Variance Estimation for Regression Imputed Quantiles and Inequality Indicators

Résumé |
This work is done in the framework of sampling theory. It is based
on a scenario in which a sample survey has been carried out and
only a sub-part of the selected sample has accepted to answer
(total non-response). Moreover, some respondents did not answer all
questions (partial non-response). This is common scenario in
practice. We are particularly interested in income type variables.
Generally, total non-response is treated by re-weighting and
partial non-response through imputation. One further supposes here
that the imputation is carried out by a regression model adjusted
on the respondents. We then resume the idea presented by
\citet{dev:sar:94} and tested afterwards by \citet{LeeRancSar:1994}
which consists in constructing an unbiased estimator of the variance
of a total based solely on the information at our disposal: the
information known on the selected sample and the subset of
respondents. While the two cited articles dealt with the exercise
for a conventional total of an interest variable $y$, we reproduce
here a similar development in the case where the considered total
is one of the linearized variable of quantiles or of inequality
indicators, and that, furthermore, it is computed from the imputed
variable $y$. We show by means of simulations that regression
imputation can have an important impact on the bias estimation as
well as on the variance estimation of inequality indicators. This
leads us to a method capable of taking into account the variance
due to imputation in addition to the one due to the sampling design
in the cases of quantiles. This method could be generalized to some
of the inequality indicators. |

Mots-clés |
Influence function; SILC survey; linearization; bias; simulations; Laeken indicators |

Citation | Graf, E. (2014). Variance Estimation for Regression Imputed Quantiles and Inequality Indicators. UNINE, ISTAT. |

Type | Working paper (Anglais) |

Année | 2014 |

Institution | UNINE, ISTAT (Neuchâtel) |

Nombre de pages | 33 |