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Bridge Estimation for Linear Regression Models with Mixing Properties
Author(s) -
Lee Taewook,
Park Cheolwoo,
Yoon Young Joo
Publication year - 2014
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12075
Subject(s) - mathematics , estimator , autoregressive–moving average model , mixing (physics) , time series , autoregressive model , asymptotic distribution , linear regression , regression analysis , bridge (graph theory) , consistency (knowledge bases) , regression , series (stratigraphy) , statistics , autoregressive integrated moving average , medicine , paleontology , physics , geometry , quantum mechanics , biology
Summary Penalized regression methods have for quite some time been a popular choice for addressing challenges in high dimensional data analysis. Despite their popularity, their application to time series data has been limited. This paper concerns bridge penalized methods in a linear regression time series model. We first prove consistency, sparsity and asymptotic normality of bridge estimators under a general mixing model. Next, as a special case of mixing errors, we consider bridge regression with autoregressive and moving average (ARMA) error models and develop a computational algorithm that can simultaneously select important predictors and the orders of ARMA models. Simulated and real data examples demonstrate the effective performance of the proposed algorithm and the improvement over ordinary bridge regression.