Ph.D. Statistics

Doctor of Philosophy in Statistics

1. List of Academic Staff

Name	Status and Qualifications	Research Interests
G. M. Oyeyemi	Professor & Head of Department B.Sc., M.Sc., Ph.D. (Ilorin)	Multivariate Analysis
B. L. Adeleke	Professor B.Sc. (Ilorin); Dip. Agric Stat. (Washington); M.Sc., Ph.D. (Ilorin)	Design and Analysis of Experiment
A. A. Adewara	Professor B.Sc., M.Sc., Ph.D., PGDE (Ilorin)	Sample Survey Methods and Applications
A. O. Adejumo	Professor B.Sc., M.Sc. (Ilorin); Ph.D. (Munich).	Modelling, Biostatistics, Time Series & Categorical Data Analysis
W. B. Yahya	Professor N.C.E.(Ila-Orangun); B.Sc., M.Sc. (Ilorin); PGDFM, MBA (Ado-Ekiti); Ph.D. (Munich)	Microarray Analysis, Modelling, Data Mining, Categorical Data Analysis, Bayesian Inference & Biostatistics
A. A. Abiodun	Reader B.Sc., M.Sc., Ph.D. (Ilorin)	Survival Analysis & Statistical Modelling
A. O. Abidoye	Reader B.Sc.(Ilorin); M.Sc. (Ibadan); Ph.D. (Ilorin)	Biostatistics and Hypothesis Testing
O. Job	Senior Lecturer NCE (Ilorin); B.Sc., M.Sc., Ph.D. (Ilorin)	Econometrics
M. K. Garba	Senior Lecturer B.Sc , M.Sc., Ph.D.(Ilorin)	Econometrics, Time Series and Statistical Modeling
I. Oloyede	Senior Lecturer N.C.E.(Ila-Orangun); PGDS (UNAAB, Abeokuta); B.Sc.(OAU, Ile-Ife); M.Sc.(Ago- Iwoye); Ph.D. (Ilorin)	Bayesian Inference, Econometrics and Statistical Learning
N. A. Ikoba	Senior Lecturer B.Sc.; M.Sc. (OAU, Ile-Ife); Ph.D. (Ilorin)	Stochastic Processes and Applications, Distribution Theory, Demography
A. W. Banjoko	Senior Lecturer B.Sc , M.Sc., Ph.D.(Ilorin)	Microarray Data Analysis, Biostatistics and Statistical Quality Control

Introduction

The programme is to offer expert teaching and supervision in various aspects of theory and applications of statistics as follows: Analysis of Variance and its Applications, Categorical Data Analysis, Design and Analysis of Experiments, Econometrics, Modeling, Multivariate Analysis, Biostatistics, Repeated Measurements and Analysis, Sample Survey and Sampling techniques, Statistical Quality Control and its Application, Survival Analysis, Stochastic Processes, and Time Series Analysis. The programme will equip students with the skills needed to begin a career as a professional statistician. Graduates from the programme are expected to have a varied skill set including core professional skills, and a portfolio of substantive applied and practical work.

C.                 Philosophy

The philosophy of the programme is anchored on the unbiased and systematic observations, accurate documentation and interpretation of facts and phenomena with view to generate a body of knowledge.

D.                 Aim and Objectives

The primary objective of the Ph. D. in Statistics is to enable graduates of:

1. Master of Science (M.Sc.) Degree in Statistics with a CGPA between 4.00 and 5.00 or weighted score average of 60.00% and above to pursue higher degree programme in Doctor of Philosophy in Statistics or; and
2. Master of Philosophy (M. Phil.) Degree in Statistics with a CGPA between 4.00 and 5.00 or weighted score average of 60.00% and above to pursue higher degree programme in Doctor of Philosophy in Statistics.

E.                 Admission Requirements for Doctor of Philosophy (Ph.D.) in Statistics

1. Admission to the Ph.D. Programme in Statistics is open to candidates who have obtained CGPA between 4.00 and 5.00 or a minimum weighted score of 60.00% or its equivalent in their final Master Degree Examination to qualify for admission into the Doctor of Philosophy Programme. All such candidates must have scored at least 60% (B) in their dissertation.
2. Candidates with Master of Philosophy from the University of Ilorin or any other recognized University must have scored at least 60% or its equivalent in their final Examination to qualify for admission to the Doctor of Philosophy Programme.

In addition, all such candidates shall appear for an interview to be conducted by the Department. Final admission depends on the outcome of the interview.

F.                 Programme Duration

The duration of Ph.D. in Statistics shall be a minimum of thirty (36) Calendar months and a maximum of sixty (60) months for full-time students; a minimum of forty-eight (48) months and a maximum of seventy-two (72) months for part-time students. On the expiration of the minimum duration, a candidate may apply for extension of not more than two consecutive periods of 12 calendar months, after which the programme lapses.

G.                Details of Courses in Ph. D. Statistics

STA920                      Scientific Research Methodology 4 Credits

Essentials of Spreadsheets, Internet technology, Statistical Packages, Precision and Accuracy of Estimates, Principles of Scientific Research, Concepts of Hypotheses Formulation and Testing, Organization of Research and Report Writing. 60h (T); C

STA901                      Statistical Inference 4 Credits

Elements of theory of statistical games and decision. Reduction of decision problems into problems of statistical inference. Admissibility and completeness. Methods of estimation. Lehman Scheffe Theorem. Invari-ance, Confidence sets. Large sample theory for confidence bounds. Construction of tests: MP, UMP, UMPU, UMPI and likelihood ratio criterion with their applications. 60h (T); C

STA902                      Sample Surveys 4 Credits

Use of auxiliary information; multivariate ratio, regression and difference estimators and their extension to double sampling procedure. Quenouille‘s technique of bias reduction. Sampling on successive occasions, non-sampling errors. Some specialized sampling techniques 60h (T); E

STA903                      Design and Analysis of Experiments 4 Credits

General Linear Models; generalized inverse of a Matrix. Factorial Experiments; Symmetric and Assymmetric. Balanced and Partially Balanced Incomplete Block Designs. Resolvable, Group Divisible, Connected, Lattice Designs. Row, Column Designs; Latin Squares, Lattice, Youden, Cross-Over designs. Response Surface Methodology, Construction of designs. 60h (T); E

STA904                      Econometric Methods I  4 Credits

OLS, Gauss – Markoff Theorem. MLE Specification and misspecification test. Predicative and non- predictive test; Tests of hypotheses in the linear model. The likelihood ratio, the Wald and the Language multiplier tests, Multi-colinearity. Specification bias, GLS. Dummy variables and seasonal variations. Inferences about linear model based on asymptotic distribution theory. 60h (T); E

STA905                      Measure Theory and Advanced Probability 4 Credits

Measure Theory: Measure and Measurable functions. Conditional spaces and measures. Probability: Probability measure and random variable, Distribution and Characteristic functions, Strong law of large numbers. Convergence theorems in probability and probability distributions. Central limit theorems for iid and correlated random variables. Conditional probability measures and expectation. 60h (T); E

STA906                      Multivariate Analysis 4 Credits

Fundamental Theory of Matrices and their properties. Multivariate Normal Distribution and associated multiple and partial correlation and gression  theory.  Estimation of  parameters. Hotelling‘s  and Mahalanobis‘s  . Wishart distribution. Tests concerning mean vectors and variance covariance matrices. Test for independence of two sets of variables and associated confidence bounds. Some other multivariance distributions. 60h (T); E

STA907                      Analysis of Categorical Data 4 Credits

Probability models for 2 x 2 tables. Measures of association for 2 x 2 tables. Probability models for s x r tables. Goodness of fit tests. Square tables and their applications. Structural models for two and higher dimensions. Iterative, proportional fitting of log linear models. Complete and incomplete multiway table. Quasi symmetry and complete symmetry. 60h (T); E

STA908                      Quality Control and Its Management I 4 Credits

Analysis and control of variations in a production rocess. Operating characteristic of Concharts. Control chart for attributes and variables. Cumulative sum control   charts. Control charts based on  Weighted  average. Methods of controlling several related characteristics. Process capability analysis. Economic, Design of Control charts, Specifications and Tolerances. 60h (T); E

STA909                      Stochastic Processes With Applications 4 Credits

Classification of stochastic processes. Random walk models, discrete queuing Chain, inventory model, branching processes. Poisson, Birth, and Death processes, waiting time models. Gaussian processes. Martingales, Mean covariance and sample functions. Integration and differentiation of SPs. Estimation problems. 60h (T); E

STA911                      Non-Parametric and Sequential Methods 4 Credits

Distribution of order statistics and quantities. One and two sample tests. Confidence intervals. Transformations of statistics and their asymptotic properties. OC and ASN functions of the SPRT.              SPRT for composite hypotheses. Elements of sequential estimation, stein‘s two stage sampling method for point and interval estimation. 60h (T); E

STA912                      Theory of Games and Decision 4 Credits

Elements of theory of Games; Rectangular game.  Non-randomized and randomized strategies. Optimum strategies. Numerical and graphical methods for solution of games. Elements of Decision Theory:    Relationship between Games Theory, Decision Theory and    Statistical Inference. Non- randomized, randomized. Bayes, and Min-max. Unbiased and invariants decision rules. Optimal decisions. 60h (T); E

STA913                      Time Series Analysis and its Application 4 Credits

Discrete time series models. Principles of interactive model building. ARIMA Models Identification, fitting diagnostic checking of models. Application of discrete time series models illustrated by transfer function estimation, multiple forecasting and intervention function estimation. Seasonal model application for forecasting. 60h (T); E

STA914                      Methods of Operations Research 4 Credits

Linear Programming; Simplex and graphical methods of optimum solution. Application to transportation and other problems. Sensitivity testing and duality. Non-linear programming; dynamic optimization models, Stochastic Programming models, Waiting time models; element of queuing theory. Single and multiple server models. Network analysis; Shortest-route models. Generalized network problem. Multi-commodity network, Maximum-flow problem. 60h(T); E

STA915                      Econometric Methods II  4 Credits

Non-linear models. Dynamic models. Equation Dynamics; Distributed lags, partial adjustment, adaptive expectations, difference and differential equations. Estimation of dynamic models. Dynamics; ARIMA models and forecasting. Simultaneous equation systems. Discrete choice model. 60h (T); E

Requirements for Graduation

• Candidates shall present and defend a Research Protocol not later than 3 months after the first registration and at least two additional seminar presentations before the thesis Title Registration. Candidates will be required to carry out original research in statistics and to submit a thesis not exceeding 45,000 words in length and abstract not more than 500 words on a topic chosen in consultation with their supervisor and approved by the Department. Their research work shall commence in the first year of their registration. The Title Registration must be approved by the Postgraduate School Board before the final examination.
• The Degree shall be awarded on the basis of a thesis resulting from original independent research and Open Oral Examination.

I.                   Summary

Compulsory Courses:     STA920 (4), STA901 (4) = 8 Credits

Optional Courses: At least one course in the student‘s area of specialization (minimum of 4 Credits)

There are options for specialization. The options are:

Option 1:         Sample Survey STA902 (4)

Option 2:         Quality Control STA908 (4)

Option 3:         Multivariate Analysis STA906 (4)

Option 4:         Design & Analysis of Experiment STA903 (4) Option 5: Econometric STA904 (4), STA915 (4),

Option 6:         Time Series STA909 (4), STA913 (4)

Option 7:         Stochastic Processes STA905 (4) Option 8:  Categorical Data Analysis STA907 (4) Option 9:                        Non-Parametric STA911 (4)

Note:   Availability of the options depend on staff on ground.

Minimum total written Courses credits for Graduation = 12 Credits.