GECal (version 0.1.7)

estimate: Performing statistical inference after calibration

Description

estimate performs statistical inference after calibration.

Usage

estimate(formula, data = NULL, calibration, pimat = NULL)

Value

A list of class estimation including the point estimates and its standard error.

Arguments

formula

An object of class "formula" specifying the calibration model.

data

An optional data frame containing the variables in the model (specified by formula).

calibration

An object of class "calibration", generated by GECalib.

pimat

An optional matrix contatining the joint inclusion probability matrix used for variance estimation.

References

Kwon, Y., Kim, J., & Qiu, Y. (2024). Debiased calibration estimation using generalized entropy in survey sampling. Arxiv preprint <https://arxiv.org/abs/2404.01076>

Deville, J. C., and Särndal, C. E. (1992). Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418), 376-382.

Examples

set.seed(11)
N = 10000
x = data.frame(x1 = rnorm(N, 2, 1), x2= runif(N, 0, 4))
pi = pt((-x[,1] / 2 - x[,2] / 2), 3);
pi = ifelse(pi >.7, .7, pi)

delta = rbinom(N, 1, pi)
Index_S = (delta == 1)
pi_S = pi[Index_S]; d_S = 1 / pi_S
x_S = x[Index_S,,drop = FALSE]
# pimat = diag(d_S^2 - d_S) / N^2 # 1 / pi_i * (1 - 1 / pi_i)

e = rnorm(N, 0, 1)
y = x[,1] + x[,2] + e;
y_S = y[Index_S] # plot(x_S, y_S)

calibration0 <- GECal::GEcalib(~ 1, dweight = d_S, data = x_S,
                               const = N,
                               entropy = "SL", method = "DS")
GECal::estimate(y_S ~ 1, calibration = calibration0)$estimate # Hajek estimator
# sum(y_S * d_S) * N / sum(d_S)

calibration <- GECal::GEcalib(~ 0, dweight = d_S, data = x_S,
const = numeric(0),
entropy = "SL", method = "DS")
GECal::estimate(y_S ~ 1, calibration = calibration)$estimate # HT estimator

calibration1 <- GECal::GEcalib(~ ., dweight = d_S, data = x_S,
                               const = colSums(cbind(1, x)),
                               entropy = "ET", method = "DS")
GECal::estimate(y_S ~ 1, calibration = calibration1)$estimate

calibration2 <- GECal::GEcalib(~ ., dweight = d_S, data = x_S,
                               const = colSums(cbind(1, x)),
                               entropy = "ET", method = "GEC0")
GECal::estimate(y_S ~ 1, calibration = calibration2)$estimate

calibration3 <- GECal::GEcalib(~ . + g(d_S), dweight = d_S, data = x_S,
                               const = colSums(cbind(1, x, log(1 / pi))),
                               entropy = "ET", method = "GEC")
GECal::estimate(y_S ~ 1, calibration = calibration3)$estimate

calibration4 <- GECal::GEcalib(~ . + g(d_S), dweight = d_S, data = x_S,
                               const = colSums(cbind(1, x, NA)),
                               entropy = "ET", method = "GEC")
GECal::estimate(y_S ~ 1, calibration = calibration4)$estimate

calibration5 <- GECal::GEcalib(~ . + g(d_S), dweight = d_S, data = x_S,
                               const = colSums(cbind(1, x, NA)),
                               entropy = "ET", method = "GEC", K_alpha = "log")
GECal::estimate(y_S ~ 1, calibration = calibration5)$estimate