The robust estimation of autoregressive processes by functional least squares

1983 ◽  
Vol 20 (4) ◽  
pp. 737-753 ◽  
Author(s):  
C. R. Heathcote ◽  
A. H. Welsh
Keyword(s):  
Weak Convergence ◽  
Least Squares ◽  
Robust Estimation ◽  
Autoregressive Model ◽  
Minimum Variance ◽  
Error Distribution ◽  
Autoregressive Processes ◽  
Uniform Consistency ◽  
The Family ◽  
Error Distributions

The stationary autoregressive model but with a long-tailed error distribution is analysed using the method of functional least squares. A family of estimators indexed by a real parameter is obtained and uniform consistency and weak convergence established. The optimum member of the family is chosen to have minimum variance with respect to the parameter, and the parameter value chosen detects and adjusts for long-tailed error distributions. Results of a simulation are given.

The robust estimation of autoregressive processes by functional least squares

1983 ◽  
Vol 20 (04) ◽  
pp. 737-753 ◽  
Author(s):  
C. R. Heathcote ◽  
A. H. Welsh
Keyword(s):  
Weak Convergence ◽  
Least Squares ◽  
Robust Estimation ◽  
Autoregressive Model ◽  
Minimum Variance ◽  
Error Distribution ◽  
Autoregressive Processes ◽  
Uniform Consistency ◽  
The Family ◽  
Error Distributions

The stationary autoregressive model but with a long-tailed error distribution is analysed using the method of functional least squares. A family of estimators indexed by a real parameter is obtained and uniform consistency and weak convergence established. The optimum member of the family is chosen to have minimum variance with respect to the parameter, and the parameter value chosen detects and adjusts for long-tailed error distributions. Results of a simulation are given.

Autoregressive processes with infinite variance

1977 ◽  
Vol 14 (02) ◽  
pp. 411-415 ◽  
Author(s):  
E. J. Hannan ◽  
Marek Kanter
Keyword(s):  
Least Squares ◽  
Autoregressive Model ◽  
Infinite Variance ◽  
Autoregressive Processes ◽  
Stable Law ◽  
Least Squares Estimators ◽  
Data Points

The least squares estimators β i(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(β i(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi (N).

Functional least squares estimators in an additive effects outliers model

1990 ◽  
Vol 48 (2) ◽  
pp. 299-319 ◽  
Author(s):  
Sunil K. Dhar
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Least Squares ◽  
Strong Consistency ◽  
Additive Effects ◽  
Uniform Consistency ◽  
Least Squares Estimators

AbstractConsider the additive effects outliers (A.O.) model where one observes , with The sequence of r.v.s is independent of and , are i.i.d. with d.f. , where the d.f.s Ln, n ≦ 0, are not necessarily known and εj's are i.i.d.. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.

Autoregressive processes with infinite variance

1977 ◽  
Vol 14 (2) ◽  
pp. 411-415 ◽  
Author(s):  
E. J. Hannan ◽  
Marek Kanter
Keyword(s):  
Least Squares ◽  
Autoregressive Model ◽  
Infinite Variance ◽  
Autoregressive Processes ◽  
Stable Law ◽  
Least Squares Estimators ◽  
Data Points

The least squares estimators βi(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(βi(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi(N).

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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