M-estimation in Multistage Sampling Procedures

Atul Mallik (), Moulinath Banerjee () and George Michailidis ()
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Atul Mallik: Wells Fargo Securities
Moulinath Banerjee: University of Michigan
George Michailidis: University of Florida

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 1, 309 pages

Abstract: Abstract Multi-stage (designed) procedures, obtained by splitting the sampling budget suitably across stages, and designing the sampling at a particular stage based on information about the parameter obtained from previous stages, are often advantageous from the perspective of precise inference. We develop a generic framework for M-estimation in a multistage setting and apply empirical process techniques to develop limit theorems that describe the large sample behavior of the resulting M-estimates. Applications to change-point estimation, inverse isotonic regression, classification, mode estimation and cusp estimation are provided: it is typically seen that the multistage procedure accentuates the efficiency of the M-estimates by accelerating the rate of convergence, relative to one-stage procedures. The step-by-step process induces dependence across stages and complicates the analysis in such problems, which we address through careful conditioning arguments.

Keywords: Cusp estimation; M-Estimation; Multistage sampling procedures; Primary 62E20; 62G20; Secondary 62L99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13171-019-00194-z

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