ESTIMATION OF FINITE POPULATION TOTAL USING ROBUST GEOGRAPHICALLY WEIGHTED REGRESSION APPROACH
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Date
2020
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Indian Agricultural Statistics Research Institute Indian Agricultural Research Institute, New Delhi
Abstract
In many surveys (e.g. agriculture, forestry, environmental, ecological surveys etc.), observations are
often spatially correlated, thus, the relationship between dependent and independent variables varies
across the locations in the study area. The commonly used survey estimation methods ignore spatial
non-stationarity present in the population data. The sample survey data often contains outliers which
lead to an increase in bias and variance of estimator of finite population total. In view of the abovementioned problem of estimation, outlier robust estimators of finite population total have been
proposed in this study which are based on Geographically Weighted Regression (GWR) model to
capture the spatial non-stationarity present in the survey data. This method is also robust against the
presence of outliers in survey data. The proposed Outlier Robust Geographically Weighted Regression
(ORGWR) estimators have been developed under the five different shapes of spatial weighting
functions (i.e. bi-square, boxcar, exponential, gaussian, tri-cube). Based on the simulation study, some
of the proposed ORGWR estimators have been found better as compared to a non-robust GWR
estimator as well as a robust estimator proposed by Chamber (1986). For estimation of variance of
non-robust GWR estimator of finite population total, three bootstrap techniques of variance estimation
i.e. Spatial Rescaled Residual Bootstrap (SRRB) method, Spatial Centered Residual Bootstrap (SCRB)
method and Spatial Pair Bootstrap (SPB) method have been proposed. Based on the simulation study,
the SRRB method has been found to be the best among all the proposed bootstrap procedures. Further,
Spatial Weighted Residual Bootstrap (SWRB) method of variance estimation technique for ORGWR
estimator under the five different shapes of spatial weighting functions (i.e. bi-square, boxcar,
exponential, gaussian, tri-cube) have been proposed. Based on the simulation study, the SWRB method
with bi-square shape of spatial weighting function has been found to be the best performing bootstrap
procedure of variance estimation for ORGWR estimator. Further, a Proportional Spatial Weighted
Residual Bootstrap (PSWRB) technique to estimate the variance of ORGWR estimator in the presence
of missing observations in the survey data set has been proposed. GWR model-based imputation has
been found to be the most efficient imputation technique in estimating the variance using the PSWRB
technique in the presence of missing observations in survey data. The proposed methodology
(ORGWR) has also been applied to the real data set and application of the developed methodology has
resulted in obtaining reliable estimates of average yield of cotton with significantly reduced number of
CCEs.
Description
T-10423