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 $${\hat{f}}_n(x)=\frac{1}{n{h}_n^{1/2}}\sum _{j=1}^n\frac{1}{h_j^{1/2}}K\left(\frac{x-X_j}{h_j}\right)$$ 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