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This paper studies the inference about linear functionals of high-dimensional
low-rank matrices. While most existing inference methods would require
consistent estimation of the true rank, our procedure is robust to rank
misspecification, making it a promising approach in applications where rank
estimation can be unreliable. We estimate the low-rank spaces using
pre-specified weighting matrices, known as diversified projections. A novel
statistical insight is that, unlike the usual statistical wisdom that
overfitting mainly introduces additional variances, the over-estimated low-rank
space also gives rise to a non-negligible bias due to an implicit ridge-type
regularization. We develop a new inference procedure and show that the central
limit theorem holds as long as the pre-specified rank is no smaller than the
true rank. Empirically, we apply our method to the U.S. federal grants
allocation data and test the existence of pork-barrel politics.
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