2014/01/07 by Atul Mallik, Mallik, Atul, Moulinath Banerjee +3
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1401.1403
arxiv created 2014/01/07 · arxiv updated 2014/01/08
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.