A cost effective stratified two-stage sampling design to estimate the forest land area of southern Chile

2011 ◽  
Vol 41 (7) ◽  
pp. 1509-1521
Author(s):  
Mario E. Niklitschek ◽  
Guillermo Trincado
Keyword(s):  
Mean Square Error ◽  
Optimal Allocation ◽  
Native Forest ◽  
Ratio Estimator ◽  
Mean Square ◽  
Forest Plantation ◽  
Southern Chile ◽  
Unified Framework ◽  
Two Stage ◽  
Ratio Estimators

There is a growing demand for improving the measurement of forest resources, with more frequent updating and better information on environmental variables. We explore the cost efficiency of a stratified two-stage design using area sampling to estimate the forest plantation and native forest areas in southern Chile. Analytical expressions for the approximate mean square error of combined and separate ratio estimators are derived applying Taylor linearization. Under a unified framework, this procedure allows the evaluation of the precision of design and post-design estimators for unequal unit area sizes at both stages. Monte Carlo simulations were used to assess empirically the approximate analytical measures of the mean square error and the biases associated with the ratio estimators. Adopting proportional allocation among strata and clusters, the optimal allocation among the two stages is determined. A substantial improvement in sampling precision was achieved using the separate ratio estimator and the bias was found to be small. Post-stratification based on categorical information on growing zones also improved the precision of estimating the forest plantation area and a smaller extent the native forest area. The results of this paper support a wider adoption of sampling methods to estimate land use and land cover at regional or national levels.

scholarly journals On Computing Mean Square Error of Ratio Estimator

2014 ◽  
Vol 7 (9) ◽  
pp. 1896-1899
Author(s):  
Muhammad Ismail ◽  
Muhammad Qaiser Shahbaz ◽  
Saman Shahbaz ◽  
Muhammad Rashad ◽  
Muhammad Hanif
Keyword(s):  
Mean Square Error ◽  
Ratio Estimator ◽  
Mean Square

scholarly journals Ameliorated Ratio Estimator of Population Mean Using New Linear Combination

2020 ◽  
pp. 76-79
Author(s):  
T. A. Raja ◽  
S. Maqbool
Keyword(s):  
Linear Combination ◽  
Mean Square Error ◽  
Auxiliary Variable ◽  
Ratio Estimator ◽  
Mean Square ◽  
Population Mean ◽  
Main Variable ◽  
Better Than

We propose a new modified ratio estimator of population mean of the main variable using the linear combination of known values of Co-efficient of Kurtosis and Tri-Mean of the auxiliary variable. Mean Square Error (MSE) and bias of the proposed estimator is calculated and compared with the existing estimator. The comparison is demonstrated numerically which shows that the proposed estimator performs better than the existing estimators.

Estimating volumes from systematic hyperplane sections

1985 ◽  
Vol 22 (3) ◽  
pp. 518-530 ◽  
Author(s):  
Luis-M. Cruz-Orive
Keyword(s):  
Mean Square Error ◽  
Empirical Studies ◽  
Volume Ratio ◽  
Theoretical Models ◽  
Volume Estimation ◽  
Ratio Estimator ◽  
Mean Square ◽  
Drastic Increase ◽  
The Mean ◽  
Hyperplane Sections

A theory for volume estimation from independent, unbounded plane probes is available. In practice, however, probes cannot be unbounded and independent at the same time, hence the interest of systematic sectioning. Previous empirical studies on real specimens showed that the mean square error of a volume ratio estimator obtained from m systematic sections behaved roughly as m–3 for small m. This drastic increase in efficiency with respect to independent sectioning prompted us to develop some theoretical models in this paper. We study specimens consisting of two ellipsoids in Rn. In virtue of an invariance result, an ellipsoid–ellipsoid model can be studied via a simple model consisting of two concentric n-balls. Explicit results are obtained for n = 1 and n = 3. In the latter case the bias and the mean square error of the relevant volume ratio estimator are both shown to be of O (m–4).

scholarly journals Robustness Test of the Two Stage K-L Estimator in Models with Multicollinear Regressors and Autocorrelated Error Term

2021 ◽  
pp. 22-33
Author(s):  
Zubair Mohammed Anono ◽  
Adenomon Monday Osagie
Keyword(s):  
Maximum Likelihood ◽  
Mean Square Error ◽  
Linear Regression Analysis ◽  
Real Life ◽  
Multiple Linear Regression Analysis ◽  
Least Square ◽  
Mean Square ◽  
Two Stage ◽  
Data Set ◽  
Real Life Data

In a classical multiple linear regression analysis, multicollinearity and autocorrelation are two main basic assumption violation problems. When multicollinearity exists, biased estimation techniques such as Maximum Likelihood, Restricted Maximum Likelihood and most recent the K-L estimator by Kibria and Lukman [1] are preferable to Ordinary Least Square. On the other hand, when autocorrelation exist in the data, robust estimators like Cochran Orcutt and Prais-Winsten [2] estimators are preferred. To handle these two problems jointly, the study combines the K-L with the Prais-Winsten’s two-stage estimator producing the Two-Stage K-L estimator proposed by Zubair & Adenomon [3]. The Mean Square Error (MSE) and Root Mean Square Error (RMSE) criterion was used to compare the performance of the estimators. Application of the estimators to two (2) real life data set with multicollinearity and autocorrelation problems reveals that the Two Stage K-L estimator is generally the most efficient.

scholarly journals Estimation of current population mean using two-occasion successive sampling with one auxiliary variable

2018 ◽  
Vol 18 (2) ◽  
pp. 74-77
Author(s):  
R. Zoramthanga
Keyword(s):  
Mean Square Error ◽  
Auxiliary Information ◽  
Auxiliary Variable ◽  
Ratio Estimator ◽  
Mean Square ◽  
Current Estimate ◽  
Successive Sampling ◽  
Population Mean ◽  
Female Workers ◽  
Chain Type

In this study, two-occasion successive sampling for ratio-to-regression estimator was used to determine the current estimate of the population mean using only the matched part and one auxiliary variable, which is available on both the occasions. The data used were based on the total number of female workers in villages in Mizoram with the total number of literate female in villages in Mizoram as an auxiliary variables. The data were gotten from Census of India 2001 and 2011. The optimum mean square error of the combined ratio-to-regression and ratio estimator has been compared with (i) the optimum mean square error of the chain-type ratio estimator (ii) mean per unit estimator and (iii) combined estimator when no auxiliary information is used at any occasion. This result showed that the combined ratio-to-regression and ratio estimator is more efficient than the other three existing estimators.

scholarly journals Poisson Regression-Based Mean Estimator

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Usman Shahzad ◽  
Shabnam Shahzadi ◽  
Noureen Afshan ◽  
Nadia H. Al-Noor ◽  
David Anekeya Alilah ◽  
...  
Keyword(s):  
Regression Model ◽  
Mean Square Error ◽  
Random Sampling ◽  
Poisson Regression ◽  
Simple Random Sampling ◽  
Mean Square ◽  
Poisson Regression Model ◽  
The Mean ◽  
Ratio Estimators

The most frequent method for modeling count responses in numerous investigations is the Poisson regression model. Under simple random sampling, this paper offers utilizing Poisson regression-based mean estimator and discovers its associated formula of the mean square error (MSE). The MSE of the proposed estimator is compared to the MSE of traditional ratio estimators in theory. As a result of these evaluations, the proposed estimator has been proven to be more efficient than traditional estimators. Furthermore, the practical results corroborated the theoretical findings.

scholarly journals Performance analysis of two stage adaptive FIR Filter Algorithms for PLI and BW artifact cancellation in ECG

2018 ◽  
Vol 7 (1.8) ◽  
pp. 123
Author(s):  
B. Bhaskara Rao ◽  
B. Prabhakara Rao
Keyword(s):  
Mean Square Error ◽  
Adaptive Filters ◽  
Signal To Noise Ratio ◽  
Adaptive Algorithms ◽  
Mean Square ◽  
Signal To Noise ◽  
Two Stage ◽  
Baseline Wander ◽  
Power Line Interference ◽  
Line Interference

Electrocardiogram (ECG) is a measure of the electrical movement of the heart, and is obtained by surface electrodes at standardized locations on the patient’s chest. During acquisition, various artifacts/noises such as power-line interference (PLI), baseline wander (BW), muscle artifacts (MA) and motion artifacts (EM) obscure the ECG. It is important that these artifacts are minimized for the clinicians to make better diagnosis on heart problems. This paper researches the creative idea of adaptive noise cancellation (ANC) using two stage form of adaptive filters. The concept of cascading and its algorithm for real-time application is simulated on MATLAB. The proposed algorithm utilizes two adaptive filters to estimate gradients accurately which results in good adaptation and performance. The objective of the present investigation is to provide solution in order to improve the performance of noise canceller in terms of filter parameters which are obtained with the help of adaptive algorithms. Different kinds of two stage ANC algorithms are used to eliminate artifacts in ECG by considering the noises such as power line interference and baseline wander. The simulation results show that the performance of the two stage ANC is superior to the conventional single stage ANC system in terms of higher signal-to-noise ratio. Two stage adaptive algorithms are applied on real time ECG signals and compared their performance with the conventional single stage adaptive algorithms in terms of parameters Signal-to-Noise Ratio (SNR), Mean Square Error (MSE), Root Mean Square Error (RMSE) and Distortion.

scholarly journals Modified Ratio Estimators of Population Mean Based on Ranked Set Sampling

2019 ◽  
pp. 445-449 ◽  
Author(s):  
Zahid Khan ◽  
Muhammad Ismail
Keyword(s):  
Mean Square Error ◽  
Coefficient Of Variation ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Variation Coefficient ◽  
Mean Square ◽  
Population Mean ◽  
The Mean ◽  
Ratio Estimators ◽  
Coefficient Of Skewness

In this paper, we propose modified ratio estimators using some known values of coefficient of variation, coefficient of skewness and coefficient of kurtosis of auxiliary variable under ranked set sampling (RSS).  The mean square error (MSE) of the proposed ratio estimators under ranked set sampling is derived and compared with some existing ratio estimators under RSS. Through this comparison, we prove theoretically that MSC of proposed estimators is less than some existing ratio estimators in RSS under some conditions. The MSE of proposed estimators along with some existing estimator are also calculated numerically. We observe from numerical results that the suggested ratio estimators are more efficient than some existing ratio estimators under RSS.

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