BUKU ABSTRAK - Universiti Putra Malaysia

New Geometric Approach to Static and Dynamic Measurements of Risk,
Bankruptcy and Market Ranking
Assoc. Prof. Dr. Noor Akma Ibrahim
Alireza Bahiraie, AKM Azhar and Ismail Mohd.
Institute of Mathematical Research, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
+603-8946 6873; nakma@putra.upm.edu.my
Semiparametric Modelling of Longitudinal Ordinal Data
Assoc. Prof. Dr. Noor Akma Ibrahim
Suliadi Isa Daud and Isthrinayagy S. Krishnarajah
Institute of Mathematical Research, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
+603-8946 6873; nakma@putra.upm.edu.my
201
Science, Technology & Engineering
Recently, geometrics are more frequently used in business, finance, scientific, and engineering applications.
The increasing popularity of geometry is due to its adaptability and simplicity. In this research, a new geometric
methodology for forecasting were developed and implemented. Our new static (Risk Box, RB) and dynamic
(Dynamic Risk Space, DRS) geometric methodology and our new copy righted software (Dynamic Geometric
Risk Space Software, DGRSS) can be used to solve the most important factors when errors are engaged in
financial forecastings. This methodology takes into account every related component of financial predictions. Our
algorithm combined the powerful search of geometric approach and its capability to learn about the relationship
patterns of past data in order to forecast future values. This new geometric forecasting method consists of two
steps: forecasting and learning steps. We used our new geometric indexes in the forecasting step to estimate
parameters of the problem domain. Patterns learning are taken into account in the software algorithm to capture
the patterns relationship of learning data. Then the effectiveness of the methodology is examined by applying
them in bankruptcy prediction field of finance.
Keywords: Geometric approach, risk box, bankrupcty, genetic programming, robust logistic regression
This research considers semiparametric model for longitudinal ordinal data. The model consists of two
components, parametric and nonparametric components. We propose GEE-Smoothing spline to estimate both
components by extending parametric generaliszed estimating equation (GEE) to semiparametric GEE. The
nonparametric component is estimated using smoothing spline while the association parameter is estimated
through another set of estimating equation. We use profile algorithm in the estimation of both components. In this
algorithm, the components are treated in different manner. The properties of the parametric and nonparametric
components of the proposed model are evaluated through simulation study. Both components are consistent
regardless of misspecification of the working correlation. The bias of the parametric component is small and
negligible whereas the nonparametric component is bias. The most efficient estimate for the parametric component
is obtained if the true correlation structure is used and assumed independence results in a less efficient estimate.
The efficiency behaviour of the nonparametric component is different from parametric where the most efficient
estimate is obtained when independence is assumed.
Keywords: Semiparametric equation, longitudinal ordinal data, generalised estimating equation, smoothing spline, property
of estimator