Varying kernel marginal density estimator for a positive time series |
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Authors: | N Balakrishna Hira L Koul |
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Institution: | 1. Department of Statistics, Cochin University of Science and Technology Kochi, Kerala, India;2. Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA |
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Abstract: | This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel. |
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Keywords: | Strongly mixing almost sure |
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