scholarly journals Asymptotically Unbiased Estimator of the Informational Energy with kNN

2013 ◽  
Vol 8 (5) ◽  
pp. 689 ◽  
Author(s):  
Angel Caţaron ◽  
Răzvan Andonie ◽  
Yvonne Chueh
Keyword(s):  
Unbiased Estimator ◽  
Informational Energy ◽  
Asymptotically Unbiased Estimator

scholarly journals Estimation of Population Prevalence of COVID-19 Using Imperfect Tests

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1900
Author(s):  
Leonid Hanin
Keyword(s):  
Statistical Analysis ◽  
Upper Bound ◽  
Unbiased Estimator ◽  
Probability Distributions ◽  
Heterogeneous Population ◽  
Prevalence Studies ◽  
Population Prevalence ◽  
Statistical Assumptions ◽  
Testing Data ◽  
Asymptotically Unbiased Estimator

I formulate three basic biomedical/statistical assumptions that should ideally guide well-designed population prevalence studies of the present or past disease including COVID-19. On the basis of these assumptions alone, I compute several probability distributions required for statistical analysis of testing data collected from a sample of individuals drawn from a heterogeneous population. I also construct a consistent asymptotically unbiased estimator of the population prevalence of the disease or infection from the collected data and derive a simple upper bound for its variance. All the results are rigorously proved and valid for any test for COVID-19 or other disease provided that the sum of the test’s sensitivity and specificity is larger than 1. A few recommendations for the design of COVID-19 prevalence studies informed by the results of this work are formulated. The methodology developed in this article may prove applicable to diseases and conditions other than COVID-19 as well as in some non-epidemiological settings.

scholarly journals A new proof of geometric convergence for the adaptive generalized weighted analog sampling (GWAS) method

2016 ◽  
Vol 22 (3) ◽  
Author(s):  
Rong Kong ◽  
Jerome Spanier
Keyword(s):  
General Theory ◽  
Importance Sampling ◽  
Unbiased Estimator ◽  
Reducing Power ◽  
Radiative Transport ◽  
Unbiased Estimators ◽  
Geometric Convergence ◽  
Correlated Sampling ◽  
Asymptotically Unbiased Estimator ◽  
Transport Problems

AbstractGeneralized Weighted Analog Sampling is a variance-reducing method for solving radiative transport problems that makes use of a biased (though asymptotically unbiased) estimator. The introduction of bias provides a mechanism for combining the best features of unbiased estimators while avoiding their limitations. In this paper we present a new proof that adaptive GWAS estimation based on combining the variance-reducing power of importance sampling with the sampling simplicity of correlated sampling yields geometrically convergent estimates of radiative transport solutions. The new proof establishes a stronger and more general theory of geometric convergence for GWAS.

Estimation of the criticality parameter of a superitical branching process with random environments

1979 ◽  
Vol 16 (04) ◽  
pp. 890-896 ◽  
Author(s):  
K. Nanthi
Keyword(s):  
Unbiased Estimator ◽  
Branching Process ◽  
Consistent Estimator ◽  
Random Environments ◽  
Asymptotically Normal ◽  
Asymptotically Unbiased Estimator ◽  
Image Position ◽  
Strongly Consistent

For a supercritical branching process x = {xn ; n ≧ 0, x 0 = 1} with random environments, define when xn > 0; and = 1 when xn = 0. When x is assumed to satisfy the standard regularity assumptions, under the non-extinction hypothesis, is a strongly consistent and asymptotically unbiased estimator for the criticality parameter π and is asymptotically normal. A strongly consistent estimator, is also proposed for the associated variance, σ 2.

Estimation of the criticality parameter of a superitical branching process with random environments

1979 ◽  
Vol 16 (4) ◽  
pp. 890-896 ◽  
Author(s):  
K. Nanthi
Keyword(s):  
Unbiased Estimator ◽  
Branching Process ◽  
Consistent Estimator ◽  
Random Environments ◽  
Asymptotically Normal ◽  
Asymptotically Unbiased Estimator ◽  
Image Position ◽  
Strongly Consistent

For a supercritical branching process x = {xn; n ≧ 0, x0 = 1} with random environments, define when xn > 0; and = 1 when xn = 0. When x is assumed to satisfy the standard regularity assumptions, under the non-extinction hypothesis, is a strongly consistent and asymptotically unbiased estimator for the criticality parameter π and is asymptotically normal. A strongly consistent estimator, is also proposed for the associated variance, σ2.

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

Kernel-kNN: A New kNN Algorithm Based on Informational Energy Metric

2011 ◽  
Vol 36 (12) ◽  
pp. 1681-1688 ◽  
Author(s):  
Song-Hua LIU ◽  
Jun-Ying ZHANG ◽  
Jin XU ◽  
Hong-En JIA
Keyword(s):  
Informational Energy
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