Statistics and Probability Commons^™

The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose that we observe a sample of independent and identically distributed realizations of a random variable. Assume that the parameter of interest can be defined as the minimizer, over a suitably defined parameter space, of the expectation (with respect to the distribution of the random variable) of a particular (loss) function of a candidate parameter value and the random variable. Examples of commonly used loss functions are the squared error loss function in regression and the negative log-density loss function in density estimation. Minimizing the empirical risk (i.e., the empirical mean of the loss function) over the entire parameter space …