Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 274-292

LARGE SAMPLE INFERENCE FOR IRREGULARLY SPACED DEPENDENT OBSERVATIONS BASED ON SUBSAMPLING

By

DIMITRIS N. POLITIS, *University of California, San Diego*

EFSTATHIOS PAPARODITIS, *University of Cyprus, Cyprus*

and

JOSEPH P. ROMANO, *Stanford University, Stanford*

*SUMMARY. *In many contexts, e.g., queueing theory, spatial statistics, etc.,
the data may consist of measurements of some quantity at irregularly
scattered points in time and/or space; in other words, the data
might correspond to a realization of a marked point process over
a compact subset of the space of points.
In this paper, we formulate a modified version of the
general subsampling methodology which was originally
put forth in Politis and Romano~(1994)
for data observed over points on a lattice, and show that it leads
to valid large sample inferences in a very general estimation set-up
involving data from a marked point process.

*AMS (1991) subject classification.*62M20; secondary 62G05.

*Key words and phrases. *Confidence limits, large sample inference,
marked point processes, nonparametric estimation, Poisson processes, random fields, subsampling.