We develop new procedures to quantify the statistical uncertainty of data-driven clustering algorithms. In our panel setting, each unit belongs to one of a finite number of latent groups with group-specific regression curves. We propose methods for computing unit-wise and joint confidence sets for group membership. The unit-wise sets give possible group memberships for a given unit and the joint sets give possible vectors of group memberships for all units . We also propose an algorithm that can improve the power of our procedures by detecting units that are easy to classify. The confidence sets invert a test for group membership that is based on a characterization of the true group memberships by a system of moment inequalities. To construct the joint confidence, we solve a high-dimensional testing problem that tests group membership simultaneously for all units . We justify this procedure under N, T \to \infty asymptotics where we allow T to be much smaller than N. As part of our theoretical arguments, we develop new simultaneous anti-concentration inequalities for the MAX and the QLR statistics. Monte Carlo results indicate that our confidence sets have adequate coverage and are informative. We illustrate the practical relevance of our confidence sets in two applications .
Our confidence set quantifies the statistical uncertainty from data-driven cluster assignment in clustered panel models. It covers the true cluster memberships jointly for all units with pre-specified probability and is constructed by inverting many simultaneous unit-specific one-sided tests for group membership . We justify our approach under N, T \to \infty asymptotics using tools from high-dimensional statistics, some of which we extend or develop in this paper. We provide an empirical application as well as Monte Carlo evidence that the confidence set has adequate coverage in finite samples .
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clustering algorithms. In our panel setting, each unit belongs to one of a finite number of latent groups with group-specific regression curves. We propose methods for computing unit-wise and joint confidence sets for group membership. The unit-wise sets give possible group memberships for a given unit and the joint sets give possible vectors of group memberships
cluster assignment in clustered panel models. It covers the true cluster memberships jointly
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. We also propose an algorithm that can improve the power of our procedures by detecting units that are easy to classify. The confidence sets invert a test for group membership that is based on a characterization of the true group memberships by a system of moment inequalities. To construct the joint confidence, we solve a high-dimensional testing problem that tests group membership simultaneously for all units
with pre-specified probability and is constructed by inverting many simultaneous unit-specific one-sided tests for group membership
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where we allow T to be much smaller than N. As part of our theoretical arguments, we develop new simultaneous anti-concentration inequalities for the MAX and the QLR statistics. Monte Carlo results indicate that our confidence sets have adequate coverage and are informative. We illustrate the practical relevance of our confidence sets in two applications
using tools from high-dimensional statistics, some of which we extend or develop in this paper. We provide an empirical application as well as Monte Carlo evidence that the confidence set has adequate coverage in finite samples