We present a theoretical framework for strain estimation in optical coherence elastography (OCE), based on a statistical analysis of displacement measurements obtained from a mechanically loaded sample. We define strain sensitivity, signal-to-noise ratio and dynamic range, and derive estimates of strain using three methods: finite difference, ordinary least squares and weighted least squares, the latter implemented for the first time in OCE. We compare theoretical predictions with experimental results and demonstrate a ~12 dB improvement in strain sensitivity using weighted least squares compared to finite difference strain estimation and a ~4 dB improvement over ordinary least squares strain estimation. We present strain images (i.e., elastograms) of tissue-mimicking phantoms and excised porcine airway, demonstrating in each case clear contrast based on the sample’s elasticity.