Sentence examples for trend functions and from inspiring English sources

Several approaches are proposed, one of them enforcing orthogonality between the trend functions and the complementary random field.

The test is based on the separation between an empirical version of the relative trend function and its greatest convex minorant.

See Appendix S1 for additional details regarding both the secular trend function and three phase calibration.

No further investigation concerning optimal variance partition between spatial trend-function and random plot effects was made at this point.

where f(t) and g(t) represent the polynomial time trend functions, ε dt and ε st are the error terms.

The residuals for the models with more complex spatial trend functions (Eq. 8.51 and Eq. 8.51 Duchon) showed no spatial dependencies anymore (Figure 9C and 9D).

Finally, we considered using the temporal trend functions estimated from other pollutant time series, such as PM2.5 and NOx, instead of those from PM2.5 components in the full spatiotemporal model framework (Approach 3).

Therefore simple empirical semi-variograms of the randomized quantile residuals were calculated for various models with spatial trend functions of different complexity.

Using different secular trend functions, the model was fit to the calibration targets over the 28 year span using a three phase calibration procedure described below.

Fitting the full spatiotemporal models using substituted trend functions in Approach 3 would be justified when there is good agreement between the two trend functions (i.e., the PM2.5/NOx and the PM2.5 component trend functions).

Temporal trends include spatially homogenous temporal trend functions scaled by spatially varying trend coefficients.