Abstract: In this paper we give three examples of adaptive estimation. Example I. Let x_1, \cdots \alpha_3 be a sequence of i.i.d. random variables having density function f(x, \theta)=q(\theta) r(x), as a \leqslant \infty \leqslant \theta_;=0, otherwies then \hat\theta_n=\boldsymbolx_(\mathrmn)^*+\frac\log 2n\left(\frac2\sqrt2 \pi n^-2 / s \sum_i=1^n \exp \left\-\frac12 n^2 / 8\left(\alpha_(*)^*-x_v\right)^3\right\\right)^-1 is an adaptive estimation of \theta or has asymptotical efficiency. Example 2. Les x_1, \cdots, x_n be a sequence of i. i. d. random variables having density function f(x-\theta), f(u)>0 and continuous as |u|< 1, f(-1+0)>0, f(1 \sim 0)>0, but f is unknown, then \hat\theta_n=\frac12\left(x_(1)^*+x_(n)^*\right)+\frac12 n A_n \log \frac2 B_nA_n+B_n is an adaptive estimation of \theta. where \beginaligned & A_n=\frac2\sqrt2 \pi n^-2 / 3 \sum_i=1^n \exp \left\-\frac12 n^2 / 3\left(x_4-x_(n)^*\right)^2\right\ \\ & B_n=\frac2\sqrt2 \pi n^-2 / 8 \sum_i=1^n \exp \left\-\frac12 n^2 / 3\left(x_i-x_(1)^*\right)^2\right\ \endaligned Example 3. Let \alpha_1, \cdots, x_n be a sequence of i.i.d. random variable having density function \beta(\theta) e^\sigma R(x) r(x), but \beta(\theta) is unknown, then estimator for E_s T^\prime(x) T+\frac16 n \frac\sum_i=1^n\left(T\left(a_4-T\right)^3\right.\sum_i=1^n\left(T\left(a_4\right)-T\right)^2 has a second order asymptotical effieiency.