Misspectification 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. On the other hand, 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. In Section 1 estimators based on a correctly and incorrectly specified constant mean are compared with estimators based on an unspecified constant mean. The comparison is done by calculating the corresponding values for the MSE. The ratios of the mean squared errors decreases with decreasing correlation between observations, and are, in general, very close to one. In section 2 estimation done with a specified linear trend function is compared to an estimation with an unspecified linear trend function. For interpolation, in general, the MSE's tend to be close except for high underlying correlation models. For extrapolation - the MSE values can be very different. The third section deals wiyh a biased partially constrained estimator versus a fully constrained universally unbiased estimator in the presence of a linear trend. In general, the biased and unbiased estimators have similar performance, except for very steep linear slopes of the trend. In Section 4 the Driging method was used for interpolating (mapping) values of oxidant levels from 1973 at 16 stations located in the San Francisco Bay Area. For this purpose constant and linear trends were used. The method requires for its application 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
- DOE Contract Number:
- EY-76-S-02-2874
- OSTI ID:
- 5759167
- Report Number(s):
- DOE/EY/22874-59
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
54 ENVIRONMENTAL SCIENCES
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
AIR POLLUTION
HEALTH HAZARDS
EPIDEMIOLOGY
CORRELATIONS
DATA COMPILATION
DIAGRAMS
EXTRAPOLATION
GRAPHS
HUMAN POPULATIONS
INTERPOLATION
MAPPING
MONITORING
OXIDIZERS
PUBLIC HEALTH
SAMPLING
SPATIAL DISTRIBUTION
STOCHASTIC PROCESSES
TABLES
TIME DEPENDENCE
DATA
DATA FORMS
DISTRIBUTION
HAZARDS
INFORMATION
NUMERICAL DATA
NUMERICAL SOLUTION
POLLUTION
POPULATIONS
560306* - Chemicals Metabolism & Toxicology- Man- (-1987)
500200 - Environment
Atmospheric- Chemicals Monitoring & Transport- (-1989)
990200 - Mathematics & Computers