Inferential Statisticshard
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In a study involving a non-regular distribution where the support of the density f(xθ)f(x|\theta) depends on the parameter θ\theta, such as XiUniform(θ,θ+1)X_i \sim \text{Uniform}(\theta, \theta + 1), why does the standard Cramer-Rao Lower Bound (CRLB) fail to provide a meaningful limit for the variance of the Maximum Likelihood Estimator?