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A Massive Data Framework for M-Estimators with Cubic-Rate.

Chengchun Shi1, Wenbin Lu1, Rui Song1

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695.

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Summary
This summary is machine-generated.

This study introduces a divide and conquer strategy for massive data, developing aggregated M-estimators with faster convergence rates and normal distributions for improved computation and inference. The method enhances cubic-rate estimators in massive datasets.

Keywords:
Cubic rate asymptoticsM-estimatorsdivide and conquermassive data

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Massive data analysis presents computational and inferential challenges.
  • The divide and conquer strategy is a common approach for handling large datasets.
  • Cubic-rate estimators are frequently used but can be computationally intensive with massive data.

Purpose of the Study:

  • To develop a general theory for aggregated M-estimators using divide and conquer under a massive data framework.
  • To establish the asymptotic distribution of these aggregated estimators.
  • To demonstrate improved convergence rates and computational tractability compared to traditional M-estimators.

Main Methods:

  • Developing a general theory for asymptotic distribution of aggregated M-estimators.
  • Utilizing a weighted average aggregation method with weights dependent on subgroup sample sizes.
  • Applying the theory to a class of M-estimators with cube root convergence rates.

Main Results:

  • Aggregated M-estimators achieve faster convergence rates under specific conditions on subgroup numbers.
  • The resulting estimators exhibit asymptotic normal distributions, simplifying computation and inference.
  • The theory is validated through simulations and a real-world data application.

Conclusions:

  • The divide and conquer method offers a computationally efficient and statistically sound approach for massive data analysis.
  • Aggregated M-estimators provide a tractable alternative to pooled M-estimators, especially for large-scale cubic-rate estimation.
  • The findings are applicable to various M-estimators, including location, maximum score, and value search estimators.