I'm going to interpret "in OR" as appearing in OR journals and/or written by people who identify as OR/MS/IE researchers. I'm a bit familiar with the intersection of optimization and statistical estimation. Machine learning, OLS and LAV regression, lasso regression etc. all rely on solving optimization problems to fit models. In addition, optimization models have been proposed for feature selection (choosing which predictors to include in a model) and classification analysis, and I imagine for other types of inference problems.
As far "interesting" papers, that's in the eye of the beholder. One of the seminal papers on optimization models for classification (discriminant analysis) was Mangasarian's 1965 paper in the journal Operations Research . Around 1988, researchers including Fred Glover reopened interest in optimization models for classification, including in a paper in Decision Sciences . Following a workshop in April 1989 at the University of Florida, a number of related papers were published in a special issue of Managerial and Decision Economics, including one by me . (Mine is not overly interesting, but I'll use it to provide the volume information.) Based on the occasional new citation of it, I would say that research on discriminant models continues today (presumably with an improvement in models and heuristics).
I'm less familiar with the work on feature selection (particularly its current state), but I'll toss in a reference to my sole contribution to the area , which also ties into discriminant analysis.
One last disclaimer: The question mentions the theory of statistical inference, but most (all?) of the papers I've listed have to do with methods rather than theory.
 Mangasarian, O. L. Linear and Nonlinear Separation of Patterns by Linear Programming. Operations Research, 1965, 13, 444-452.
 Glover, F.; Keene, S. & Duea, R. W. A New Class of Models for the Discriminant Problem. Decision Sciences, 1988, 19, 269-280.
 Rubin, P. A. Heuristic Solution Procedures for a Mixed-Integer Programming Discriminant Model. Managerial and Decision Economics, 1990, 11, 255-266.
 Iannarilli Jr., F. J. & Rubin, P. A. Feature Selection for Multi-class Discrimination via Mixed-integer Linear Programming. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25, 779-783.