Minimax Rate
A core concept in statistical estimation theory that characterizes the optimal convergence rate achievable among all estimators over all possible data-generating distributions. The minimax risk is defined as the optimal error obtained by taking the supremum over all parameters and the infimum over all estimators, providing both a benchmark of statistical difficulty and a performance standard for optimal algorithms.
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The instance-optimal rate refers to the convergence rate of an algorithm on each specific problem instance, rather than only a uniform suboptimal rate in the worst case; the minimax rate characterizes the worst-case optimality of an algorithm over all problem instances.
For simple non-trivial eigenpairs, the paper establishes a minimax rate of n^{-s/(d+2s)} for eigenvalue and eigenfunction approximation.
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The instance-optimal rate refers to the convergence rate of an algorithm on each specific problem instance, rather than only a uniform suboptimal rate in the worst case; the minimax rate characterizes the worst-case optimality of an algorithm over all problem instances.
50%UnverifiedFor simple non-trivial eigenpairs, the paper establishes a minimax rate of n^{-s/(d+2s)} for eigenvalue and eigenfunction approximation.
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