In this thesis, we consider a sampling design problem for a distributed parameter estimation system. The system contains a number of remotely located local sensors that can preprocess the observed signal and convey the processed data to a data fusion center to make the final estimate. Two issues are considered for this system. One is a sampling scheme design for a parameter estimation problem in a single context. The other is how to assign the appropriate number of sampling points to each of the sensors when a constraint on the total sample size is assumed. Here we propose to design this two issues by maximizing the criterion of Fisher's information or minimizing the Fisher's information loss . A sampling design procedure will be established and some numerical simulations will be also carried out for illustration purpose.