Consider the regression model Y i=x τ iβ+g(t i)+ε i for i=1,…, n. Here (x i, t i) are known and nonrandom design points and ε i are i.i.d. random errors.The family of nonparametric estimates n(·) of g(·) including some known estimates is proposed. Based on the model Y i=x τ i+ n(t i)+ε i, the Berry-Esseen bounds of the distribution of the least-squares estimator of β are investigated.