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.

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