۲۱۱۳۱پ
per
آزمون فرض خطی عام در تحلیل واریانس چند متغیری ی طرفه با بعد الا
Linear hypothesis testing in high-dimensional one-way MANOVA
/آی سان علیپور
: علوم ریاضی
، ۱۳۹۷
، راشدی
۵۳ص
چاپی - الکترونیکی
کارشناسی ارشد
آمار گرایش آمار ریاضی
۱۳۹۷/۱۰/۲۶
تبریز
امروزه با رشد سریع علم و تکنولوژی، توانائ محققین بر جمع آوری داده های متناظر با کمیت های مورد مطالعه افزایش یافته است .به عبارت دی‌ر بعد داده ها در بسیاری از مطالعات بر خلاف زمان های قبل بزرگ شده است .چنین داده هائ را داده های با بعد بالا گویند .همانطور که م دانیم، در ادبیات چند متغیره، آزمون برابری میانگین های چندین جامعه که در قالب تحلیل واریانس چند متغیره )(MANOV A ی طرفه انجام م شود، ی از شناخته شده ترین آزمون ها در این حوزه است .برای داده هائ با بعد بالا این نوع از تحلیل مورد مطالعه قرار گرفته است .آزمون فرض خط عام، در تحلیلMANOV A به مانند داده های کلاسی در داده هائ با بعد بالا نیز از اهمیت خاص برخوردار است .در این پایان نامه قصد داریم به بحث در مورد آزمون این فرض یعن آزمون فرض خط عام در تحلیلMANOV A ی طرفه، بپردازیم .برای این کار آماره ی آزمون معرف و با اعمال ی سری شرایط روی ماتریس های کوواریانس این جوامع، توزیع تقریبی نرمال برای توزیع این آماره ارائه م دهیم
In recent years, with the rapid development of data collecting technologies, highdimensional data have become increasingly prevalent. Much work has been done for testing hypotheses on mean vectors, especially for high-dimensional two-sample problems. Rather than considering a specific problem, we are interested in a general linear hypothesis testing (GLHT) problem on mean vectors of several populations, which includes many existing hypotheses about mean vectors as special cases. A few existing methodologies on this important GLHT problem impose strong assumptions on the underlying covariance matrix so that the null distributions of the associated test statistics are asymptotically normal. In this paper, we propose a simple and adaptive test based on the L2-norm for the GLHT problem. For normal data, we show that the null distribution of our test statistic is the same as that of a chi-squared type mixture which is generally skewed. Therefore, it may yield misleading results if we blindly approximate the underlying null distribution of our test statistic using a normal distribution. In fact, we show that the null distribution of our test statistic is asymptotically normal only when a necessary and sufficient condition on the underlying covariance matrix is satisfied. This condition, however, is not always satisfied and it is not an easy task to check if it is satisfied in practice. To overcome this difficulty, we propose to approximate the null distribution of our test statistic using the well-known WelchSatterthwaite chisquared approximation so that our new test is applicable without any assumption on the underlying covariance matrix. Simple ratio-consistent estimators of the unknown parameters are obtained. The asymptotic and approximate powers of our new test are also investigated. The methodologies are then extended for non-normal data. Four simulation studies and a real data application are presented to demonstrate the good performance of our new test compared with some existing testing procedures available in the literatureIn recent years, with the rapid development of data collecting technologies, highdimensional data have become increasingly prevalent. Much work has been done for testing hypotheses on mean vectors, especially for high-dimensional two-sample problems. Rather than considering a specific problem, we are interested in a general linear hypothesis testing (GLHT) problem on mean vectors of several populations, which includes many existing hypotheses about mean vectors as special cases. A few existing methodologies on this important GLHT problem impose strong assumptions on the underlying covariance matrix so that the null distributions of the associated test statistics are asymptotically normal. In this paper, we propose a simple and adaptive test based on the L2-norm for the GLHT problem. For normal data, we show that the null distribution of our test statistic is the same as that of a chi-squared type mixture which is generally skewed. Therefore, it may yield misleading results if we blindly approximate the underlying null distribution of our test statistic using a normal distribution. In fact, we show that the null distribution of our test statistic is asymptotically normal only when a necessary and sufficient condition on the underlying covariance matrix is satisfied. This condition, however, is not always satisfied and it is not an easy task to check if it is satisfied in practice. To overcome this difficulty, we propose to approximate the null distribution of our test statistic using the well-known WelchSatterthwaite chisquared approximation so that our new test is applicable without any assumption on the underlying covariance matrix. Simple ratio-consistent estimators of the unknown parameters are obtained. The asymptotic and approximate powers of our new test are also investigated. The methodologies are then extended for non-normal data. Four simulation studies and a real data application are presented to demonstrate the good performance of our new test compared with some existing testing procedures available in the literature
Linear hypothesis testing in high-dimensional one-way MANOVA
علیپور، آی سان
Alipoor, Aysan
سیاه و سفید
نمایه‌سازی قبلی
