LARGE SAMPLE INFERENCE FOR IRREGULARLY SPACED DEPENDENT OBSERVATIONS BASEDON SUBSAMPLING

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.

[1]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[2]  BISPECTRAL ANALYSIS OF RANDOMLY SAMPLED DATA , 1995 .

[3]  P. Hall,et al.  On blocking rules for the bootstrap with dependent data , 1995 .

[4]  George G. Roussas,et al.  Moment inequalities for mixing sequences of random variables , 1987 .

[5]  P. Doukhan.  Mixing: Properties and Examples , 1994 .

[6]  Alan F. Karr,et al.  Inference for stationary random fields given Poisson samples , 1986, Advances in Applied Probability.

[7]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[8]  C. F. Wu.  On the Asymptotic Properties of the Jackknife Histogram , 1990 .

[9]  M. Sherman.  Subsampling and asymptotic normality for a general statistic from a random field , 1992 .

[10]  Antonio Possolo,et al.  Subsampling a random field , 1991 .

[11]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[12]  K. Krickeberg,et al.  Processus ponctuels en statistique , 1982 .

[13]  Joseph P. Romano,et al.  On Subsampling Estimators with Unknown Rate of Convergence , 1999 .

[14]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[15]  Elias Masry,et al.  Poisson sampling and spectral estimation of continuous-time processes , 1978, IEEE Trans. Inf. Theory.

[16]  Random sampling of continuous-parameter stationary processes: statistical properties of joint density estimators , 1988 .

[17]  E. Carlstein.  The Use of Subseries Values for Estimating the Variance of a General Statistic from a Stationary Sequence , 1986 .

[18]  Edward Carlstein,et al.  Nonparametric Estimation of the Moments of a General Statistic Computed from Spatial Data , 1994 .

[19]  Elias Masry,et al.  Spectral estimation of continuous-time stationary processes from random sampling , 1994 .

[20]  A. Karr,et al.  Point Processes and Their Statistical Inference. 2nd edn. , 1993 .

[21]  Joseph P. Romano,et al.  A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation , 1992 .