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We present an efficient method to estimate cross-validation bandwidthparameters for kernel density estimation in very large datasets where ordinarycross-validation is rendered highly inefficient, both statistically andcomputationally. Our approach relies on calculating multiple cross-validationbandwidths on partitions of the data, followed by suitable scaling andaveraging to return a partitioned cross-validation bandwidth for the entiredataset. The partitioned cross-validation approach produces substantialcomputational gains over ordinary cross-validation. We additionally show thatpartitioned cross-validation can be statistically efficient compared toordinary cross-validation. We derive analytic expressions for theasymptotically optimal number of partitions and study its finite sampleaccuracy through a detailed simulation study. We additionally propose apermuted version of partitioned cross-validation which attains even higherefficiency. Theoretical properties of the estimators are studied and themethodology is applied to the Higgs Boson dataset with 11 million observations

Partitioned Cross-Validation for Divide-and-Conquer Density Estimation