In many practical detection and classification problems, the signals of interest exhibit some uncertain nuisance parameters, such as the unknown delay and Doppler in radar. For optimal performance, the form of such parameters must be known and exploited as is done in the generalized likelihood ratio test (GLRT). In practice, the statistics required for designing the GLRT processors are not available a priori and must be estimated from limited training data. Such design is virtually impossible in general due to two major difficulties: identifying the appropriate nuisance parameters, and estimating the corresponding GLRT statistics. We address this problem by using recent results that relate joint signal representations (JSRs), such as time-frequency and time-scale representations, to quadratic GLRT processors for a wide variety of nuisance parameters. We propose a general data-driven framework that: 1) identifies the appropriate nuisance parameters from an arbitrarily chosen finite set, and 2) estimates the second-order statistics that characterize the corresponding JSR-based GLRT processors.