An extension of Horvitz–Thompson estimator used in adaptive cluster sampling to continuous universe

ABSTRACT

In this paper, an extension of Horvitz–Thompson estimator used in adaptive cluster sampling to continuous universe is developed. Main new results are presented in theorems. The primary notions of discrete population are transferred to continuous population. First and second order inclusion probabilities for networks are delivered. Horvitz–Thompson estimator for adaptive cluster sampling in continuous universe is constructed. The unbiasedness of the estimator is proven. Variance and unbiased variance estimator are delivered. Finally, the theory is illustrated with an example.

KEYWORDS:

• Adaptive sampling
• continuous universe
• Horvitz–Thompson estimator
• spatial sampling.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05