  In this paper, we provide a general methodology to draw statistical
inferences on individual signal coordinates or linear combinations of them in
sparse phase retrieval. Given an initial estimator for the targeting parameter
(some simple function of the signal), which is generated by some existing
algorithm, we can modify it in a way that the modified version is
asymptotically normal and unbiased. Then confidence intervals and hypothesis
testings can be constructed based on this asymptotic normality. For
conciseness, we focus on confidence intervals in this work, while a similar
procedure can be adopted for hypothesis testings. Under some mild assumptions
on the signal and sample size, we establish theoretical guarantees for the
proposed method. These assumptions are generally weak in the sense that the
dimension could exceed the sample size and many non-zero small coordinates are
allowed. Furthermore, theoretical analysis reveals that the modified estimators
for individual coordinates have uniformly bounded variance, and hence
simultaneous interval estimation is possible. Numerical simulations in a wide
range of settings are supportive of our theoretical results.
