Survey quantile by inversion of the weighted CDF

The estimator inverts the Horvitz-Thompson estimator of the distribution function, F_w(t) = sum_{y_i <= t} w_i / sum_i w_i. With equal weights it is exactly the type-1 sample quantile. The interval is Woodruff's: invert the CDF at p -/+ z times the linearized standard error of F_w at the point estimate.

Usage

Svyqtl(y, weights = NULL, quantile = 0.5)

Arguments

y

Numeric observations.

weights

Optional design weights; equal weights if NULL.

quantile

Probability in (0, 1).

Value

List with estimate, se, lower, upper, p, F, sumw, neff, n, method.

Details

Formula: Q_p = inf{t : F_w(t) >= p}.

References

Francisco, C. A. and Fuller, W. A. (1991). Quantile estimation with a complex survey design. The Annals of Statistics 19(1):454-469. doi:10.1214/aos/1176347993

Examples

Svyqtl(c(4, 1, 3, 2, 5), NULL, 0.5)
#> $estimate
#> [1] 3
#> 
#> $se
#> [1] 0.219089
#> 
#> $lower
#> [1] 1
#> 
#> $upper
#> [1] 5
#> 
#> $p
#> [1] 0.5
#> 
#> $F
#> [1] 0.6
#> 
#> $sumw
#> [1] 5
#> 
#> $neff
#> [1] 5
#> 
#> $n
#> [1] 5
#> 
#> $method
#> [1] "weighted CDF inversion with Woodruff interval [Francisco & Fuller 1991]"
#>