On some properties of one nonparametric estimate of poisson regression function

The paper considers the nonparametric Poisson regression problem with a regular equidistant design on the unit interval. The nonparametric estimation of the Poisson regression function is studied. The uniform consistency conditions are established and the limit theorems are proved for continuous functionals on \(C[a,1-a]\) $C[a,1-a]$ , \(0<a<\frac{1}{2}\) $0<a<\frac{1}{2}$  .