VARIANCE PREDICTION FOR POPULATION SIZE ESTIMATION

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.

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

Journal of Applied Mathematics ◽

10.1155/2012/584140 ◽

2012 ◽

Vol 2012 ◽

pp. 1-25 ◽

Cited By ~ 7

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.

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On Smoothed MWSD Estimation of Mixing Proportion

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v17i4.2512 ◽

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.

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ASYMPTOTIC MEAN SQUARE ERRORS OF VARIANCE ESTIMATORS FOR U-STATISTICS AND THEIR EDGEWORTH EXPANSIONS

JOURNAL OF THE JAPAN STATISTICAL SOCIETY ◽

10.14490/jjss1995.28.1 ◽

1998 ◽

Vol 28 (1) ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

Yoshihiko Maesono

Keyword(s):

Mean Square ◽

Edgeworth Expansions ◽

Variance Estimators ◽

U Statistics ◽

Mean Square Errors

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Estimation of Areal Mean Rainfall in Remote Areas Using B-SHADE Model

Advances in Meteorology ◽

10.1155/2016/7643753 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Tao Zhang ◽

Baolin Li ◽

Jinfeng Wang ◽

Maogui Hu ◽

Lili Xu

Keyword(s):

Root Mean Square ◽

Rain Gauge ◽

Unbiased Estimation ◽

The Tibetan Plateau ◽

Mean Square ◽

Traditional Methods ◽

Arithmetic Average ◽

Remote Areas ◽

Thiessen Polygon ◽

Mean Square Errors

This study presented a method to estimate areal mean rainfall (AMR) using a Biased Sentinel Hospital Based Area Disease Estimation (B-SHADE) model, together with biased rain gauge observations and Tropical Rainfall Measuring Mission (TRMM) data, for remote areas with a sparse and uneven distribution of rain gauges. Based on the B-SHADE model, the best linear unbiased estimation of AMR could be obtained. A case study was conducted for the Three-River Headwaters region in the Tibetan Plateau of China, and its performance was compared with traditional methods. The results indicated that B-SHADE obtained the least estimation biases, with a mean error and root mean square error of −0.63 and 3.48 mm, respectively. For the traditional methods including arithmetic average, Thiessen polygon, and ordinary kriging, the mean errors were 7.11, −1.43, and 2.89 mm, which were up to 1027.1%, 127.0%, and 358.3%, respectively, greater than for the B-SHADE model. The root mean square errors were 10.31, 4.02, and 6.27 mm, which were up to 196.1%, 15.5%, and 80.0%, respectively, higher than for the B-SHADE model. The proposed technique can be used to extend the AMR record to the presatellite observation period, when only the gauge data are available.

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Biserial Estimators in the Presence of Guessing

Journal of Educational Statistics ◽

10.3102/10769986004004325 ◽

1979 ◽

Vol 4 (4) ◽

pp. 325-355 ◽

Cited By ~ 4

Author(s):

Daniel Ashler

Keyword(s):

Monte Carlo ◽

Sample Size ◽

Test Item ◽

Latent Variable ◽

Mean Square ◽

Criterion Variable ◽

Item Score ◽

Chi Square ◽

Monte Carlo Studies ◽

Mean Square Errors

As estimators of correlation of a criterion variable with the continuous latent variable that underlies a dichotomous test item score, both the biserial correlation coefficient, rb, and Brogden’s coefficient of selective efficiency, S*, are severely depressed (negatively biased) by guessing, regardless of sample size or true latent correlation. Formulas and charts are given for computing better estimates, r̂ and Ŝ*, free of guessing bias, based on observed proportions of right, wrong, and omitted answers. In Monte Carlo studies both r̂ and Ŝ* had smaller mean square errors in the presence of guessing than rb and S*, and Ŝ* stayed on target even when the latent and criterion variable were given (the same) rectangular, bimodal, or chi square distribution.

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ON THE PRECISION OF THE ISOTROPIC CAVALIERI DESIGN

Image Analysis & Stereology ◽

10.5566/ias.1947 ◽

2018 ◽

Vol 37 (3) ◽

pp. 225

Author(s):

Javier González-Villa ◽

Marcos Cruz ◽

Luis M. Cruz-Orive

Keyword(s):

Monte Carlo ◽

Rat Brain ◽

Surface Area ◽

Error Variance ◽

Total Surface Area ◽

Unbiased Estimation ◽

Object Shape ◽

Constant Distance ◽

Volume Estimates

The isotropic Cavalieri design is based on a isotropically oriented set of parallel systematic sections a constant distance apart. Its advantage over the ordinary Cavalieri design is twofold - first, besides volume it allows the unbiased estimation of surface area, and second, the error variance predictor for the volume estimator is much simpler, involving only the surface area of the object, and the distance between sections. In an earlier paper, the two hemispheres of a rat brain were arranged perpendicular to each other before sectioning, aiming at reducing the error variance with respect to other arrangements (such as the aligned one) by exploiting an intuitively plausible antithetic effect. Because the total surface area of the objects is unchanged under any arrangements, however, the error variance predictor for the volume estimator does not depend on object shape, which looks intriguing. Using reconstructions of the mentioned hemispheres, we dilucidate the aparent paradox by means of automatic Monte Carlo replications of the relevant volume estimates under the antithetic and the aligned arrangements.

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Estimating the population size of people who inject drugs in Ho Chi Minh City, Vietnam: A two-survey capture-recapture exercise (Preprint)

10.2196/preprints.16459 ◽

2019 ◽

Author(s):

Abu Abdul-Quader

Keyword(s):

Population Size ◽

Illicit Drugs ◽

People Who Inject Drugs ◽

Care Service ◽

Ho Chi Minh City ◽

Size Estimation ◽

Population Size Estimates ◽

Capture Recapture ◽

The City ◽

Size Estimates

BACKGROUND Population size estimation of people who inject drugs (PWID) in Ho Chi Minh City (HCMC), Vietnam relied on the UNAIDS Estimation and Projection Package and reports from the city police department. The two estimates vary widely. OBJECTIVE To estimate the population size of people who inject drugs in Ho Chi Minh City, Vietnam METHODS Using Respondent-driven sampling (RDS), we implemented two-source capture-recapture method to estimate the population size of PWID in HCMC in 2017 in 7 out of 24 districts. The study included men or women aged at least 18 years who reported injecting illicit drugs in the last 90 days and who had lived in the city the past six months. We calculated two sets of size estimates, the first assumed that all participants in each survey round resided in the district where the survey was conducted, the second, used the district of residence as reported by the participant. District estimates were summed to obtain an aggregate estimate for the seven districts. To calculate the city total, we weighted the population size estimates for each district by the inverse of the stratum specific sampling probabilities. RESULTS The first estimate resulted in a population size of 19,155 (95% CI: 17,006–25,039). The second one generated a smaller population size estimate of 12,867 (95% CI: 11,312–17,393). CONCLUSIONS The two-survey capture-recapture exercise provided two disparate estimates of PWID in HCMC. For planning HIV prevention and care service needs among PWID in HCMC, both estimates may need to be taken into consideration together with size estimates from other sources.

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An Effective Adaptive Combination Strategy for Distributed Learning Network

Applied Sciences ◽

10.3390/app11125723 ◽

2021 ◽

Vol 11 (12) ◽

pp. 5723

Author(s):

Chundong Xu ◽

Qinglin Li ◽

Dongwen Ying

Keyword(s):

Minimum Variance ◽

Iteration Scheme ◽

Estimation Problem ◽

Lms Algorithm ◽

Unbiased Estimation ◽

Mean Square ◽

Least Mean Square ◽

Combination Strategy ◽

Adaptive Combination ◽

Diffusion Networks

In this paper, we develop a modified adaptive combination strategy for the distributed estimation problem over diffusion networks. We still consider the online adaptive combiners estimation problem from the perspective of minimum variance unbiased estimation. In contrast with the classic adaptive combination strategy which exploits orthogonal projection technology, we formulate a non-constrained mean-square deviation (MSD) cost function by introducing Lagrange multipliers. Based on the Karush–Kuhn–Tucker (KKT) conditions, we derive the fixed-point iteration scheme of adaptive combiners. Illustrative simulations validate the improved transient and steady-state performance of the diffusion least-mean-square LMS algorithm incorporated with the proposed adaptive combination strategy.

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Histamine Control in Raw and Processed Tuna: A Rapid Tool Based on NIR Spectroscopy

Foods ◽

10.3390/foods10040885 ◽

2021 ◽

Vol 10 (4) ◽

pp. 885

Author(s):

Sergio Ghidini ◽

Luca Maria Chiesa ◽

Sara Panseri ◽

Maria Olga Varrà ◽

Adriana Ianieri ◽

...

Keyword(s):

Root Mean Square ◽

Near Infrared ◽

Nir Spectroscopy ◽

Partial Least Square ◽

Least Square ◽

Partial Least Square Regression ◽

Coefficient Of Determination ◽

Mean Square ◽

Tuna Fish ◽

Mean Square Errors

The present study was designed to investigate whether near infrared (NIR) spectroscopy with minimal sample processing could be a suitable technique to rapidly measure histamine levels in raw and processed tuna fish. Calibration models based on orthogonal partial least square regression (OPLSR) were built to predict histamine in the range 10–1000 mg kg−1 using the 1000–2500 nm NIR spectra of artificially-contaminated fish. The two models were then validated using a new set of naturally contaminated samples in which histamine content was determined by conventional high-performance liquid chromatography (HPLC) analysis. As for calibration results, coefficient of determination (r2) > 0.98, root mean square of estimation (RMSEE) ≤ 5 mg kg−1 and root mean square of cross-validation (RMSECV) ≤ 6 mg kg−1 were achieved. Both models were optimal also in the validation stage, showing r2 values > 0.97, root mean square errors of prediction (RMSEP) ≤ 10 mg kg−1 and relative range error (RER) ≥ 25, with better results showed by the model for processed fish. The promising results achieved suggest NIR spectroscopy as an implemental analytical solution in fish industries and markets to effectively determine histamine amounts.

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