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Regression analysis and ratio analysis for domains: A randomization‐theory approach
Author(s) -
Elvers Eva,
SÄRNDAL Carl Erik,
Wretman Jan H.,
ÖRNBERG Göran
Publication year - 1985
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315149
Subject(s) - statistics , regression analysis , inference , monte carlo method , statistical inference , sample size determination , econometrics , regression , mathematics , sampling (signal processing) , computer science , population , artificial intelligence , demography , filter (signal processing) , sociology , computer vision
In most surveys, inference for domains poses a difficult problem because of data shortage. This paper presents a probability sampling theory approach to some common types of statistical analysis for domains of a surveyed population. Simple and multiple regression analysis, and analysis of ratios are considered. Two new methods are constructed and explored which can improve substantially over the common method based on sample‐weighted sums of squares and products. These new methods use auxiliary variables whose importance depends on the extent to which they succeed in explaining certain patterns in the regression residuals. The theoretical conclusions are supported by empirical results from Monte Carlo experiments.