Goldsmiths College is hosting the joint University of London Statistics
seminar this term.
Friday May 7th
2.00pm Suojin Wang (Texas A & M University, visiting Southampton)
Higher-Order Accurate Methods for Retrospective Sampling Problems
3.30pm Roger Sugden (Goldsmiths)
Cochran's rule and Edgeworth expansions for simple random sampling
Friday 21st May
2.00pm Martin Newby (City University)
Fatigue crack growth
3.30pm Paul Blackwell (University of Sheffield)
Bayesian inference for random tessalation models
The talks will be held in room 137a, Main Building, Goldsmiths College,
New Cross. The college is 5 minutes walk from New Cross and New Cross Gate
railway and underground stations. Anyone who wishes to attend is welcome
to contact me ([log in to unmask]) for directions.
In this presentation we will discuss the relationship between prospective
and retrospective sampling problems. Estimates of the parameter of
interest may be obtained by solving suitable estimating equations under
both sampling schemes. Most common examples of such estimates include the
maximum likelihood estimates. Some classical results and more recent
development on the first order asymptotic relationship between the
estimators will be reviewed. Higher-order expansions for the distributions
of the retrospective estimators will be given. Expansions for the marginal
distributions of interest will be described for both prospective and
retrospective data. Furthermore, it may be shown that the two expansions
are asymptotically equal, at least up to the order of 1/n. This implies
that readily available prospective saddlepoint methods may be applied to
the analysis of retrospective data without loss of high-order accuracy.
The results will be briefly illustrated numerically also.
Cochran's rule gives the minimum sample size for a nominal 95% confidence
interval (for the population mean based on a Normal approximation to the
sampling distribution of the sample mean) to have at least 94% coverage.
We show how his rule can be derived using Edgeworth expansions, and extend
it from considering just the effects of skewness in the population to
considering also the effects of estimating (i) the variance, for a
studentised rather than standardised interval (ii) the finite population
size (iii) the kurtosis of the population. For smaller sample sizes we
suggest use of the expansion to estimate the coverage of a nominal 95%
interval, and test all these assertions by simulation.
Dept of Mathematical and Computing Sciences
[log in to unmask]
0171 919 7863