Description Usage Arguments Details Value References See Also Examples

Produces estimates for population totals and means using the Fuller - Burmeister estimator from survey data obtained from a dual frame sampling desing. Confidence intervals are also computed, if required.

1 |

`ysA` |
A numeric vector of length |

`ysB` |
A numeric vector of length |

`pi_A` |
A numeric vector of length |

`pi_B` |
A numeric vector of length |

`domains_A` |
A character vector of size |

`domains_B` |
A character vector of size |

`conf_level` |
(Optional) A numeric value indicating the confidence level for the confidence intervals. |

Fuller-Burmeister estimator of population total is given by

*\hat{Y}_{FB} = \hat{Y}_a^A + \hat{β_1}\hat{Y}_{ab}^A + (1 - \hat{β_1})\hat{Y}_{ab}^B + \hat{Y}_b^B + \hat{β_2}(\hat{N}_{ab}^A - \hat{N}_{ab}^B)*

where optimal values for *\hat{β}* to minimize variance of the estimator are:

*
≤ft( \begin{array}{c}
\hat{β}_1\\
\hat{β}_2
\end{array} \right)
= -
≤ft( \begin{array}{cc}
\hat{V}(\hat{Y}_{ab}^A - \hat{Y}_{ab}^B) & \widehat{Cov}(\hat{Y}_{ab}^A - \hat{Y}_{ab}^B, \hat{N}_{ab}^A - \hat{N}_{ab}^B)\\
\widehat{Cov}(\hat{Y}_{ab}^A - \hat{Y}_{ab}^B, \hat{N}_{ab}^A - \hat{N}_{ab}^B) & \hat{V}(\hat{N}_{ab}^A - \hat{N}_{ab}^B)
\end{array} \right)^{-1}
\times*

*
≤ft( \begin{array}{c}
\widehat{Cov}(\hat{Y}_a^A + \hat{Y}_b^B + \hat{Y}_{ab}^B, \hat{Y}_{ab}^A - \hat{Y}_{ab}^B)\\
\widehat{Cov}(\hat{Y}_a^A + \hat{Y}_b^B + \hat{Y}_{ab}^B, \hat{N}_{ab}^A - \hat{N}_{ab}^B)
\end{array} \right)
*

Due to Fuller-Burmeister estimator is not defined for estimating population sizes, estimation of the mean is computed as *\hat{Y}_{FB} / \hat{N}_H*, where *\hat{N}_H*
is the estimation of the population size using Hartley estimator.
Estimated variance for the Fuller-Burmeister estimator can be obtained through expression

*\hat{V}(\hat{Y}_{FB}) = \hat{V}(\hat{Y}_a^A) + \hat{V}(\hat{Y}^B) +
\hat{β}_1[\widehat{Cov}(\hat{Y}_a^A, \hat{Y}_{ab}^A) - \widehat{Cov}(\hat{Y}^B, \hat{Y}_{ab}^B)]*

* + \hat{β}_2[\widehat{Cov}(\hat{Y}_a^A, \hat{N}_{ab}^A) - \widehat{Cov}(\hat{Y}^B, \hat{N}_{ab}^B)]
*

If both first and second order probabilities are known, variances and covariances involved in calculation of *\hat{β}* and *\hat{V}(\hat{Y}_{FB})* are estimated using functions `VarHT`

and `CovHT`

, respectively. If
only first order probabilities are known, variances are estimated using Deville's method and covariances are estimated using following expression

*\widehat{Cov}(\hat{X}, \hat{Y}) = \frac{\hat{V}(X + Y) - \hat{V}(X) - \hat{V}(Y)}{2}*

`FB`

returns an object of class "EstimatorDF" which is a list with, at least, the following components:

`Call` |
the matched call. |

`Est` |
total and mean estimation for main variable(s). |

`VarEst` |
variance estimation for main variable(s). |

If parameter `conf_level`

is different from `NULL`

, object includes component

`ConfInt` |
total and mean estimation and confidence intervals for main variables(s). |

In addition, components `TotDomEst`

and `MeanDomEst`

are available when estimator is based on estimators of the domains. Component `Param`

shows value of parameters involded in calculation of the estimator (if any).
By default, only `Est`

component (or `ConfInt`

component, if parameter `conf_level`

is different from `NULL`

) is shown. It is possible to access to all the components of the objects by using function `summary`

.

Fuller, W.A. and Burmeister, L.F. (1972).
*Estimation for Samples Selected From Two Overlapping Frames* ASA Proceedings of the Social Statistics Sections, 245 - 249.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
data(DatA)
data(DatB)
data(PiklA)
data(PiklB)
#Let calculate Fuller-Burmeister estimator for variable Clothing
FB(DatA$Clo, DatB$Clo, PiklA, PiklB, DatA$Domain, DatB$Domain)
#Now, let calculate Fuller-Burmeister estimator and a 90% confidence interval
#for variable Leisure, considering only first order inclusion probabilities
FB(DatA$Lei, DatB$Lei, DatA$ProbA, DatB$ProbB, DatA$Domain,
DatB$Domain, 0.90)
``` |

Frames2 documentation built on May 29, 2017, 9:39 p.m.

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