This thesis presents two frameworks for parameter estimation in neuron models and assesses parameter accuracy by constructing confidence regions of parameter estimates. Parameter estimation helps advance the understanding of how neurons process sensory information. Nonlinear least squares have previously been used to fit biophysical neuron models. Yet, little attention has been devoted to handling rank-deficient problems, and to identifying and characterizing possible degeneracy in model parameters. To identify parameter degeneracy and resolve the rank deficiency, an SVD-based subset selection algorithm is used. Additional biophysical experiments are constructed, which constrain the least identifiable parameters. The approach is applied to the HCN neuron model. Moreover, an all-at-once optimization approach is applied, which includes the neuron model as a constraint and views parameters and model solution as optimization variables. This approach is demonstrated on the Pinsky-Rinzel model. The framework is designed to support the goal of applying them to complex compartmental neuron models.