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 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 On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

scholarly journals Estimating Systematic Risk under Extremely Adverse Market Conditions*

2017 ◽  
Vol 17 (3) ◽  
pp. 432-461 ◽  
Author(s):  
Maarten R C van Oordt ◽  
Chen Zhou
Keyword(s):  
Mean Squared Error ◽  
Explanatory Variable ◽  
Asymptotic Properties ◽  
Estimation Method ◽  
Tail Dependence ◽  
Stock Portfolios ◽  
Squared Error ◽  
Regression Approach ◽  
Model Coefficient ◽  
Heavy Tailed

AbstractThis paper considers the problem of estimating a linear model between two heavy-tailed variables if the explanatory variable has an extremely low (or high) value. We propose an estimator for the model coefficient by exploiting the tail dependence between the two variables and prove its asymptotic properties. Simulations show that our estimation method yields a lower mean-squared error than regressions conditional on tail observations. In an empirical application, we illustrate the better performance of our approach relative to the conditional regression approach in projecting the losses of industry-specific stock portfolios in the event of a market crash.

Finite Sample Properties of Several Predictors From an Autoregressive Model

1987 ◽  
Vol 3 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Koichi Maekawa
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Asymptotic Expansions ◽  
Autoregressive Model ◽  
Mean Squared Error ◽  
The Other ◽  
Finite Sample ◽  
Squared Error ◽  
Distributional Properties ◽  
Finite Sample Properties

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O(T−1), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to O(T−1).

scholarly journals Parameter Estimation of Photovoltaic Models via Cuckoo Search

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jieming Ma ◽  
T. O. Ting ◽  
Ka Lok Man ◽  
Nan Zhang ◽  
Sheng-Uei Guan ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Cuckoo Search ◽  
High Accuracy ◽  
Flight Behavior ◽  
Squared Error ◽  
Simulation Results ◽  
Bioinspired Algorithms ◽  
Significant Attention

Since conventional methods are incapable of estimating the parameters of Photovoltaic (PV) models with high accuracy, bioinspired algorithms have attracted significant attention in the last decade. Cuckoo Search (CS) is invented based on the inspiration of brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior. In this paper, a CS-based parameter estimation method is proposed to extract the parameters of single-diode models for commercial PV generators. Simulation results and experimental data show that the CS algorithm is capable of obtaining all the parameters with extremely high accuracy, depicted by a low Root-Mean-Squared-Error (RMSE) value. The proposed method outperforms other algorithms applied in this study.

Comparison of some annual forest inventory estimators

2002 ◽  
Vol 32 (11) ◽  
pp. 1992-1995 ◽  
Author(s):  
Paul C Van Deusen
Keyword(s):  
Forest Inventory ◽  
Mean Squared Error ◽  
Moving Average ◽  
Current Status ◽  
Quadratic Growth ◽  
Growth Trends ◽  
Squared Error ◽  
Mixed Estimator ◽  
The One ◽  
Panel Design

Three estimators of current status and trend are compared for an annual interpenetrating panel design. The five-panel annual inventory design is simulated over a 10-year period with flat, increasing, and quadratic growth trends. The simulated comparisons show that the mixed estimator performs well relative to the 5-year moving average in terms of bias and mean squared error in all cases. The one-panel mean can have less bias than the moving average when there is a trend, but it is more variable. The moving average tends to lag evolving trends, which can result in very large bias.

scholarly journals On Shrinkage Estimation for R(s, k) in Case of Exponentiated Pareto Distribution

2019 ◽  
Vol 32 (1) ◽  
pp. 152 ◽  
Author(s):  
Eman Ahmed Abdulateef ◽  
Abbas Najim Salman
Keyword(s):  
Pareto Distribution ◽  
Mean Squared Error ◽  
Multicomponent System ◽  
Estimation Method ◽  
Shrinkage Estimation ◽  
Scale Parameters ◽  
Squared Error ◽  
Simulation Based ◽  
Independent Distribution ◽  
Two Parameters

   This paper concerns with deriving and estimating the reliability of the multicomponent system in stress-strength model R(s,k), when the stress and strength are identical independent distribution (iid), follows two parameters Exponentiated Pareto Distribution(EPD) with the unknown shape and known scale parameters. Shrinkage estimation method including Maximum likelihood estimator (MLE), has been considered. Comparisons among the proposed estimators were made depending on simulation based on mean squared error (MSE) criteria.

scholarly journals Pre-Test Single and Double Stage Shrunken Estimators for the Mean of Normal Distribution with Known Variance

2010 ◽  
Vol 7 (4) ◽  
pp. 1432-1441
Author(s):  
Baghdad Science Journal
Keyword(s):  
Sample Size ◽  
Normal Distribution ◽  
Relative Efficiency ◽  
Mean Squared Error ◽  
Numerical Results ◽  
Squared Error ◽  
Expected Sample Size ◽  
Test Region ◽  
Prior Estimate ◽  
The Mean

This paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.

scholarly journals Evaluation of Penman-Monteith Model Based on Sentinel-2 Data for the Estimation of Actual Evapotranspiration in Vineyards

2021 ◽  
Vol 13 (3) ◽  
pp. 478
Author(s):  
Víctor García-Gutiérrez ◽  
Claudio Stöckle ◽  
Pilar Macarena Gil ◽  
Francisco Javier Meza
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Actual Evapotranspiration ◽  
Vitis Vinifera L ◽  
Landsat 8 ◽  
Temporal Scales ◽  
Root Mean Squared Error ◽  
Squared Error ◽  
Sentinel 2

Water scarcity is one of the most important problems of agroecosystems in Mediterranean and semiarid areas, especially for species such as vineyards that largely depend on irrigation. Actual evapotranspiration (ET) is a variable that represents water consumption of a crop, integrating climate and biophysical variables. Actual evapotranspiration models based on remote sensing data from visible bands of Sentinel-2, including Penman-Monteith–Stewart (RS-PMS) and Penman-Monteith–Leuning (RS-PML), were evaluated at different temporal scales in a Cabernet Sauvignon vineyard (Vitis vinifera L.) located in central Chile, and their performance compared with independent ET measurements from an eddy covariance system (EC) and outputs from models based on thermal infrared data from Landsat 7 and Landsat 8, such as Mapping EvapoTranspiration with high Resolution and Internalized Calibration (METRIC) and Priestley–Taylor Two-Source Model (TSEB-PT). The RS-PMS model showed the best goodness of fit for all temporal scales evaluated, especially at instantaneous and daily ET, with root mean squared error (RMSE) of 28.9 Wm−2 and 0.52 mm day−1, respectively, and Willmott agreement index (d1) values of 0.77 at instantaneous scale and 0.7 at daily scale. Additionally, both approaches of RS-PM model were evaluated incorporating a soil evaporation estimation method, one considering the soil water content (fSWC) and the other hand, using the ratio of accumulated precipitation and equivalent evaporation (fZhang), achieving the best fit at instantaneous scale for RS-PMS fSWC method with relative root mean squared error (%RMSE) of 15.2% in comparison to 58.8% of fZhang. Finally, the relevance of the RS-PMS model was highlighted in the assessment and monitoring of vineyard drip irrigation in terms of crop coefficient (Kc) estimation, which is one of the methods commonly used in irrigation planning, yielding a comparable Kc to the one obtained by the EC tower with a bias around 9%.

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