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New Diagnostic Methods for Influential Observations in Linear Regression With Some Biased Estimation Methods

Thesis Info

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Author

Kashif, Muhammad

Program

PhD

Institute

Bahauddin Zakariya University

City

Multan

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11952/1/Muhammad%20Kashif%20statistics%202019%20bzu%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726751259

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This thesis is concerned with the expansion of diagnostic methods in parametric regression models with some biased estimators. Of which, the Liu estimator, modified ridge estimator, improved Liu estimator and ridge estimator have been developed as an alternative to the ordinary least squares estimator in the presence of multicollinearity in linear regression models. Firstly, we introduce a type of Pena’s statistic for each point in Liu regression. Using the forecast change property, we simplify the Pena’s statistic in a numerical sense. It is found that the simplified Pena’s statistic behaves quite well as far as detection of influential observations is concerned. We express Pena’s statistic in terms of the Liu leverages and residuals. For numerical evaluation, simulated studies are given and a real data set has been analyzed for illustration. Secondly, we formulated Pena’s statistic for each point while considering the modified ridge regression estimator. Using this statistic, we showed that when modified ridge regression was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The normality of this statistic was also discussed and it was proved that it could detect a subset of high modified ridge leverage outliers. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. Next, we introduce a type of Pena’s statistic for each point in the improved Liu estimator. Using this statistic, we showed that when the improved Liu estimator was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. The ridge estimator having growing and wider applications in statistical data analysis as an alternative technique to the ordinary least squares estimator to combat multicollinearity in linear regression models. In regression diagnostics, a large number of influence diagnostic methods based on numerous statistical tools have been discussed. Finally, we focus on ridge version of Nurunnabi et al. (2011) method for identification of multiple influential observation in linear regression. The efficiency of the proposed method is presented through several well-known data sets, an artificial large data with high-dimension and heterogeneous sample and a Monte Carlo simulation study.
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ولیم میکڈوگل

ولیم میکڈوگل
گذشتہ نومبر میں انگلستان کے مشہور ماہر نفسیات ولیم میکڈوگل کا انتقال ہوگیا، وہ ۱۸۷۱؁ء میں لنکاشائر میں پیدا ہوا،مانچسٹر میں تعلیم پاکر کیمبرج یونیورسٹی میں داخل ہوا، اور آخر میں لندن یونیورسٹی سے طب کی ڈگری حاصل کی، لیکن نفسیات میں اس کا مطالعہ اتنا گہرا تھا کہ وہ لندن یونیورسٹی میں اس کا لکچرار مقرر ہوا، اور پھر ذہنی فلسفہ کا پروفیسر ہوکر آکسفورڈ چلاگیا، ۱۹۲۰؁ء میں وہ ممالک متحدہ بلالیا گیا، جہاں وہ ہارورڈ اور ڈیوک یونیورسٹی میں معلمی کے فرائض انجام دیتا رہا۔
اس نے مندرجہ ذیل کتابیں لکھی ہیں، جن میں سے ہر ایک کے بہت سے اڈیشن شائع ہوچکے ہیں، (۱)خلاف معمول نفسیات کا ایک خاکہ، (۲)ذہین اجتماع، (۳)نفسیات کردار کا مطالعہ، (۴)مردوں کی قوتیں، (۵)زندگی کا مذہب اور سائنس، (۶)بورنیو کے غیر شائستہ قبائل، (۷)معاشرتی نفسیات کا مقدمہ، (۸)نفسیات کا ایک خاکہ، (۹)’’زندگی کی سیرت اور طور طریقے، ان میں ’’معاشرتی نفسیات کا مقدمہ‘‘ زیادہ مقبول ہے، نفسیات سے دلچسپی رکھنے والے طلبہ کے لئے ’’نفسیات کا ایک خاکہ‘‘ بھی مفید اور ضروری کتاب ہے، زندگی کی سیرت اور طور طریقے‘‘ آسان اور عام پسند ہے۔
ولیم میکڈوگل نے نفسیات کے اتنے مختلف نظریئے قائم کئے ہیں، کہ ان پر آئندہ بہت سی کتابیں اور شرحیں لکھی جائیں گی، لیکن اس نے سب سے زیادہ ’’جبلت‘‘ پر لکھا ہے، جبلت کی تعریف اس نے یہ کی ہے کہ یہ حسب منشا کام کرنے کی ایک فطری اور پیدائشی صلاحیت کا نام ہے، جو انسان کے علاوہ جانوروں، پرندوں اور کیڑوں پر بھی پائی جاتی ہے، ولیم میکڈوگل کے خیال کے مطابق چودہ جبلتیں ہوتی ہیں، مثلاً نقل، کھیل، خوشی، محبت، نفرت، غصہ، رنج، لڑائی، فرار، بے چینی، غول بندی، جنسی خواہش وغیرہ، بعض ماہرین نفسیات کا خیال ہے کہ جبلتیں صرف تین ہی ہوتی ہیں، خود غرضانہ، معاشرتی...

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