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- W4322624769 abstract "Abstract The Markov property is shared by several popular models for time series such as autoregressive or integer-valued autoregressive processes as well as integer-valued ARCH processes. A natural assumption which is fulfilled by corresponding parametric versions of these models is that the random variable at time t gets stochastically greater conditioned on the past, as the value of the random variable at time $$t-1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> increases. Then the associated family of conditional distribution functions has a certain monotonicity property which allows us to employ a nonparametric antitonic estimator. This estimator does not involve any tuning parameter which controls the degree of smoothing and is therefore easy to apply. Nevertheless, it is shown that it attains a rate of convergence which is known to be optimal in similar cases. This estimator forms the basis for a new method of bootstrapping Markov chains which inherits the properties of simplicity and consistency from the underlying estimator of the conditional distribution function." @default.
- W4322624769 created "2023-03-01" @default.
- W4322624769 creator A5012251494 @default.
- W4322624769 date "2023-02-28" @default.
- W4322624769 modified "2023-09-25" @default.
- W4322624769 title "Estimation and bootstrap for stochastically monotone Markov processes" @default.
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- W4322624769 doi "https://doi.org/10.1007/s00184-023-00903-7" @default.
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