  The accurate specification of the number of factors is critical to the
validity of factor models and the topic almost occupies the central position in
factor analysis. Plenty of estimators are available under the restrictive
condition that the fourth moments of the factors and idiosyncratic errors are
bounded. In this paper we propose efficient and robust estimators for the
factor number via considering a more general static Elliptical Factor Model
(EFM) framework. We innovatively propose to exploit the multivariate Kendall's
tau matrix, which captures the correlation structure of elliptical random
vectors. Theoretically we show that the proposed estimators are consistent
without exerting any moment condition when both cross-sections N and time
dimensions T go to infinity. Simulation study shows that the new estimators
perform much better in heavy-tailed data setting while performing comparably
with the state-of-the-art methods in the light-tailed Gaussian setting. At
last, a real macroeconomic data example is given to illustrate its empirical
advantages and usefulness.
