# Common features of good statistics research

1.      Good statistics research is application relevant. There must be real data sets for which the proposed statistical procedure(s) are useful. The use of such procedure(s) and the results must be validated by experts from the disciplines, and by leading statisticians, rather than by a closely-knitted tiny faction of like-minded people. To see examples of such research, one only needs to read the books by some of today’s leading statisticians Bosq (1998), Doukhan (1993), Fan and Yao (2003), Härdle (1989), Hastie and Tibshirani (1990), Horowitz (1998), Li and Racine (2007), Ruppert, Wand and Carroll (2003).

2.      Good statistics research is mathematically sophisticated. It almost always involves using deep results from analytical theory of special functions (Besov space, Sobolev space, kernel, spline and wavelets/orthogonal series); empirical processes; extreme value theory; geometry (statistics on Riemannian manifold); large random matrices (eigenvalues and norms, inversion, etc.); dependent data; normal approximations; stochastic calculus; uniform convergence, etc. Simple algebra plus some calculus may be sufficient in the early development stage of a new area until problems that can be solved by such are exhausted.

3.      Good statistics research is computationally challenging. Implementation of good statistical method may require heavy programming in either matrix/array based Matlab/R/SASIML/S-plus or C++/Fortran. High power computing for large data necessitates such efforts. Simply downloading free software written by experts and running on one's own data does not qualify as original substantive research.

4.      Good statistics research leads to theoretically superior methods, often enjoying such neat theoretical properties as oracle efficiency, exact and simple form of asymptotic distribution, uniform confidence regions, etc. In some cases, weak consistency may be the best one can achieve. To develop theoretically superior methods does not mean to be “theoretical” in the negative sense. Some very theoretical people have had significant impacts on the development of contemporary statistical methodology because they are willing to work on the kind of theoretical problems of broad applications, rather than those problems designed by themselves only for their own entertainment.

5.      Good statistics research produces user-friendly procedures, which are intuitively appealing, fast, numerically accurate and easily interpretable. Again, it demands hard work on the statisticians to design such methods and study their properties, leaving the users all convenience.