Font Size:

Testing for independence in analytic inference

Last modified: 2018-05-13

#### Abstract

In analytic inference, data usually come from complex sampling designs, possibly with different inclusion probabilities, stratification, clustering of units. The effect of a complex sampling design is that sampling data are not i.i.d., even if they are at a superpopulation level.

This dramatically changes the probability distribution of usual test-statistics, such as Spearman's Rho. An approach based on a special form of resampling is proposed, and its properties are studied.

This dramatically changes the probability distribution of usual test-statistics, such as Spearman's Rho. An approach based on a special form of resampling is proposed, and its properties are studied.

#### References

\bibitem{cifetal} Cifarelli D M., Conti P L., Regazzini E.:

On the asymptotic distribution of a general measure of monotone dependence.

The Annals of Statistics, \textbf{24}, 1386--1399 (1996)

\bibitem{cochran39} Cochran W G.: The use of the analysis of variance in enumeration by sampling.

Journal of the American Statistical Association, \textbf{34}, 492--510 (1939)

\bibitem{efron79} Efron B.: Bootstrap methods: another look at the jackknife. The Annals of Statistics, \textbf{7},

1--26 (1979)

\bibitem{hajek64} H\'{a}jek J.: Asymptotic Theory of Rejective Sampling With Varying Probabilities from a Finite Population.

The Annals of Mathematical Statistics, \textbf{35}, 1491--1523 (1964)

\bibitem{pfeffer93} Pfeffermann D.: The role of sampling weights when modeling survey data.

International Statistical Review, \textbf{61}, 317--337 (1993)

\bibitem{pfeff04} Pfeffermann D., Sverchkov M.: Prediction of finite population totals based on the

sample distribution. Survey Methodology,Â \textbf{30}, 79-â€“92 (2004)

\bibitem{sarndaletal92} S{\"a}rdnal C -E., Swensson B., Wretman, J H.: Model Assisted Survey Sampling.

Springer-Verlag, New York (1992)

\bibitem{tille06}Â Till\'{e}, Y.: Sampling {A}lgorithms. Springer Verlag, New York (2006)

On the asymptotic distribution of a general measure of monotone dependence.

The Annals of Statistics, \textbf{24}, 1386--1399 (1996)

\bibitem{cochran39} Cochran W G.: The use of the analysis of variance in enumeration by sampling.

Journal of the American Statistical Association, \textbf{34}, 492--510 (1939)

\bibitem{efron79} Efron B.: Bootstrap methods: another look at the jackknife. The Annals of Statistics, \textbf{7},

1--26 (1979)

\bibitem{hajek64} H\'{a}jek J.: Asymptotic Theory of Rejective Sampling With Varying Probabilities from a Finite Population.

The Annals of Mathematical Statistics, \textbf{35}, 1491--1523 (1964)

\bibitem{pfeffer93} Pfeffermann D.: The role of sampling weights when modeling survey data.

International Statistical Review, \textbf{61}, 317--337 (1993)

\bibitem{pfeff04} Pfeffermann D., Sverchkov M.: Prediction of finite population totals based on the

sample distribution. Survey Methodology,Â \textbf{30}, 79-â€“92 (2004)

\bibitem{sarndaletal92} S{\"a}rdnal C -E., Swensson B., Wretman, J H.: Model Assisted Survey Sampling.

Springer-Verlag, New York (1992)

\bibitem{tille06}Â Till\'{e}, Y.: Sampling {A}lgorithms. Springer Verlag, New York (2006)

Full Text:
PDF