer equivariant estimation (Teunissen in J Geodesy 77:402–410, 2003) by developing the principle of best integer equivariant (BIE) estimation for the class of elliptically contoured distributions. The presented theory provides new minimum mean squared error solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Next to the BIE estimator for the multivariate normal distribution, special attention is given to the BIE estimators for the contaminated normal and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution.

scholarly journals Efficient Method of Estimating the Finite Population Mean Based on Two Auxiliary Variables in the Presence of Non-Response Under Stratified Sampling

2021 ◽  
Author(s):  
Housila P. Singh ◽  
Pragati Nigam
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Variables ◽  
Optimum Conditions ◽  
Study Variable ◽  
Numerical Illustration ◽  
Population Mean ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Class Of Estimators ◽  
Better Than

This article addresses the problem of estimating the population mean using information on two auxiliary variables in presence of non-response on study variable only under stratified random sampling. A class of estimators has been defined. We have derived the bias and mean squared error up to first order of approximation. Optimum conditions are obtained in which the suggested class of estimators has minimum mean squared error. In addition to Chaudhury et al. (2009) estimator, many estimators can be identified as a member of the suggested class of estimators. It has been shown that the suggested class of estimators is better than the Chaudhury et al. (2009) estimator and other estimators. Results of the present study are supported through numerical illustration.

scholarly journals Some Improved Estimators in Double Sampling Using two Auxiliary Variables

2015 ◽  
Vol 19 (2) ◽  
pp. 97
Author(s):  
Mohammad S. Ahmed
Keyword(s):  
Mean Squared Error ◽  
Double Sampling ◽  
Auxiliary Variables ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Series Expression ◽  
Optimum Estimator ◽  
Class Of Estimators ◽  
Improved Estimators ◽  
Taylor’S Series

Dash and Mishra [1] suggested an improved class of estimators without defining the optimum estimator. However, they gave the wrong Taylor’s series expression of their class of estimator and their minimum mean squared error expressions are also incorrect. Here we show that Ahmed et al.’s [2] class of chain estimators is more efficient than Dash and Mishra’s [1], with minimum mean squared error.  

Multi-AUV Aided Cooperative 3D-localization for Underwater Sensor Networks

2020 ◽  
Vol 13 (1) ◽  
pp. 80-90 ◽  
Author(s):  
Meiyan Zhang ◽  
Wenyu Cai
Keyword(s):  
Sensor Networks ◽  
Mean Squared Error ◽  
Autonomous Underwater Vehicles ◽  
Estimation Method ◽  
Location Estimation ◽  
Underwater Sensor Networks ◽  
Coverage Ratio ◽  
Minimum Mean Squared Error ◽  
3D Localization ◽  
Localization Scheme

Background: Effective 3D-localization in mobile underwater sensor networks is still an active research topic. Due to the sparse characteristic of underwater sensor networks, AUVs (Autonomous Underwater Vehicles) with precise positioning abilities will benefit cooperative localization. It has important significance to study accurate localization methods. Methods: In this paper, a cooperative and distributed 3D-localization algorithm for sparse underwater sensor networks is proposed. The proposed algorithm combines with the advantages of both recursive location estimation of reference nodes and the outstanding self-positioning ability of mobile AUV. Moreover, our design utilizes MMSE (Minimum Mean Squared Error) based recursive location estimation method in 2D horizontal plane projected from 3D region and then revises positions of un-localized sensor nodes through multiple measurements of Time of Arrival (ToA) with mobile AUVs. Results: Simulation results verify that the proposed cooperative 3D-localization scheme can improve performance in terms of localization coverage ratio, average localization error and localization confidence level. Conclusion: The research can improve localization accuracy and coverage ratio for whole underwater sensor networks.

scholarly journals A New Class of Estimators Based on a General Relative Loss Function

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1138
Author(s):  
Tao Hu ◽  
Baosheng Liang
Keyword(s):  
Loss Function ◽  
Asymptotically Normal ◽  
New Class ◽  
Statistical Inferences ◽  
Relative Loss ◽  
Special Cases ◽  
Class Of Estimators ◽  
Box Cox Transformation ◽  
Loss Estimator ◽  
Prostate Cancer Study

Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making statistical inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided.

scholarly journals Complete subset averaging with many instruments

2020 ◽  
Author(s):  
Seojeong Lee ◽  
Youngki Shin
Keyword(s):  
Demand Function ◽  
Simulation Experiment ◽  
Mean Squared Error ◽  
Asymptotic Optimality ◽  
Weighted Average ◽  
Subset Size ◽  
Extensive Simulation ◽  
Squared Error ◽  
Many Instruments ◽  
Class Of Estimators

Summary We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalise the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry et al. (1995) and find that the CSA-2SLS estimate is better supported by economic theory than are the alternative estimates.

scholarly journals Coupling between the JULES land-surface scheme and the CCATT-BRAMS atmospheric chemistry model (JULES-CCATT-BRAMS1.0): applications to numerical weather forecasting and the CO<sub>2</sub> budget in South America

2013 ◽  
Vol 6 (1) ◽  
pp. 453-494 ◽  
Author(s):  
D. S. Moreira ◽  
S. R. Freitas ◽  
J. P. Bonatti ◽  
L. M. Mercado ◽  
N. M. É. Rosário ◽  
...  
Keyword(s):  
South America ◽  
Atmospheric Chemistry ◽  
Land Surface ◽  
Amazon Basin ◽  
Mean Squared Error ◽  
Weather Forecasting ◽  
Dew Point ◽  
Surface Model ◽  
Co2 Concentrations ◽  
Wide Range

Abstract. This article presents the development of a new numerical system denominated JULES-CCATT-BRAMS, which resulted from the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. The performance of this system in relation to several meteorological variables (wind speed at 10 m, air temperature at 2 m, dew point temperature at 2 m, pressure reduced to mean sea level and 6 h accumulated precipitation) and the CO2 concentration above an extensive area of South America is also presented, focusing on the Amazon basin. The evaluations were conducted for two periods, the wet (March) and dry (September) seasons of 2010. The statistics used to perform the evaluation included bias (BIAS) and root mean squared error (RMSE). The errors were calculated in relation to observations at conventional stations in airports and automatic stations. In addition, CO2 concentrations in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with aircraft data. The results of this study show that the JULES model coupled to CCATT-BRAMS provided a significant gain in performance in the evaluated atmospheric fields relative to those simulated by the LEAF (version 3) surface model originally utilized by CCATT-BRAMS. Simulations of CO2 concentrations in Amazonia and a comparison with observations are also discussed and show that the system presents a gain in performance relative to previous studies. Finally, we discuss a wide range of numerical studies integrating coupled atmospheric, land surface and chemistry processes that could be produced with the system described here. Therefore, this work presents to the scientific community a free tool, with good performance in relation to the observed data and re-analyses, able to produce atmospheric simulations/forecasts at different resolutions, for any period of time and in any region of the globe.

scholarly journals Attack-resilient minimum mean-squared error estimation

2014 ◽  
Author(s):  
James Weimer ◽  
Nicola Bezzo ◽  
Miroslav Pajic ◽  
Oleg Sokolsky ◽  
Insup Lee
Keyword(s):  
Error Estimation ◽  
Mean Squared Error ◽  
Minimum Mean Squared Error ◽  
Squared Error

scholarly journals Threshold selection in univariate extreme value analysis

Extremes ◽  
2021 ◽  
Author(s):  
Laura Fee Schneider ◽  
Andrea Krajina ◽  
Tatyana Krivobokova
Keyword(s):  
Mean Squared Error ◽  
Extreme Value ◽  
Hill Estimator ◽  
Small Samples ◽  
Extreme Value Analysis ◽  
Threshold Selection ◽  
Value Analysis ◽  
Wide Range ◽  
Asymptotic Mean Squared Error ◽  
The Hill

AbstractThreshold selection plays a key role in various aspects of statistical inference of rare events. In this work, two new threshold selection methods are introduced. The first approach measures the fit of the exponential approximation above a threshold and achieves good performance in small samples. The second method smoothly estimates the asymptotic mean squared error of the Hill estimator and performs consistently well over a wide range of processes. Both methods are analyzed theoretically, compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time.

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