Each chapter of this dissertation examines a different econometric problem of interest and proposes a new approach to the data analysis problem at hand. The chapter titles may give the impression that some of these topics lie in disparate areas of focus. The topic and approach of Chapter 3, for example, shares less commonalities with Chapters 1 and 2 than the first two chapters share with one another. A connecting theme between all three chapters is the combination of foundational problems with modern data or methodologies designed to accommodate modern data analysis techniques. In the first two chapters, the PAC-Bayesian analytical framework, which has developed alongside the growth of machine learning applications, drives analyses of more traditional problems involving binary decision and individual treatment rules. In Chapter 1, this facilitates the derivation of new individual treatment rule estimators in the setting where a policy maker faces a general budget or resource constraint. In Chapter 2, this suggests new decision rules when a policy maker has a general utility function over payoffs that may have asymmetries and vary with covariates relevant to the decision problem. In each case the rules possess desirable theoretical properties, perform competitively against state-of-the-art alternatives, and have additional advantages in terms of applicability, estimation options, and modeling flexibility. Chapter 3 considers hypothesis testing in linear regressions when observations may be sampled at short time intervals. Whereas monthly or even quarterly observations were once ubiquitous in time series regression applications, it is becoming more common to have weekly, daily or even intraday observations. However, higher frequency data can pose challenges for classical inference procedures. F tests are proposed that utilize series long run variance estimation. Under reasonable discrete-time or continuous-time settings, the procedures yield valid inference so that the proposed hypothesis tests are robust to the sampling interval available to the practitioner. The tests have competitive size and power properties against the limited set of alternatives in a simulation study. Finally, an empirical example examining a relationship between interest rates associated with shorter and longer duration bonds illustrates the usefulness of the procedure.