Distributed estimation uses many inexpensive sensors to compose an accurate estimate of a given parameter. It is frequently implemented using wireless sensor networks. There have been several studies on optimizing power allocation in wireless sensor networks used for distributed estimation, the vast majority of which assume linear radio-frequency amplifiers. Linear amplifiers are inherently inefficient, so in this dissertation nonlinear amplifiers are examined to gain efficiency while operating distributed sensor networks. This research presents a method to boost efficiency by operating the amplifiers in the nonlinear region of operation. Operating amplifiers nonlinearly presents new challenges. First, nonlinear amplifier characteristics change across manufacturing process variation, temperature, operating voltage, and aging. Secondly, the equations conventionally used for estimators and performance expectations in linear amplify-and-forward systems fail. To compensate for the first challenge, predistortion is utilized not to linearize amplifiers but rather to force them to fit a common nonlinear limiting amplifier model close to the inherent amplifier performance. This minimizes the power impact and the training requirements for predistortion. Second, new estimators are required that account for transmitter nonlinearity. This research derives analytically and confirms via simulation new estimators and performance expectation equations for use in nonlinear distributed estimation. An additional complication when operating nonlinear amplifiers in a wireless environment is the influence of varied and potentially unknown channel gains. The impact of these varied gains and both measurement and channel noise sources on estimation performance are analyzed in this paper. Techniques for minimizing the estimate variance are developed. It is shown that optimizing transmitter power allocation to minimize estimate variance for the most-compressed parameter measurement is equivalent to the problem for linear sensors. Finally, a method for operating distributed estimation in a multipath environment is presented that is capable of developing robust estimates for a wide range of Rician K-factors. This dissertation demonstrates that implementing distributed estimation using nonlinear sensors can boost system efficiency and is compatible with existing techniques from the literature for boosting efficiency at the system level via sensor power allocation. Nonlinear transmitters work best when channel gains are known and channel noise and receiver noise levels are low.