Adaptive estimator

In statistics, an adaptive estimator is an estimator in a parametric or semiparametric model with nuisance parameters such that the presence of these nuisance parameters does not affect efficiency of estimation. In statistics, an adaptive estimator is an estimator in a parametric or semiparametric model with nuisance parameters such that the presence of these nuisance parameters does not affect efficiency of estimation. Formally, let parameter θ in a parametric model consists of two parts: the parameter of interest ν ∈ N ⊆ Rk, and the nuisance parameter η ∈ H ⊆ Rm. Thus θ = (ν,η) ∈ N×H ⊆ Rk+m. Then we will say that ν ^ n {displaystyle scriptstyle {hat { u }}_{n}} is an adaptive estimator of ν in the presence of η if this estimator is regular, and efficient for each of the submodels