Oblique plans for a binomial process

The following random walk (Xt, t=0,1,2,⋯) in the set T= {(x,y):x,y are nonnegative integers} is considered: X0=(0,0), Prob{Xt+1=(x+1,y)|Xt=(x,y)}==1-Prob{Xt+1=(x,y+1)|Xt=p(x,y)}, p∈(0,1) being unknown. For a given B⊂T, define the stopping variable τ=min{t>0:Xt∈B}. A sequential procedure of estimation of a parameter Q=g(p) by a function f(Xτ,τ) is said to be an oblique plan if B is of the form {(x,y):y=(x-k)/s}, where k and s are positive integers. Some properties of estimates in oblique plans are discussed. .