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Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average

100%

Bryk A.

Applicationes Mathematicae

2014

tom 41

nr 1

67-80

We consider a fixed-design regression model with errors which form a Borel measurable function of a long-range dependent moving average process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We show that the Priestley-Chao kernel estimator of the regression fuction exhibits a dichotomous asymptotic behaviour depending on the amount of smoothing employed. Moreover, the resulting estimator is shown to exhibit weak consistency (i.e. in probability). Simulation results indicate significant improvement when randomization is employed.

Using randomization to improve performance of a variance estimator of strongly dependent errors

100%

Bryk A.

Applicationes Mathematicae

2012

tom 39

nr 3

273-282

We consider a fixed-design regression model with long-range dependent errors which form a moving average or Gaussian process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We estimate the variance of the errors using the Rice estimator. The estimator is shown to exhibit weak (i.e. in probability) consistency. Simulation results confirm this property for moderate and large sample sizes when randomization is employed.

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2 Applicationes Mathematicae

2 Bryk A.

1 2014

1 2012

Wyniki wyszukiwania

Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average

Using randomization to improve performance of a variance estimator of strongly dependent errors