I am reading about point estimation from Theory of Point Estimation by Lehmann and Casella (1999). I couldn't understand the following point mentioned in p.24, under the exponential family of distributions :
An exponential family of distributions of dimension $s$ (in canonical form) is the set of distributions $p_\theta$ such that. $p_\theta = h(x) . \exp[\sum_{i=1}^s \{\eta_iT_i(x) - A(\eta)\}]$.
It is mentioned that if the $\{T_i(x)\} $'s are linearly dependent (i.e one of $T_i(x)$ can be written as a linear combination of others) then the number of parameters of $\eta_i$ can be reduced (from $s$ to $s-1$). I understand why this is so.
What I don't understand is the following:
"if the $\{T_i(x)\}$ are linearly dependent, then the corresponding parameters $\{\eta_i\}$ cannot be estimated individually."