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arXiv · 1401.1403

M-estimation in multistage sampling procedures

Atul Mallik·Moulinath Banerjee·George Michailidis
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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 and mode 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.

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Atul Mallik, Moulinath Banerjee, George Michailidis. 2014-01-07. M-estimation in multistage sampling procedures. https://arxiv.org/abs/1401.1403

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