Approximation of Finite Population Totals Using Lagrange Polynomial  

作　　者：Lamin Kabareh Thomas Mageto Benjamin Muema 

机构地区：[1]Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya [2]Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

出　　处：《Open Journal of Statistics》2017年第4期689-701,共13页统计学期刊（英文）

摘　　要：Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, this approximation technique is based on annual population total in order to fit in the best approximating polynomial within a given period of time (years) in this study. This proposed technique has shown to be unbiased under a linear polynomial. The use of real data indicated that the polynomial is efficient and can approximate properly even when the data is unevenly spaced.Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, this approximation technique is based on annual population total in order to fit in the best approximating polynomial within a given period of time (years) in this study. This proposed technique has shown to be unbiased under a linear polynomial. The use of real data indicated that the polynomial is efficient and can approximate properly even when the data is unevenly spaced.

关 键 词：LAGRANGE POLYNOMIAL APPROXIMATION Finite Population Total AUXILIARY Information Local POLYNOMIAL Regression Horvitz Thompson and Ratio ESTIMATOR 

分 类 号：O1[理学—数学]