Abstract: Let \(\{X_k, k\ge 1\}\) be a sequence of independent identically distributed random variables with common probability density function \(f\), and let \(\hat f_n\) denote a Wegman–Davies recursive density estimator \[ \hat f_n(x)=\frac{1}{nh_n^{1/2}}\sum_{j=1}^n\frac{1}{h_j^{1/2}} K\left(\frac{x-X_j}{h_j}\right) \] where \(K\) is a kernel function and \(h_n\) is a band sequence. In the present paper, the moderate deviation principle and the large deviation principle for the estimator \(\hat f_n\) are established.

2010 AMS Mathematics Subject Classification: Primary 62G07; Secondary 60F10.

Keywords and phrases: moderate deviation principle, large deviation principle, recursive kernel estimator