NONPARAMETRIC ESTIMATION OF THE VARIANCE OF SAMPLE MEANS BASED ON NONSTATIONARY SPATIAL DATA

ABSTRACT In Politis and Romano (Politis, D.N.; Romano, J.P. Nonparametric Resampling for Homogeneous Strong Mixing Random Fields. Journal of Multivariate Analysis 1993, 47, 301–328.), different block resampling estimators of variance of general linear statistics, e.g., a sample mean, were proposed under the assumption of stationarity. In the present paper such estimators of variance of sample means, computed from nonstationary spatially indexed data , where 𝒜 is a finite subset of the integer lattice , are studied. Consistency of estimators of variance will be shown for the following kind of data: Observations taken from different lattice points are allowed to come from different distributions, and the dependence structure is allowed to differ over the lattice. We assume that all observed values are from distributions with the same expected value, or with expected values that decompose additively into directional components. Furthermore, it will be assumed that observations separated by a certain distance are independent.

[1]  Nils Broman,et al.  Mätfel i provträdsvariabler och dess inverkan på precision och noggrannhet i volymskattningar , 1999 .

[2]  Joseph P. Romano,et al.  Nonparametric Resampling for Homogeneous Strong Mixing Random Fields , 1993 .

[3]  Michael Sherman,et al.  Data-Based Choice of Batch Size for Simulation Output Analysis , 1998, Simul..

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

[5]  Gustaf von Segebaden.  Komplement till rikstaxen 75 år , 2000 .

[6]  Ulrika Dahlberg,et al.  Fältinstruktion för och erfarenheter från vegetationsinventering i Abisko, sommaren 1997 , 1998 .

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

[8]  Bo Ohlsson,et al.  People's options on forest land use , 1998 .

[9]  Resampling m-Dependent Random Variables with Applications to Forecasting , 2000 .

[10]  Daniel Eriksson.  Spatial modeling of nature conservation variables useful in forestry planning , 2000 .

[11]  Y. Belyaev,et al.  Weakly approaching sequences of random distributions , 2000, Journal of Applied Probability.

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

[13]  V. V. Petrov.  Limit Theorems of Probability Theory: Sequences of Independent Random Variables , 1995 .

[14]  Arnold J Stromberg,et al.  Subsampling , 2001, Technometrics.

[15]  Per Löfgren,et al.  Metodutveckling för vegetationsövervakning i fjällen , 2000 .

[16]  Hans Petersson,et al.  Biomassafunktioner för trädfaktorer av tall, gran och björk i Sverige , 1999 .

[17]  Yuri K Belyaev,et al.  Bootstrap, Resampling and Mallows Metric , 1995 .

[18]  Kenneth Nyström.  Funktioner för att skatta höjdtillväxten i ungskog , 2000 .

[19]  Per Nilsson,et al.  Skogsskötseln vid 90-talets mitt - läge och trender , 1999 .

[20]  Heather Reese,et al.  Using Landsat TM and NFI data to estimate wood volume, tree biomass and stand age in Dalarna , 1999 .

[21]  Torgny Lind.  Kolinnehåll i skog och mark i Sverige , 2001 .

[22]  Torgny Lind.  Quantifying the area of edge zones in Swedish forest to assess the impact of nature conservation on timber yields , 1998 .

[23]  The Experimental Error in Field Trials 1 , 1919 .

[24]  Hampus Holmstrom,et al.  Averaging Absolute GPS Positionings Made Underneath Different Forest Canopies - A Splendid Example of Bad Timing in Research , 2001 .

[25]  Michiel von Kerkvoorde.  A sequential approach in mathematical programming to include spatial aspects of biodiversity in long range forest management planning , 1996 .

[26]  Per Löfgren,et al.  Metodik för skattning av lokala skogsbränsleresurser , 2000 .

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

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

[29]  M. Sherman.  Variance Estimation for Statistics Computed from Spatial Lattice Data , 1996 .

[30]  Regina Y. Liu.  Bootstrap Procedures under some Non-I.I.D. Models , 1988 .

[31]  Göran Ståhl,et al.  Om detektering av förändringar av populationer i begränsade områden , 1997 .

[32]  Jörgen Wallerman,et al.  Plot-level stem volume estimation and tree species discrimination with CASI remote sensing , 1999 .

[33]  Magnus Ekström,et al.  Estimation of the variance of sample means based on nonstationary spatial data with varying expected values , 2001 .

[34]  M. Nilsson,et al.  Regional forest biomass and wood volume estimation using satellite data and ancillary data , 1999 .