{'fraction_non_alphanumeric': 0.031512605042016806, 'fraction_numerical': 0.01050420168067227, 'mean_word_length': 5.037974683544304, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Moment convergence of M‐estimators

This study extends the rate of convergence theorem of M‐estimators presented by van der Vaart and Wellner (weak convergence and empirical processes: with applications to statistics, Springer‐Verlag, Newyork, 1996) who gave a result of the form r to a result of the form supnE | r , for any p≥1. This result is useful for deriving the moment convergence of the rescaled residual. An application to maximum likelihood estimators is discussed.