برآوردگر آستانه موجک تابع رگرسیون نیمه‌پارامتری با خطاهای همبسته

نویسندگان
محمود افشاری
ابوذر بازیاری
حمید کرمی کبیر
دانشگاه خلیج فارس بوشهر، گروه آمار
چکیده
آنالیز موجکی یکی از تکنیک‌های مفید در ریاضی است که در سال‌های اخیر در علم آمار بسیار مورد استفاده قرار گرفته شده است. در این مقاله، ضمن معرفی تبدیل موجک، برآورد آستانه موجک تابع رگرسیون نیمه‌پارامتری با خطاهای همبسته تعیین شده و سپس نرخ همگرایی برآوردگر محاسبه می‌شود. برای ارزیابی برآوردگر آستانه موجک، از دو تابع سینوسی و تابع بلوکی به عنوان توابع هدف استفاده خواهد شد و با استفاده از روش شبیه‌سازی، متوسط میانگین مربع خطا و مقدار انحراف معیار این برآوردگر با متوسط میانگین مربعات خطاها و مقادیر انحراف معیارهای بدست آمده با روش هسته‌ موجک مقایسه می‌شوند. همچنین برای ارزیابی روش ارائه شده، تابع رگرسیون نیمه‌پارامتری موجکی بر روی داده‌های مربوط به میزان رشد دندان برازش داده شده است.
کلیدواژه‌ها
آستانه موجک
خطاهای همبسته
رگرسیون نیمه‌پارامتری
نرخ همگرایی

عنوان مقاله English

Wavelet Threshold Estimator of Semiparametric Regression Function with Correlated Errors

نویسندگان English

Mahmoud Afshari
Abouza Bazyari
Hamid Karamikabir
Department of Statistics, Persian Gulf University, Bushehr, Iran
چکیده English

Wavelet analysis is one of the useful techniques in mathematics which is used much in statistics science recently. In this paper, in addition to introduce the wavelet transformation, the wavelet threshold estimation of semiparametric regression model with correlated errors with having Gaussian distribution is determined and the convergence ratio of estimator computed. To evaluate the wavelet threshold estimation, the block function and sinusoidal function are used as objective functions and using the simulation method the average of mean square error and standard deviation of this estimator are compared with the average of mean square error and standard deviation of kernel method. Also, the wavelet semiparametric regression model has been fitted to data on the growth rate of the teeth.

کلیدواژه‌ها English

Convergence ratio
Correlated errors
Semiparametric regression
Wavelet threshold
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