scholarly journals PENERAPAN METODE PENDUGAAN AREA KECIL (SMALL AREA ESTIMATION) PADA PENENTUAN PROPORSI RUMAH TANGGA MISKIN DI KABUPATEN KLUNGKUNG

2013 ◽  
Vol 2 (3) ◽  
pp. 35 ◽  
Author(s):  
PUTU EKA ARIWIJAYANTHI ◽  
I WAYAN SUMARJAYA ◽  
TJOKORDA BAGUS OKA
Keyword(s):  
Small Area ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Parameter Estimates ◽  
Bayes Methods ◽  
Mean Squared Errors ◽  
Direct Estimation ◽  
Squared Error ◽  
Empirical Bayes Methods

Small area is an area with insufficient sample for direct estimation. Limited survey objects, cause direct estimation can not produce better parameter estimates. Based on this, an indirect estimation method called empirical Bayes is used to obtain a better estimate. This study will compare means squared error by  direct estimation method and empirical Bayes method to find a better method on a small area. Jackknife is used to get the means squared error in the empirical Bayes. The results is, empirical Bayes methods give a better parameters based on mean squared errors. Empirical Bayes can produce a smaller mean squared error more than direct estimation in small area.

scholarly journals SMALL AREA ESTIMATION METHOD WITH EMPIRICAL BAYES BASED ON BETA BINOMIAL MODEL IN GENERATED DATA

2020 ◽  
Vol 14 (1) ◽  
pp. 1-9
Author(s):  
Ferra Yanuar ◽  
Rahmatika Fajriyah ◽  
Dodi Devianto
Keyword(s):  
Binary Data ◽  
Small Area ◽  
Empirical Bayes ◽  
Small Area Estimation ◽  
Estimation Method ◽  
Estimation Methods ◽  
Auxiliary Variables ◽  
Indirect Estimation ◽  
Area Estimation ◽  
Direct Estimation

Small Area Estimation is one of the methods that can be used to estimate parameters in an area that has a small population. This study aims to estimate the value of the binary data parameter using the direct estimation method and an indirect estimation method by using the Empirical Bayes approach. To illustrate the method, we consider three conditions: direct estimator, empirical Bayes (EB) with auxiliary variables, and empirical Bayes without auxiliary variables. The smaller value of Mean Square Error is used to determine the better method. The results showed that the indirect estimation methods (EB method) gave the parameter value that was not much different from the direct estimation value. Then, the MSE values of indirect estimation with an auxiliary variable are smaller than the direct estimation method.

Constrained empirical Bayes estimates for cell values in a two-way table

1992 ◽  
Vol 22 (12) ◽  
pp. 1983-1987
Author(s):  
Edwin J. Green ◽  
Michael Kohl ◽  
William E. Strawderman
Keyword(s):  
Sample Size ◽  
Forest Inventory ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Individual Cell ◽  
Estimation Method ◽  
Simultaneous Estimation ◽  
Bayes Estimates ◽  
Squared Error ◽  
Large Standard Error

It is common to summarize the results of a forest inventory in two-way tables. Unfortunately, while the overall sample size may be large, the sample size for an individual cell in the table may be quite small. Thus the estimate may have a large standard error. We propose a simultaneous estimation method to reduce the variance and (or) mean squared error of individual cell estimates while retaining table additivity, i.e., preserving the observed row and column sums of the table.

scholarly journals Robust empirical Bayes small area estimation with density power divergence

Biometrika ◽  
2020 ◽  
Vol 107 (2) ◽  
pp. 467-480 ◽  
Author(s):  
S Sugasawa
Keyword(s):  
Small Area ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Bayes Estimator ◽  
Model Parameters ◽  
Density Power Divergence ◽  
Simple Modification ◽  
Squared Error ◽  
Power Divergence ◽  
Empirical Bayes Estimator

Summary A two-stage normal hierarchical model called the Fay–Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.

scholarly journals Comparison of different lactation curve models in Holstein cows raised on a farm in the south-eastern Anatolia region

2008 ◽  
Vol 51 (4) ◽  
pp. 329-337
Author(s):  
Ö. Koçak ◽  
B. Ekiz
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Exponential Model ◽  
Eastern Anatolia ◽  
Mean Squared Errors ◽  
Squared Error ◽  
Lactation Curve ◽  
Daily Milk Yield ◽  
Daily Milk

Abstract. The objective of this study was to compare the goodness of fit of seven mathematical models (including the gamma function, the exponential model, the mixed log model, the inverse quadratic polynomial model and their various modifications) on daily milk yield records. The criteria used to compare models were mean R2, root mean squared errors (RMSE) and difference between actual and predicted lactation milk yields. The effect of lactation number on curve parameters was significant for models with three parameters. Third lactation cows had the highest intercept post-calving, greatest incline between calving and peak milk yield and greatest decline between peak milk yield and end of lactation. Latest peak production occurred in first lactation for all models, while third lactation cows had the earliest day of peak production. The R2 values ranged between 0.590 and 0.650 for first lactation, between 0.703 and 0.773 for second lactation and between 0.686 and 0.824 for third lactation, depending on the model fitted. The root mean squared error values of different models varied between 1.748 kg and 2.556 kg for first parity cows, between 2.133 kg and 3.284 kg for second parity cows and between 2.342 kg and 7.898 kg for third parity cows. Lactation milk yield deviations of Ali and Schaeffer, Wilmink and Guo and Swalve Models were close to zero for all lactations. Ali and Schaeffer Model had the highest R2 for all lactations and also yielded smallest RMSE and actual and predicted lactation milk yield differences. Wilmink and Guo and Swalve Models gave better fit than other three parameter models.

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