Tid: 15 december 1997 kl 1515-1700

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Bengt Rosén, (Statistiska Centralbyrån - Statistics Sweden). - (List of Publications)

Titel: Order Sampling with Inclusion Probabilities Proportional to Size

Sammanfattning: One vehicle for utilization of auxiliary information in sample surveys is to use pps sampling, i.e. to sample (without replacement) with inclusion probabilities proportional to given size measures. When searching for good pps schemes, the following aspects are of main interest. The scheme should

1. be simple to implement
2. lead to good estimation precision
3. have nice variance estimation properties.
Ohlsson (1990) introduced a novel pps scheme called sequential Poisson sampling, which the speaker has generalized. Rosén (1997a) introduces and studies a class called "order sampling schemes", and Rosén (1997b) focuses on a subclass of these, "order pps schemes". In an order pps scheme a probability distribution H enters as an optional "parameter". Hence, it is natural to wonder if there is an optimal H (with regard to estimation precision)? In fact, there is an (asymptotically) uniformly optimal H, namely the Pareto distribution H(t) = 1/(1+t), t > 0. Comparisons of the corresponding Pareto pps scheme with other pps schemes, also outside the order pps schemes, lead to the following (at least tentative) conclusion : Pareto pps is superior (at least up to now) among pps schemes that admit objective assessment of sampling errors.

References:

Ohlsson, E. (1990). Sequential Poisson Sampling from a Business Register and its Application to the Swedish Consumer Price index., Stat. Sweden R&D Report 1990:6. Forthcoming in J. Official Statist.

Rosén, B. (1997a). Asymptotic Theory for Order Sampling, J. Statist. Planning and Inf., 62 135 - 158.

Rosén, B. (1997b). On Sampling with Probability Proportional to Size., J Statist. Planning and Inf., 62 159 - 191.