Misspecification of trend in spatial random-function interpolation with application to oxidant mapping. Technical report No. 28
In epidemiological studies of the effects of air pollution it is desirable to obtain estimates of the exposure to various pollutants of persons living throughout a geographical region under study. It is typically the case that pollution levels are measured at only a few locations. The problems of interpolating these values and of determining the accuracy of interpolation are amenable to analysis by way of spatial stochastic models. Such models can lead to an optimal interpolation technique, in a manner which is reviewed here. Estimators based on a correctly and incorrectly specified constant mean are compared with estimators based on an unspecified constant mean. The ratios of the mean squared errors (MSE) decreases with decreasing correlation between observations, and are very close to one. Estimation done with a specified linear trend function to estimation are compared with an unspecified linear trend function. For interpolation, the MSE's tend to be close except for high underlying correlation models. For extrapolation - the MSE values can be very different. A biased partially constrained estimator versus a fully constrained universally unbiased estimator in the presence of a linear trend is discussed. The biased and unbiased estimators have similar performance, except for very steep linear slopes of the trend. The comparisons of these sections are made in the context of rather special and perhaps unrealistic model assumptions. The Kriging method is used for interpolating (mapping) values of oxidant levels from 1973 at 16 stations located in the San Francisco Bay Area. Constant and linear trends are used for the purpose. The method requires knowledge of the spatial covariance structure of the pollutant to which it is applied. Some difficulties encountered in estimating this for oxidant levels in the San Francisco Bay Area are mentioned.
- Research Organization:
- Stanford Univ., CA (USA). Dept. of Statistics
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- EY-76-S-02-2874
- OSTI ID:
- 5341869
- Report Number(s):
- DOE/EV/02874-59
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
AIR POLLUTION
SPATIAL DISTRIBUTION
INTERPOLATION
STATISTICAL MODELS
ANISOTROPY
CALIFORNIA
ISOTROPY
OXIDIZERS
SAN FRANCISCO BAY
STOCHASTIC PROCESSES
DISTRIBUTION
MATHEMATICAL MODELS
NORTH AMERICA
NUMERICAL SOLUTION
PACIFIC OCEAN
POLLUTION
SEAS
SURFACE WATERS
USA
WESTERN REGION
500200* - Environment
Atmospheric- Chemicals Monitoring & Transport- (-1989)