Some Robust methods for Estimates the power Spectrum in ARMA Models Simulation Study

Abstract

Abstract:

Robust statistics Known as, resistance to errors caused by deviation from the stability hypotheses of the statistical operations (Reasonable, Approximately Met, Asymptotically Unbiased, Reasonably Small Bias, Efficient ) in the data selected in a wide range of probability distributions whether they follow a normal distribution or a mixture of other distributions deviations different standard .

power spectrum function lead to, President role in the analysis of Stationary random processes, form stable random variables organized according to time, may be discrete random variables or continuous. It can be described by measuring its total capacity as function in frequency.

 As supposed distribution of the data mistakes in accordance with the normal or approach to the normal distribution ،Share estimation methods fortified with the concept of nonparametric in the absence of a clear model parameters (Free distribution) as the contamination is unknown model has distributed part of it in accordance with the normal distribution, while the other part is unknown distribution, and thus became the distribution of tainted its parameters unknown, so it can be considered the highest level in grades nonparametric methods are based on the conversion calculable test to a standard degree held by the convergence class standard process.

The aim of the Search: compared to some of the Robust estimation methods and non-parametric, So find the best estimator of Power spectrum With the mixed ARMA model for time series follow a Normal distribution, Then,  applied the most accurate on realistic data About the diagnosis of the factors that reflect the sources of change in time series of the electrical reference (ECG - Electrocardiogram) in normal state (unsatisfactory), through the analysis of the power spectrum. By finding the best estimator of the ability of spectrum according to the mixed spectrum for Series follow a particular dist. & applied to Real data(ECG), The method adopted other Parameters to get realistic results are related to the behavior of the real System reference (ECG)the Capabilities of ability Normal dist. Increase with the size of the Section ,and the highest at Section 200 in a manner Tokey