Abstract
Let’s consider a finite population of P units, each of them assumes a specific amount of the quantitative variable X. Moreover we assume that the range of values of X is subdivided into k classes and the sampling data come out from a two stage stratified sampling. The main purpose of the work is to determine the estimators, as well as their asymptotic distribution, of the partial means of classes, each of them is defined as a non linear function of the other parameters. Particularly, we are interested in determining the linear approximation estimators and, under convergence theorems, the asymptotic distribution. Afterwards we define the estimator of the vector of the partial means of classes and its asymptotic convergence to multivariate normal distribution is determined. These results are useful to develop simultaneous inferential procedures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banca d’Italia (2006) I bilanci delle famiglie italiane nell’anno 2004, Supplemento al Bollettino Statistico 7: anno XVI
Cochran WG (1977) Sampling techniques, 2nd edn. Wiley, New York
Cozzucoli P (1992) Simultaneous confidence intervals for relative shares in simple random sampling without replacement. Quad Stat Mat Appl Sci Econ Soc 14(1–2): 103–116
Cozzucoli P (1993) Asymptotic normality of statistics in the two-stage stratified sampling. Quad Stat Mat Appl Sci Econ Soc 15(1): 87–94
Fuller WA (1976) Introduction to statistical time series. Wiley, New York
Goodman LA (1965) On simultaneous confidence intervals for multinomial proportion. Technometrics 7: 247–254
Krewski D, Rao JNK (1981) Inference from stratified samples: properties of the linearization, Jackknife and balanced repeated replication methods. Ann Stat 9(5): 1010–1019
Latorre G (1991) Simultaneous inference for proportions in two-stage sampling on income data. Quad Stat Mat Appl Sci Econ Soc 13(3): 33–49
Latorre G (1992) Simultaneous confidence intervals for relative shares in simple random sampling with replacement. Quad Stat Mat Appl Sci Econ Soc 14(1–2): 93–101
Latorre G (1995) Simultaneous inference for proportions in stratified random sampling. Res Econ Inequal 6: 255–268
Miller RG (1981) Simultaneous statistical inference, 2nd edn. Springer, New York
Monfort A (1980) Cours de probabilités, 2nd edn. Economica, Paris
Quesenberry CP, Hurst DC (1964) Large sample simultaneous confidence intervals for multinomial proportions. Technometrics 6: 191–195
Rao CR (1973) Linear statistical inference and its applications. Wiley, New York
Šidák Z (1967) Rectangular confidence regions for the means of multivariate normal distributions. J Am Stat Assoc 62: 626–633
Šidák Z (1968) On multivariate normal probabilities of rectangles: their dependence on correlations. Ann Math Stat 39: 1425–1434
Srivastava MS, Khatri CG (1979) An introduction to multivariate statistics. North-Holland, New York
Sukhatme PV, Sukhatme BV, Sukhatme S, Asok C (1984) Sampling theory of surveys with applications. Iowa State University Press, Ames
Wolter KM (1985) Introduction to variance estimation. Springer, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cozzucoli, P.C. Simultaneous confidence intervals on partial means of classes in the two-stage stratified sampling. Stat Papers 51, 673–685 (2010). https://doi.org/10.1007/s00362-008-0152-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-008-0152-1