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On inference for modes under long memory
Author(s) -
Beran Jan,
Telkmann Klaus
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12476
Subject(s) - mathematics , estimator , inference , maxima , consistency (knowledge bases) , kernel density estimation , kernel (algebra) , multivariate kernel density estimation , set (abstract data type) , multivariate statistics , density estimation , probability density function , strong consistency , function (biology) , statistics , variable kernel density estimation , kernel method , discrete mathematics , artificial intelligence , computer science , art , performance art , evolutionary biology , support vector machine , programming language , biology , art history
Abstract We consider inference for local maxima of the marginal density function of strongly dependent linear processes. Weak consistency of the estimated modular set and the number of modes is derived. A uniform reduction principle for kernel density estimators is used to obtain confidence sets for the set of modes. The results can be extended to multivariate modes. Simulations illustrate the asymptotic results.