ABSTRACT
Our objective is statistical inference pertaining to features of the unknown probability law Px on the basis of data; in particular, this paper will focus on estimation of the common mean μ. For the case where the data are of the form {A"(t), t g E}, with E being a finite subset of the rectangular lattice Zd, different block-resampling techniques have been developed in the literature; see, for example, Hall (1985),
Carlstein (1986), Kunsch (1989), Lahiri (1991), Liu and Singh (1992), Politis and Romano (1992a,b,c, 1993, 1994), Rais (1992), and Sherman and Carlstein (1994, 1996). However, in many important cases, for example, queueing theory, spatial statistics, mining and geostatistics, meteorology, etc., the data correspond to observations of X(t) at nonlattice, irregularly spaced points. For instance, if d — 1, X(i) might represent the required service time for a customer arriving at a service station at time t. If d = 2, X(t) might represent a measurement of the quality or quantity of the ore found in location t, or a measurement of precipitation at location t during a fixed time interval, etc. As a matter of fact, in case d > 1, irregularly spaced data seem to be the rule rather than the exception; see, for example, Cressie (1991), Karr (1991), and Ripley (1981).
