var_Tille

Compute an approximate variance estimate using the estimator
proposed by Tillé (1996).
Estimator of class 3, it requires only first-order inclusion probabilities but
for all population units.

internal

Variance approximations for the
Horvitz-Thompson total estimator in Unequal Probability Sampling
using only first-order inclusion probabilities.
See Matei and Tillé (2005) and Haziza, Mecatti and Rao (2008) for details.

Roberto Sichera

UPSvarApprox

Approximate the Variance of the Horvitz-Thompson Total Estimator

var_Tille function

<dl><dt>y</dt>
<dd>numeric vector of sample observations</dd>
<dt>pik</dt>
<dd>numeric vector of first-order inclusion probabilities for all population units</dd>
<dt>sample</dt>
<dd>Either a numeric vector of length equal to the sample size with
the indices of sample units, or a boolean vector of the same length of <code>pik</code>, indicating which
units belong to the sample (<code>TRUE</code> if the unit is in the sample,
<code>FALSE</code> otherwise.
Only used with estimators of the third class (see Details for more information).</dd>
<dt>maxIter</dt>
<dd>a scalar indicating the maximum number of iterations for the
fixed-point procedure</dd>
<dt>eps</dt>
<dd>tolerance value for the convergence of the fixed-point procedure</dd></dl>

Arguments

Tillé's Approximate Variance Estimator — var_Tille

<dl>

<dt>y</dt>
<dd>numeric vector of sample observations</dd>


<dt>pik</dt>
<dd>numeric vector of first-order inclusion probabilities for all population units</dd>


<dt>sample</dt>
<dd>Either a numeric vector of length equal to the sample size with
the indices of sample units, or a boolean vector of the same length of <code>pik</code>, indicating which
units belong to the sample (<code>TRUE</code> if the unit is in the sample,
<code>FALSE</code> otherwise.
Only used with estimators of the third class (see Details for more information).</dd>


<dt>maxIter</dt>
<dd>a scalar indicating the maximum number of iterations for the
fixed-point procedure</dd>


<dt>eps</dt>
<dd>tolerance value for the convergence of the fixed-point procedure</dd>

</dl>

var_Tille: Tillé's Approximate Variance Estimator

Description

Usage

Value

Arguments