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Abstract:
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We study the nonnegative garrote estimator from three different aspects: computation, consistency and flexibility. We show that the nonnegative garrote estimate has a piecewise linear solution path. Using this fact, we propose an efficient algorithm for computing the whole solution path for the nonnegative garrote estimate. We also show that the nonnegative garrote has the nice property that with probability tending to one, the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables. We propose a slight modification that retains the attractive properties of the original nonnegative garrote, but is more widely applicable. To demonstrate the flexibility of the proposed estimator, we consider an extension to the nonparametric regression setup.
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