K-sample subsampling in general spaces: The case of independent time series

The problem of subsampling in two-sample and K-sample settings is addressed where both the data and the statistics of interest take values in general spaces. We focus on the case where each sample is a stationary time series, and construct subsampling confidence intervals and hypothesis tests with asymptotic validity. Some examples are also given, and the problem of optimal block size choice is discussed.

[1]  Richard C. Bradley,et al.  Introduction to strong mixing conditions , 2007 .

[2]  Ricardo Rios,et al.  Subsampling under Weak Dependence Conditions , 2003 .

[3]  Patrice Bertail Comments on: Subsampling weakly dependent time series and application to extremes , 2011 .

[4]  H. White,et al.  Automatic Block-Length Selection for the Dependent Bootstrap , 2004 .

[5]  E. Lehmann Testing Statistical Hypotheses , 1960 .

[6]  S. Lahiri Resampling Methods for Dependent Data , 2003 .

[7]  Ken-ichi Yoshihara,et al.  Weak convergence of multidimensional empirical processes for strong mixing sequences of stochastic vectors , 1975 .

[8]  Joseph P. Romano,et al.  Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions , 1994 .

[9]  P. Bertail Second-order properties of an extrapolated bootstrap without replacement under weak assumptions , 1997 .

[10]  Paul Doukhan,et al.  Rejoinder on: Subsampling weakly dependent time series and application to extremes , 2011 .

[11]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[12]  Peter Hall,et al.  Bootstrap methods in statistics , 2000 .

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

[14]  E. J. Hannan,et al.  Multiple time series , 1970 .

[15]  A. Dasgupta Asymptotic Theory of Statistics and Probability , 2008 .

[16]  Helmut Lütkepohl,et al.  Introduction to multiple time series analysis , 1991 .

[17]  C. M. Deo,et al.  A Note on Empirical Processes of Strong-Mixing Sequences , 1973 .

[18]  D. Brillinger Time series - data analysis and theory , 1981, Classics in applied mathematics.

[19]  Elizabeth Ann Maharaj,et al.  Comparison of time series using subsampling , 2005, Comput. Stat. Data Anal..

[20]  Ian T. Jolliffe,et al.  Introduction to Multiple Time Series Analysis , 1993 .

[21]  F. Götze,et al.  Adaptive choice of bootstrap sample sizes , 2001 .

[22]  Joseph P. Romano,et al.  K-sample Subsampling , 2008 .