Conditions for approximation of the bias and mean squared error of a sample mean under nonresponse

1992 ◽  
Vol 15 (4) ◽  
pp. 267-276
Author(s):  
John L. Eltinge
Keyword(s):  
Mean Squared Error ◽  
Sample Mean ◽  
Squared Error

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals A General Class of Dual to Ratio Estimator

2020 ◽  
pp. 421-431
Author(s):  
Housila Prasad Singh ◽  
Pragati Nigam
Keyword(s):  
General Class ◽  
Mean Squared Error ◽  
Auxiliary Information ◽  
Ratio Estimator ◽  
Sample Surveys ◽  
Sample Mean ◽  
Population Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
Ratio Estimators

In this paper we have considered the problem of estimating the population mean using auxiliary information in sample surveys. A class of dual to ratio estimators has been defined. Exact expressions for bias and mean squared error of the suggested class of dual to ratio estimator have been obtained. In particular, properties of some members of the proposed class of dual to ratio estimators have been discussed. It has been shown that the proposed class of estimators is more efficient than the sample mean, ratio estimator, dual to ratio estimator and some members of the suggested class of estimators in some realistic conditions. Some numerical illustrations are given in support of the present study.

scholarly journals Using LASSO to Assist Imputation and Predict Child Well-being

2019 ◽  
Vol 5 ◽  
pp. 237802311881462 ◽  
Author(s):  
Diana Stanescu ◽  
Erik Wang ◽  
Soichiro Yamauchi
Keyword(s):  
Predictive Power ◽  
Mean Squared Error ◽  
Well Being ◽  
Fragile Families ◽  
Material Hardship ◽  
Sample Mean ◽  
Squared Error ◽  
Out Of Sample ◽  
Using Data ◽  
Selection Operator

This article documents an approach to predicting children’s well-being using data from the Fragile Families and Child Wellbeing Study, which are representative of births in large U.S. cities. The authors use the least absolute shrinkage and selection operator (LASSO) to preprocess the data. They then apply the Amelia algorithm to impute missing data. Finally, they use LASSO again for prediction with the imputed data. The authors report the performance of this approach for six outcome variables. The approach achieves the best performance for the variable material hardship. The out-of-sample mean squared error of the authors’ prediction is 0.019, the lowest among all submissions in the Fragile Families Challenge. The authors find that among variables with high predictive power, variables from mother surveys dominate. Furthermore, components of material hardship in the past strongly predict current material hardship.

scholarly journals A Two-Parameter Ratio-Product-Ratio Estimator Using Auxiliary Information

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Peter S. Chami ◽  
Bernd Sing ◽  
Doneal Thomas
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Information ◽  
Degree Of Approximation ◽  
Simple Random Sample ◽  
Ratio Estimator ◽  
Sample Mean ◽  
Product Ratio ◽  
Squared Error ◽  
Parameter Ratio ◽  
Two Parameter

We propose a two-parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in the studies of Ray and Sahai (1980), Sahai and Ray (1980), A. Sahai and A. Sahai (1985), and Singh and Espejo (2003).The bias and mean squared error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean squared error than the sample mean, ratio, and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using groundwater data taken from a geological site in the state of Florida.

A Comparison of Parent-Offspring Correlation Estimators in Terms of Large- Sample Mean Squared Error and Bias

Biometrics ◽  
1987 ◽  
Vol 43 (1) ◽  
pp. 37 ◽  
Author(s):  
M. E. O'Neill ◽  
L. H. Prasetyo ◽  
A. C. Kirby ◽  
F. W. Nicholas
Keyword(s):  
Mean Squared Error ◽  
Sample Mean ◽  
Large Sample ◽  
Squared Error

Independent sample mean squared error for adaptive detection statistics

2005 ◽  
Author(s):  
W.C. Ogle ◽  
H.E. Witzgall ◽  
M.A. Tinston ◽  
J.S. Goldstein ◽  
P.A. Zulch
Keyword(s):  
Mean Squared Error ◽  
Adaptive Detection ◽  
Sample Mean ◽  
Squared Error

scholarly journals An Improved Family of Estimators of Finite Population Mean Using Information on an Auxiliary Variable in Sample Surveys

2017 ◽  
Vol 13 (2) ◽  
pp. 77-108
Author(s):  
H. P. Singh ◽  
A. Yadav
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Information ◽  
Auxiliary Variable ◽  
Sample Surveys ◽  
Sample Mean ◽  
Population Mean ◽  
Squared Error ◽  
Parameter Ratio ◽  
Large Sample Approximation ◽  
Class Of Estimators

Abstract In this paper we have suggested a family of estimators of the population mean using auxiliary information in sample surveys. The bias and mean squared error of the proposed class of estimators have been obtained under large sample approximation. We have derived the conditions for the parameters under which the proposed class of estimators has smaller mean squared error than the sample mean, ratio, product, regression estimator and the two parameter ratio-product-ratio estimators envisaged by Chami et al (2012). An empirical study is carried out to demonstrate the performance of the proposed class of estimators over other existing estimators.

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

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