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Estimation of Covariance Matrix and Inference About Regression Coefficients and Autocorrelation in Heteroskedastic Regression Models

Thesis Info

Access Option

External Link

Author

Nuzhat Aftab

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12476/1/Nuzhat%20Aftab%20statistics%202019_UoPunjab_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726092383

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The inference about the parameters of regressionmodel and autocorrelation is a challenging task in the presence of heteroskedasticity. In this scenario the heteroskedastic consistent covariance matrix estimators (HCCMEs) and variance ratio (VR) tests are widely used methods to obtain valid inference about regression parameters and autocorrelation respectively. For this purpose, several methods have been suggested in literature. But these methods generally work well when the sample size is sufficiently large and heteroskedasticity level is not very high. In this thesis, we have studied these methods for linear regression model in small samples with high level of heteroskedasticity. In first part of this thesis, we suggest a new heteroskedastic consistent (HC) covariance matrix estimator which takes into account the effect of leverage observations and has better approximation of its true asymptotic distribution. We point out that the basic motivation behind this new modified HC estimator is to provide an estimator which does not require any user specified values. In terms of bias and mean squared error (MSE) a Monte Carlo simulation study provided evidence that this new estimator has better small sample properties over some existing estimators. Real life example also evaluated the finite sample behavior in comparison to those existing estimators. In the second part we suggest heteroskedastic consistent covariance matrix estimator, HC6d, which is based on deviance measure. We have studied the finite sample behavior of the test statistic based on this new HC estimator. We compare its performance with other HC estimators namely HC1, HC3 and HC4m, which are also used in case of leverage observations. Extensive simulation are used to study the effect of various levels of heteroskedasticity on the performance of the quasi tests based on HC estimators. Results showed that the test statistic based on new suggested estimator has better asymptotic approximation and less size distortion in small samples especially when high level heteroskedasticity is present in the data. It has been known that the autocorrelation test do not perform well in presence of heteroskedasticity and variance break case. The remedies to this have been suggested by Jeong and Kang (2012), Shim et al. (2006) and Kim (2006). In the last part of the thesis, we suggested three weighted variance ratio test to test the autocorrelation in presence of heteroskedasticity and variance break. We show through monte carlo simulation that new suggested tests perform well in small samples and are comparable with other tests in terms of size and much better in terms of power properties and also when lag length is misspecified.
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تُو تو بالکل پتھر سا ہے

تُو تو بالکل پتھّر سا ہے
پر مجھ کو اچّھا لگتا ہے

تیرے شہر میں کیا رکھا ہے
دل مجھ کو پھِر لے آیا ہے

ساری گلیاں گھُوم چُکا ہوں
تیری گلی سے ڈر لگتا ہے

اب ان سڑکوں پر تنہا ہوں
جن پر کبھی تو ساتھ چلا ہے

چاند کو دیکھ کے مجھ کو ہمیشہ
یاد ترا چہرا آتا ہے

چاند بادلوں میں چُھپ چُھپ کر
مجھ کو تنگ بہت کرتا ہے

پانی جس کو سمجھ رہا تھا
وہ تو نظر کا اِک دھوکا ہے

تُجھ کو میں کب بھول سکا ہوں
تُو تو مجھ کو بھول چکا ہے

یادیں بھی کیا چیز ہیں صادق
حال بُرا دِل کا ہوتا ہے

An Eco-critical Reading of William Wordsworth's Poetry and Pantheistic Strains in his Poetry

The relation between people and environment has long been documented through literary works. Edward white gives the example of Adam and Eve journey through the Garden of Eden in the Bible and Odyssey dangerous trek across the Mediterranean Sea in Homer’s Odyssey as early literary examples in which human path cross the nature and interact with the beauty of nature.

Role of Technology in the Enhancement of English Language Speaking Skills of High School Students of Gojal, Gilgit Baltistan

English language, the ‘lingua franca’ of the globalized world necessitates (Jenkins, 2009) even countries where it is not spoken as the first language to institute it as a second language (Caine 2008). Pakistan is also amongst one of the countries where English language is given much importance and is being taught as a compulsory subject from Early Childhood Development (ECD) to graduation level. Literature (Ahmed, 2011; Noreen, Ahmed & Esmail, 2015) says that in Pakistani English as a Second Language (ESL) classrooms, reading and writing are the two main skills that are focused on more, while the two other language sub-skills: speaking and listening are ignored. Experiential data, specifically relating to the rural and far-flung areas of Pakistan, like Gojal, traditional method teaching and learning practices are also prevalent there: due to which the learners of (English language) EL lack in speaking skills. As a result of the growing numbers of ESL learners, there is an ongoing search for new, effective and efficient instructional methods for the improvement of the teaching and learning processes in English language. In the 21st century, technology has gained substantial attention due it offering an abundance of devices and tools that make authentic language input accessible to EL learners (Frenik, 2013). Technology and its usefulness in developing language sub-skills is being explored as an option in formal and informal settings in many parts of the developing world where access to authentic language input is limited due to the areas in question being relatively remote (Hsu, 2013). However, there seems to be a dearth of descriptive data on the role technology plays or is seen as playing for EL learning in the remote areas of Pakistan. Accordingly, a sequential mixed methods design was employed to explore the role of technology in the enhancement of high school students’ English language speaking skills. The data was collected in two phases. In the first phase, semi-structured-interviews were used to collect data from English language teachers. Two Focus Group Discussions (FGDs) were also conducted to obtain data from the students. In the second phase, a mixture of open-ended, 4 and 5 point rating scale questionnaire was developed based on the emerging themes of the first phase and was administered to 116 high school ESL learners. The study findings revealed that technology is perceived as a tool that supports students in the enhancement of their speaking skills. Technologies such as television,