بعض المقدرات الحصينة لقدرة الطيف وفق الانموذج المختلط ARMA مع تطبيق عملي == Some Robust Estimators For Power Spectrum According To The Arma Models With Application
Author name:
سحر طارق محمود الرحيم
Supervisor name:
عبد المجيد حمزة الناصر
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Doctorate
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T3718 - p.pdf
Abstract:
تهدف الاطروحة ايجاد افضل مقدر(التقدير الامثل) لدرجة ارتداد الانموذج المختلط ARMA ذي الدرجات المتدنية لقدرة الطيف Power Spectrum والحصول على امثلية التنبؤ، اذ ان مشكلة الاطروحة تكمن في خطا اعتماد اساليب تقدير درجة الارتداد قبل اطفاء اثر الشواذ التجميعية ( | The Aim of The thesis is finding the best estimator (optimal estimate) the degree of rebound mixed model ARMA with low scores to Power Spectrum and get optimizing forecasting, As the problem of the thesis lies the mistake of adopting methods of estimating rebound degree before extinguishing (AO) Outliers (additives Values) in an estimate operation based on data series without getting rid of the effect of the presence of Outliers. According to This thesis addressing the Existence of the Outliers, in particular, (AO) Outliers after addressing the existence of Outliers, then starting estimate the optimization for a rebound.When interest in Robust estimates we must identify the time series contaminated Outliers with a certain probability models is defined due to lack of stability in addition to the difficulty of knowing specimen probabilistic it appears at first paragraph leap suddenly are called stereotypes Bahawaz Innovation Outlier, late to be the behavior of independent gay behavior values the other called Bahawaz aggregate Additive Outliers.When interest in estimates fortified must identify the time series contaminated Outliers with a certain probability models Unlimited Parameters is defined due to lack of Stationarity in addition to the difficulty of knowing probabilistic model ,it appears at first paragraph sudden leap are called Innovation Outlier, or be an independent behavior of other values called Additive Outliers.Shows the experimental side of the Thiess through a standard MSE, MAPE preference of Robust method on the Unrobes for all sample sizes and for all primary parameters assumed values, as well as for all default frequencies values (Wi), have an adverse impact in terms of efficiency when models ARMA (0,1), ARMA ( 0.2), and very slight variation when the model ARMA (1,1) the impact of outliers and the supposed frequencies (w) = [1/4, 1 / 3.3, 1 / 2.5, ½] small.The nature of the electrical signal surveyed of heart (ECG - Electrocardiogram) a vital signal , unstable and the form of Signal spectrum reflects the Performance of the human heart muscle and its health.is random changes sharp and irregular in time series represents the work of the heart of a natural person (without straining) include what is known Outliers caused by its actual nature not the result of errors in the measurement or the register, which makes them do not follow a particular distribution, led to the difficulty of conducting Assessments for Power spectrum according to the traditional methods of estimation that assumes distributed statistically,In addition to that the data generation processes require the availability of basic assumptions is inconsistent with the nature of the Heart signal ECG, and to minimize or reduce these assumptions adopted by the simulation approach often leads to unrealistic and far from the real system results and establishes a breakthrough for good properties of these estimates that we have made it necessary to adopt the idea of Robust estimates (M - estimate) in accordance with the Robust functions (Huber, Hample, Tukey, Andrew) in addition to the method of maximum likelihood Mle according to restricted simulations in the practical side, which serves as a purification process or soften the Estimators resulting from follow of statistical estimation methods on real data to determine the best estimators of Power spectrum and the search for the best Model and section distribution , and then apply the result of a trade - offs in according to indicator the indirect transition of the speed of the signal (?/S2) between the Estimation functions and Distributions on eight of combinations of Mixed model ARMA (p, q) and estimating MSE, RMSE and selecting the optimum combination which is ARMA (2,2) with Extreem value distribution and with Hampel function at section 200, which amounted to (MSE = 0.000109).
