1. Interdisciplinary research needs the terminology of other disciplines, not statistical theory. While some are tempted toward “applied/interdisciplinary research” as an easy way out, only statisticians strong in the core of probability theory and mathematical statistics are capable of offering authentic expertise most needed by scientists from other fields, leading to mutually beneficial interdisciplinary research. An opportunistic statistician who knows no more statistics than non statisticians often attempts to impress collaborators by parroting their language, just to get his/her name on their grant proposals. Such practice, of course, hurts one’s own credibility and the department’s reputation.
2. As long as someone is strong in theory, he/she can do excellent statistics research. Many people who are capable of manipulating mathematics and enjoying the activity stop just at that. That is, they create artificial mathematical problems exactly of the kind that they are able to solve, shying away from the more realistic and much more mathematically challenging problems of application relevance. They are like a cat playing every day the same game of chasing a yarn ball from bed to floor, certain of winning a controlled game. People weak in mathematics are like a cat too fat to win any game. Good statisticians are like a cat catching real mice around the house, with the possibility of failing and the thrill of winning a real game.
3. If someone uses fractional Brownian motion in papers, he/she is strong in theory. First, the use of sophisticated mathematics should be always for the purpose of creatively solving an interesting statistical problem, not for showing off mathematical prowess. Second, there are now graduate courses teaching people to “do stochastic calculus” by formal manipulation of symbols without any knowledge of Lebesgue measure (Email me and I can show you how to enroll in such a course). A post office worker loading boxes of laptop computers is no more high tech than another loading boxes of sweaters.