Spatial VariationThis book was first published in 1960 as No. 5 of Volume 49 of Reports of the Forest Research Institute of Sweden. It was at the same time a doctor's thesis in mathematical statistics at Stockholm University. In the second edition, a number of misprints and other errors have been corrected. An author index and a subject index have been added. Finally, a new postscript comments on the later development of the subjects treated in the book. BERTIL MATERN March r¢6 Acknowledgements The completion of this thesis was facilitated through the generous assist ance of several persons and institutions. I would wish to express my sincere gratitude to my teacher, Professor HARALD CRAMtR, now chancellor of the Swedish universities, for his valuable help and encouragement. Sincere thanks are also offered to Professor ULF GRENANDER for kindly reading the first version of the manuscript and giving valuable advice. The thesis has been prepared during two widely separated periods. A preliminary draft of Ch. 2 was written in 1948, whereas the remaining parts were completed in 1959-1960. The work originates from problems which I discussed in a publication in 1947. The problems were assigned to me by Professor MANFRED NASLUND, former head of the Swedish Forest Research Institute, now governor of the province Norrbotten. It is a pleasure to acknowledge my gratefulness to Professor Naslund for his un remitting encouragement and interest in my work. |
Contents
| 7 | |
Some particular models | 27 |
Some remarks on the topographic variation | 51 |
On the efficiency of some methods of locating sample points in Ra | 68 |
Various problems in sample surveys | 100 |
Sammanfattning | 135 |
Postscript | 149 |
Other editions - View all
Common terms and phrases
applied approximately assumed average border effects c₁ centers computed considered const cor.f correlation functions correlograms corresponding cov.f covariance function cross covariance curves denote distance distribution estimate example expression finite forest surveys formula frequency function further give integral intensity function isotropic process latin square length located Matérn means n-dimensional n-sphere number of points number of sample observations obtained point per stratum point per unit Poisson process problem quadratic forms R₁ R₂ random points random variable rectangle region sample plots sample points sample schemes sampling error sampling intensity sampling units set function spatial variation spectral density square network stationary process stationary set stochastic processes strata stratified sampling systematic sampling topographic variation tract unit area unrestricted random sampling values variance per point variance per sample variance per unit weight function x₁ z₁