  We provide a statistical analysis of a tool in nonlinear-type time-frequency
analysis, the synchrosqueezing transform (SST), for both the null and non-null
cases. The intricate nonlinear interaction of different quantities in SST is
quantified by carefully analyzing relevant multivariate complex Gaussian random
variables. Specifically, we provide the quotient distribution of dependent and
improper complex Gaussian random variables. Then, a central limit theorem
result for SST is established. {As an example}, we provide a block bootstrap
scheme based on the established SST theory to test if a given time series
contains oscillatory components.
