dopt_upper

sgaplus

coma

<a href="https://lifecycle.r-lib.org/articles/stages.html#stable"><img src="figures/lifecycle-stable.svg?package=stratallo&version=2.1.0" alt="[Stable]"></a>
Internal functions that implement the optimal sample allocation algorithms:
<code>sga</code>, <code>sgaplus</code> and <code>coma</code>.
Functions from this family compute:
$$argmin D(x_1,...,x_H) = a^2_1/x_1 + ... + a^2_H/x_H - b,$$
under the equality constraint imposed on total sample size:
$$x_1 + ... + x_H = n,$$
and upper bounds constraints imposed on strata sample sizes:
$$x_w &lt;= M_w, w = 1,...,H.$$
Here, $H$ denotes total number of strata, $x_1, ..., x_H$ are the
strata sample sizes, and $n &gt; 0$, $b$, $a_w &gt; 0$,
$M_w &gt; 0, w = 1, ..., H$ are given numbers. 
The <code>sga()</code>, <code>sgaplus()</code> and <code>coma()</code> are internal implementations of the
algorithms in subject, and hence, users should not use any of these functions
directly. Instead, the <code>dopt()</code> should be used.

Functions in this package provide solution to classical problem in
survey methodology - an optimum sample allocation in stratified sampling
schemes. In this context, the optimal allocation is in the classical
Tschuprov-Neyman's sense and it satisfies additional lower or upper bounds
restrictions imposed on sample sizes in strata. There are few different
algorithms available to use, and one them is based on popular sample
allocation method that applies Neyman allocation to recursively reduced set of
strata.
This package also provides the function that computes a solution to the minimum
sample size allocation problem, which is a minor modification of the classical
optimium sample allocation. This problem lies in the determination of a vector
of strata sample sizes that minimizes total sample size, under assumed fixed
level of the pi-estimator's variance. As in the case of the classical optimal
allocation, the problem of minimum sample size allocation can be complemented
by imposing upper bounds constraints on sample sizes in strata.

Wojciech Wojciak

stratallo

Optimum Sample Allocation in Stratified Sampling Schemes

Wojciech Wójciak

Jacek Wesołowski

Robert Wieczorkowski

dopt_upper function

<dl><dt>n</dt>
<dd>(<code>number</code>) total sample size. A strictly positive scalar.</dd>
<dt>a</dt>
<dd>(<code>numeric</code>) parameters $a_1, ..., a_H$ of variance function
$D$. Strictly positive numbers.</dd>
<dt>M</dt>
<dd>(<code>numeric</code>) upper bounds constraints imposed on strata sample
sizes. It is required that <code>n &lt;= sum(M)</code>. Strictly positive numbers.</dd></dl>

Arguments

<ul>
<li><code>sga</code>: implementation of the Stenger-Gabler type algorithm
<code>SGa</code>, described in Wesołowski et al. (2021) and in Stenger and Gabler
(2005).</li>
<li><code>sgaplus</code>: implementation of the modified Stenger-Gabler type
algorithm, described in Wójciak (2019) as
<code>Sequential Allocation (version 1)</code> algorithm.</li>
<li><code>coma</code>: implementation of the Change of Monotonicity
Algorithm, or <code>coma</code>, described in Wesołowski et al. (2021).</li>
</ul>

Functions

<a href='https://lifecycle.r-lib.org/articles/stages.html#stable'><img src='figures/lifecycle-stable.svg' alt='[Stable]' /></a>
Internal functions that implement the optimal sample allocation algorithms:
<code>sga</code>, <code>sgaplus</code> and <code>coma</code>.
Functions from this family compute:
$$argmin D(x_1,...,x_H) = a^2_1/x_1 + ... + a^2_H/x_H - b,$$
under the equality constraint imposed on total sample size:
$$x_1 + ... + x_H = n,$$
and upper bounds constraints imposed on strata sample sizes:
$$x_w &lt;= M_w, w = 1,...,H.$$
Here, $H$ denotes total number of strata, $x_1, ..., x_H$ are the
strata sample sizes, and $n &gt; 0$, $b$, $a_w &gt; 0$,
$M_w &gt; 0, w = 1, ..., H$ are given numbers. 
The <code>sga()</code>, <code>sgaplus()</code> and <code>coma()</code> are internal implementations of the
algorithms in subject, and hence, users should not use any of these functions
directly. Instead, the <code>dopt()</code> should be used.

Algorithms for Optimum Sample Allocation in Stratified Sampling Under
Under One-Sided Upper Bounds Constraints — dopt_upper

<dl>

<dt>n</dt>
<dd>(<code>number</code>) total sample size. A strictly positive scalar.</dd>


<dt>a</dt>
<dd>(<code>numeric</code>) parameters $a_1, ..., a_H$ of variance function
$D$. Strictly positive numbers.</dd>


<dt>M</dt>
<dd>(<code>numeric</code>) upper bounds constraints imposed on strata sample
sizes. It is required that <code>n &lt;= sum(M)</code>. Strictly positive numbers.</dd>

</dl>

dopt_upper: Algorithms for Optimum Sample Allocation in Stratified Sampling Under Under One-Sided Upper Bounds Constraints

Description

Usage

Value

Arguments

Functions

References

See Also

Examples