scholarly journals On Smoothed MWSD Estimation of Mixing Proportion

2021 ◽  
pp. 971-982
Author(s):  
Satish Konda ◽  
Mehra, K.L. ◽  
Ramakrishnaiah Y.S.
Keyword(s):  
Monte Carlo ◽  
Asymptotic Normality ◽  
Minimum Mean Square Error ◽  
Monte Carlo Study ◽  
Mean Square ◽  
Random Samples ◽  
Two Component ◽  
Mixing Proportion ◽  
Mean Square Error Criterion ◽  
Mean Square Errors

The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.

scholarly journals VARIANCE PREDICTION FOR POPULATION SIZE ESTIMATION

2019 ◽  
Vol 38 (2) ◽  
pp. 131 ◽  
Author(s):  
Ana Isabel Gomez ◽  
Marcos Cruz ◽  
Luis Manuel Cruz-Orive
Keyword(s):  
Monte Carlo ◽  
Population Size ◽  
Error Variance ◽  
Unbiased Estimation ◽  
Mean Square ◽  
Size Estimation ◽  
Automatic Computer ◽  
Variance Estimators ◽  
Efficient Alternative ◽  
Mean Square Errors

Design unbiased estimation of population size by stereological methods is an efficient alternative to automatic computer vision methods, which are generally biased. Moreover, stereological methods offer the possibility of predicting the error variance from a single sample. Here we explore the statistical performance of two alternative variance estimators on a dataset of 26 labelled crowd pictures. The empirical mean square errors of the variance predictors are compared by means of Monte Carlo resampling.

scholarly journals Convergence Analysis for the SMC-MeMBer and SMC-CBMeMBer Filters

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Feng Lian ◽  
Chen Li ◽  
Chongzhao Han ◽  
Hui Chen
Keyword(s):  
Monte Carlo ◽  
Convergence Analysis ◽  
Sequential Monte Carlo ◽  
Mean Square ◽  
Convergence Results ◽  
Mean Square Convergence ◽  
The Mean ◽  
Mean Square Errors

The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi-Bernoulli (MeMBer) filter and cardinality-balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC-MeMBer and SMC-CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean-square sense and the corresponding bounds for the mean-square errors are given. The significance of this paper is in theory to present the convergence results of the SMC-MeMBer and SMC-CBMeMBer filters and the conditions under which the two filters satisfy mean-square convergence.

Two-Component Catalysts for Low-Temperature CO Oxidation: A Monte Carlo Study

1993 ◽  
Vol 141 (1) ◽  
pp. 219-238 ◽  
Author(s):  
R.K. Herz ◽  
A. Badlani ◽  
D.R. Schryer ◽  
B.T. Upchurch
Keyword(s):  
Monte Carlo ◽  
Low Temperature ◽  
Co Oxidation ◽  
Monte Carlo Study ◽  
Two Component ◽  
Low Temperature Co Oxidation

scholarly journals Monte Carlo Study of a Liquid-Liquid Phase Transition Using a Modified Gibbs Ensemble

2020 ◽  
Author(s):  
Douglas Barlow
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Monte Carlo Study ◽  
Low Energy ◽  
Gibbs Ensemble ◽  
Two Component System ◽  
Liquid Phase Transition ◽  
Solution Type ◽  
Two Component ◽  
Simulation Results

<div>The carbon disulfide-methanol liquid-liquid critical point is studied using a Monte</div><div>Carlo simulation of classical Stockmayer particles. A low energy configuration for the segregated</div><div>two component system is determined using standard Monte Carlo methods then a modified</div><div>Gibbs ensemble is employed to study the effect of transferring particles from one phase to</div><div>another. Rather than use the model for the entropy of mixing in the Gibbs ensemble, which is</div><div>of the regular solution type, a semi-quasi-chemical model is used which involves an interaction</div><div>energy. We are able to simulate the mixing of the two components as the temperature approaches</div><div>the critical temperature from below. Further, a method is given whereby the simulation results</div><div>can be used to predict the critical temperature.</div>

scholarly journals Monte Carlo Study of a Liquid-Liquid Phase Transition Using a Modified Gibbs Ensemble

2020 ◽  
Author(s):  
Douglas Barlow
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Monte Carlo Study ◽  
Low Energy ◽  
Gibbs Ensemble ◽  
Two Component System ◽  
Liquid Phase Transition ◽  
Solution Type ◽  
Two Component ◽  
Simulation Results

<div>The carbon disulfide-methanol liquid-liquid critical point is studied using a Monte</div><div>Carlo simulation of classical Stockmayer particles. A low energy configuration for the segregated</div><div>two component system is determined using standard Monte Carlo methods then a modified</div><div>Gibbs ensemble is employed to study the effect of transferring particles from one phase to</div><div>another. Rather than use the model for the entropy of mixing in the Gibbs ensemble, which is</div><div>of the regular solution type, a semi-quasi-chemical model is used which involves an interaction</div><div>energy. We are able to simulate the mixing of the two components as the temperature approaches</div><div>the critical temperature from below. Further, a method is given whereby the simulation results</div><div>can be used to predict the critical temperature.</div>

Optimal Wavelength Selection for Quantitative Analysis

1986 ◽  
Vol 40 (2) ◽  
pp. 185-190 ◽  
Author(s):  
K. Sasaki ◽  
S. Kawata ◽  
S. Minami
Keyword(s):  
Quantitative Analysis ◽  
Minimum Mean Square Error ◽  
Mathematical Formulation ◽  
Computation Time ◽  
Mean Square ◽  
Wavelength Selection ◽  
Selection For ◽  
Mixture Samples ◽  
Mean Square Errors ◽  
Optimal Set

A new computer algorithm has been developed for selecting the optimal set of wavelengths for spectroscopic quantitative analysis of mixture samples. The method is based on the criterion of the minimum mean square error between concentrations of the mixture components and their estimates. The branch and bound algorithm finds the optimal set from all possible combinations of wavelengths. This algorithm saves computation time significantly, compared with the enumerative method. The mathematical formulation of the lower bound of the mean square errors for the combinations in a given subset is derived as a recurrence inequality. Experimental results of wavelength selection for infrared absorption spectra of xylene-isomer mixtures are shown to demonstrate the effectiveness of the algorithm in terms of computation complexity and accuracy in quantitative analysis for the fixed measurement time.

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