{'fraction_non_alphanumeric': 0.02558139534883721, 'fraction_numerical': 0.019767441860465116, 'mean_word_length': 5.833333333333333, '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}}
Monotone Nonparametric Regression for Functional/Longitudinal Data

Motivated by quantifying the monotonic relationship between gray matter (GM) volume and age in the older population, this study proposes a constrained nonparametric estimation and statistical inference for the monotone mean function of functional/longitudinal data. Under some mild conditions, we systematically investigate the asymptotic properties of the proposed estimators, using a general weighting scheme that includes an equal weight per observation (OBS) and an equal weight per subject (SUBJ) as special cases. Most existing methods without a structural constraint can handle sparse or dense data only. Thus, a subjective choice between the two types may lead to erroneous conclusions from statistical inferences. Our proposed 1 Statistica Sinica: Preprint doi:10.5705/ss.202018.0233