Suppose that you have grounds for believing that observations x i , y i for i 1, 2 , n are such that x i N(, i ) and also y i N(, i ) but that you are not prepared to assume that the i are equal What statistic would you expect to base inferences about on ...

Given that the observations xi and yi are normally distributed with mean and variances i and i respe ...

Suppose that you have grounds for believing that observations x i , y i for i =

Question:

Suppose that you have grounds for believing that observations x_i, y_i for i = 1, 2 ... , n are such that x_i ~ N(θ, ϕ_i) and also y_i ~ N(θ,ϕ_i) but that you are not prepared to assume that the ϕ_i are equal. What statistic would you expect to base inferences about θ on?