Özet:

Benefits of using Ranked Set Sampling (RSS) rather than Simple Random Sampling (SRS) are indeed significant when estimating population mean or estimating linear models. Significance of this sampling method clearly appears since it can increase efficiency of the estimated parameters and decrease sampling costs. This paper investigates and introduces RSS method to fit spline and penalized spline models parametrically. It shows that the estimated parameters using RSS are more efficient than the estimated parameters using SRS for both spline and penalized spline models. The superiority of RSS approach is demonstrated using a simulation study as well as the "Air pollution" environmental real data study. The approach in this paper can be illustrated for general smoothing spline models; for example B-spline,Radial spline etc, straightforwardly.

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