fa یک نرخ همگرایی در رگرسیون خطی تابعی با نقاط تأثیر آمار Stat علمی پژوهشی بنیادی S <span style="font-size:11pt"><span style="line-height:23.0pt"><span style="direction:rtl"><span style="unicode-bidi:embed"><span style="font-family:Calibri,sans-serif"><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">&nbsp;&nbsp;&nbsp; مدل رگرسیون خطی تابعی کلاسیک با پاسخ اسکالر به‌طور گسترده‌ مورد استفاده قرار گرفته است. با این حال، اثرات موضعی تابع پیشگو روی پاسخ را نمی‌توان با این مدل ارزیابی کرد، زیرا این مدل فقط یک میانگین وزنی از کل مسیر پیشگو روی پاسخ را در نظر می‌گیرد. برای رفع این مشکل تعمیمی از مدل رگرسیون خطی تابعی کلاسیک را با افزودن تعداد نامعلومی از نقاط تأثیر در نظر می‌گیریم، با این ویژگی که مقادیر پیشگو به ازای این نقاط، تأثیر معنی‌داری روی پاسخ دارند. نقاط تأثیر و ضرایب آن‌ها، تابع شیب، ویژه‌مقدارها و ویژه‌تابع‌های عملگر کوواریانس پیشگو نامعلوم هستند و باید برآورد شوند. در این مقاله نرخ همگرایی یک کمیت ساخته شده بر پایه‌ی این پارامترهای نامعلوم را به‌دست آورده‌ایم. از این نتیجه می‌توان در استنباط‌های آماری آینده برای این مدل از جمله یافتن بازه‌های اطمینان و بازه‌های اطمینان بوت استرپی استفاده کرد. علاوه بر این، یک مطالعه‌ی شبیه‌سازی نیز برای ارزیابی نتیجه‌ی به‌دست آمده انجام داده‌ایم.</span></span></span></span></span></span></span><br> &nbsp; <span style="font-size:11pt"><span style="line-height:21.0pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">T</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">h</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">e</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">cla</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">ss</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">ical</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">fun</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">cti</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">on</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">al</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">li</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">n</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">ea</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">r</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">r</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">e</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">gr</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black"><span style="letter-spacing:.05pt">e</span></span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">ss</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">i</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black"><span style="letter-spacing:.05pt">on</span></span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">m</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">od</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">el</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">w</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">it</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">h</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">a</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">s</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">cala</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">r</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">r</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">e</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">spons</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black"><span style="letter-spacing:.05pt">e</span></span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">h</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">a</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">s</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">b</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">ee</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">n</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">w</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">i</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">d</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">el</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">y</span></span></span> <span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">us</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black">e</span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black"><span style="letter-spacing:.05pt">d.</span></span></span></span><span style="font-size:10.5pt"><span new="" roman="" style="font-family:" times=""><span style="color:black"> Howev<span style="letter-spacing:.05pt">e</span><span style="letter-spacing:-.35pt">r</span>, the local e<span style="letter-spacing:-.15pt">f</span>fects of the predictor function on th<span style="letter-spacing:.05pt">e</span> re<span style="letter-spacing:.05pt">spons</span>e cannot be evaluated with thi<span style="letter-spacing:.05pt">s</span> model, as it considers only a weighted average of the entire predictor trajectory in relation to the response<span style="letter-spacing:.05pt">.</span> <span style="letter-spacing:-.7pt">T</span><span style="letter-spacing:-.05pt">o</span> ad-dress this issue, we propose a generalization of the classical functional linear regr<span style="letter-spacing:.05pt">e</span>ssi<span style="letter-spacing:.05pt">on</span> model by add<span style="letter-spacing:.05pt">i</span>ng an unknown number of points of impact, where the predictor values at thes<span style="letter-spacing:-.05pt">e</span> points have <span style="letter-spacing:-.05pt">a</span> significant e<span style="letter-spacing:-.15pt">f</span>fect on the response<span style="letter-spacing:.05pt">.</span> The poi<span style="letter-spacing:.05pt">n</span>ts of impact and their coe<span style="letter-spacing:-.15pt">f</span>ficients, the slope function, th<span style="letter-spacing:.05pt">e</span> eigenvalu<span style="letter-spacing:.05pt">e</span>s, and the eigenfunctions of the covariance operator of th<span style="letter-spacing:.05pt">e</span> predict<span style="letter-spacing:.05pt">or</span> are unknown and need t<span style="letter-spacing:.05pt">o</span> b<span style="letter-spacing:.05pt">e</span> estimated. In thi<span style="letter-spacing:.05pt">s</span> pape<span style="letter-spacing:-.4pt">r</span>, we derive the conve<span style="letter-spacing:-.15pt">r</span>gence rate of <span style="letter-spacing:-.05pt">a</span> quantity constructed based on these unknown parameters. Thi<span style="letter-spacing:.05pt">s</span> result can be used in future statistical inferences for this model, including the calculation of confidence in-tervals and bootstrap confidence intervals. Additionall<span style="letter-spacing:-.6pt">y</span>, <span style="letter-spacing:-.05pt">a</span> simulation study has been conducted to evaluate the obtained resu<span style="letter-spacing:.05pt">lt</span>s.</span></span></span></span></span></span><br> &nbsp; رگرسیون خطی تابعی, نقطه‌ی تأثیر, نرخ همگرایی Functional linear regression, Point of impact, Convergence rate 31 44 http://mmr.khu.ac.ir/browse.php?a_code=A-10-1803-1&slc_lang=fa&sid=1 Alireza Shirvani علیرضا شیروانی stat.shirvani@gmail.com 10031947532846006963 10031947532846006963 Yes Velayat University دانشگاه ولایت mohammad Hosseini-Nasab محمد حسینی نسب m_hosseininasab@sbu.ac.ir 10031947532846006964 10031947532846006964 No Shahid Beheshti University دانشگاه شهید بهشتی Omid Khademnoe امید خادم نوع khademnoe@znu.ac.ir 10031947532846006965 10031947532846006965 No University of Zanjan دانشگاه زنجان