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.

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 Bayesian Estimation Applied to Stochastic Localization with Constraints due to Interfaces and Boundaries

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Wolfgang Hoegele ◽  
Rainer Loeschel ◽  
Barbara Dobler ◽  
Oliver Koelbl ◽  
Piotr Zygmanski
Keyword(s):  
Bayesian Estimation ◽  
Minimum Mean Square Error ◽  
Computational Effort ◽  
Estimation Accuracy ◽  
Knowledge Map ◽  
Beam Model ◽  
Mean Square ◽  
Simulation Studies ◽  
Hard Constraints ◽  
Mean Square Errors

Purpose. We present a systematic Bayesian formulation of the stochastic localization/triangulation problem close to constraining interfaces.Methods. For this purpose, the terminology of Bayesian estimation is summarized suitably for applied researchers including the presentation of Maximum Likelihood (ML), Maximum A Posteriori (MAP), and Minimum Mean Square Error (MMSE) estimation. Explicit estimators for triangulation are presented for the linear 2D parallel beam and the nonlinear 3D cone beam model. The priors in MAP and MMSE optionally incorporate (A) the hard constraints about the interface and (B) knowledge about the probability of the object with respect to the interface. All presented estimators are compared in several simulation studies for live acquisition scenarios with 10,000 samples each.Results. First, the presented application shows that MAP and MMSE perform considerably better, leading to lower Root Mean Square Errors (RMSEs) in the simulation studies compared to the ML approach by typically introducing a bias. Second, utilizing priors including (A) and (B) is very beneficial compared to just including (A). Third, typically MMSE leads to better results than MAP, by the cost of significantly higher computational effort.Conclusion. Depending on the specific application and prior knowledge, MAP and MMSE estimators strongly increase the estimation accuracy for localization close to interfaces.

On Estimating Ratio and Product of Population Parameters

1982 ◽  
Vol 31 (1-2) ◽  
pp. 69-76 ◽  
Author(s):  
R. Karan Singh
Keyword(s):  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
Population Parameters ◽  
Class Of Estimators ◽  
Mean Square Errors

A generalized estimator representing a class of estimators for the estimation of ratio and product of population parameters has been proposed. A sub­class of optimum estimators from the proposed class has been investigated and it has been shown that every member of the sub­class has the same minimum mean square error. Further the optimum value (depending upon population parameters) when replaced from sample values gives the estimators having the minimum mean square errors of the optimum estimators.

Excitation wavelength selection for quantitative analysis of carotenoids in tomatoes using Raman spectroscopy

2018 ◽  
Vol 258 ◽  
pp. 308-313 ◽  
Author(s):  
Risa Hara ◽  
Mika Ishigaki ◽  
Yasutaka Kitahama ◽  
Yukihiro Ozaki ◽  
Takuma Genkawa
Keyword(s):  
Raman Spectroscopy ◽  
Quantitative Analysis ◽  
Excitation Wavelength ◽  
Wavelength Selection ◽  
Selection For

scholarly journals Weighted Semiparameter Model and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Zhengqing Fu ◽  
Guolin Liu ◽  
Ke Zhao ◽  
Hua Guo
Keyword(s):  
Quantitative Analysis ◽  
Qualitative Analysis ◽  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Least Square ◽  
Mean Square ◽  
Data Simulation ◽  
Main Research ◽  
True Value ◽  
Least Square Estimate

A weighted semiparameter estimate model is proposed. The parameter components and nonparameter components are weighted. The weights are determined by the characters of different data. Simulation data and real GPS data are both processed by the new model and least square estimate, ridge estimate, and semiparameter estimate. The main research method is to combine qualitative analysis and quantitative analysis. The deviation between estimated values and the true value and the estimated residuals fluctuation of different methods are used for qualitative analysis. The mean square error is used for quantitative analysis. The results of experiment show that the model has the smallest residual error and the minimum mean square error. The weighted semiparameter estimate model has effectiveness and high precision.

Robust Kalman-Type Filter for Non-Gaussian Noise: Performance Analysis With Unknown Noise Covariances

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Seyed Fakoorian ◽  
Alireza Mohammadi ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Optimality Criterion ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
Process Noise ◽  
Noise Covariance ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian ◽  
Mean Square Errors

The Kalman filter (KF) is optimal with respect to minimum mean square error (MMSE) if the process noise and measurement noise are Gaussian. However, the KF is suboptimal in the presence of non-Gaussian noise. The maximum correntropy criterion Kalman filter (MCC-KF) is a Kalman-type filter that uses the correntropy measure as its optimality criterion instead of MMSE. In this paper, we modify the correntropy gain in the MCC-KF to obtain a new filter that we call the measurement-specific correntropy filter (MSCF). The MSCF uses a matrix gain rather than a scalar gain to provide better selectivity in the way that it handles the innovation vector. We analytically compare the performance of the KF with that of the MSCF when either the measurement or process noise covariance is unknown. For each of these situations, we analyze two mean square errors (MSEs): the filter-calculated MSE (FMSE) and the true MSE (TMSE). We show that the FMSE of the KF is less than that of the MSCF. However, the TMSE of the KF is greater than that of the MSCF under certain conditions. Illustrative examples are provided to verify the analytical results.

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