<p>In this paper, we address a practical gap that appears frequently in signal processing; estimator comparison when parameters vary over time and no single <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> dominates the operational regime. We question the blanket use of Mean Square Error (MSE) and the Cramér-Rao Lower Bound (CRLB) in classical (non Bayesian) estimation, especially in settings where the parameter of interest (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>) does not repeat during operation. We propose an Integrated MSE (IMSE): the average -over a parameter range- of the MSE, motivated as a Bayes risk with a uniform prior, and use this to compare estimators across a range of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> rather than at a fixed <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>. We also argue that when estimating a fixed <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>, classical MSE does not capture convergence speed, and thus we advocate considering a finite sample confidence requirement as a complementary performance metric.</p>