Point Estimation

To estimate a certain parameter, we are interested in an estimator with a small bias and a small mean squared error (MSE). In many standard problems and applications, the uniformly minimum-variance unbiased estimator (UMVUE) can be derived. Moreover, estimators with reduced MSEs and relatively small biases are also popular to better balance the bias-variance trade-off. From a computational perspective, we discuss two methods to construct point estimators based on DNNs : Method 1 formulates a linear combination of several base estimators with a DNN approximating optimal weight parameters, and Method 2 directly trains a DNN as the point estimator. We further illustrate the different features of the two methods with side-by-side comparison results in a Response-adaptive Randomization (RAR) design. In general, Method 2 has a better MSE , but Method 1 has a smaller bias by integrating consistent base estimators and can better mitigate a potential risk of increased bias under model misspecification.