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POST GRADUATE DIPLOMA IN STATISTICAL METHODS AND, 1 CURRICULUM 3. 1 1 Brief Syllabi of Courses 3, Semester I 3, Semester II 6. Post Graduate Diploma in Statistical Methods and Analytics. 1 Curriculum, SEMESTER I SEMESTER II, 1 Basic Mathematics 1 Computer Intensive Statistical methods. 2 Probability Theory 2 Regression Time Series, 3 Statistical Methods 3 Statistical Machine Learning Statistical Finance. 4 Numerical Methods and Optimization 4 Clinical Trials Actuarial Methods. 5 Introduction to Packages R S and SAS 5 Project, 1 1 Brief Syllabi of Courses.
Semester I, 1 Basic Mathematics, Set theory sets set operations functions equivalence of sets finite and infinite sets countable and. uncountable sets with examples 2, Real numbers field properties and order properties representation as points on real line sup and inf. completeness rationals and irrationals and their properties intervals 2. Sequences and Series limits of sequences properties sandwich theorem bounded and monotone. sequences subsequences Cauchy criterion statement only convergence of series tests of. convergence Standard tests like comparison ratio root tests etc 6. Functions limits and continuity of functions right and left limits simple properties sum difference. product composition etc differentiability and simple properties chain rule monotonicity and. convexity of functions mean value theorem statement only geometric interpretation of the theorem. maxima minima Taylor theorem statement only 10, Integration Sketch of the idea without complete details of Riemann integration fundamental theorem. of calculus statement only properties of integral change of variable 4. 2 variable calculus continuity partial derivatives double integrals iterated integration Jacobian rule. differentiation under integration statement only 6. References, 1 Calculus Vol I II Apostol T, 2 Introduction to Real Analysis Bartle R G and Sherbert D R. 3 Introduction to Calculus and Analysis Vol I II Courant R and John F. 4 Principles of Real Analysis Rudin W, Linear Algebra.
Introduction to matrices System of linear equations matrix representation basic matrix operations 2. Vector spaces Definition and examples subspaces linear independence basis of a vector space 2. Matrix theory matrices as linear transformation elementary operations and elementary matrices rank. nullity trace inverse and determinants of matrices solutions of system of linear equations 12. Spectral theory eigenvalues and eigenvectors of matrices decomposition of matrices quadratic forms. and definiteness of a matrix with applications in Statistics 6. References, 1 Matrix Theory and Linear Algebra Hernstein I N and Winter D J. 2 Matrix Algebra Gentle J E, 3 Matrix Computations Golub G H and Van Loan C F. 4 Introduction to Linear Algebra Mirsky L, 2 Probability Theory. Elementary concepts of probability experiments outcomes sample space events 8. Conditional probability independence Bayes theorem 6. Random variable probability distribution and properties probability mass density function cumulative. distribution function expectation variance moments 8. Binomial Poisson Negative Binomial Hypergeometric Uniform Normal and Exponential. distributions 8, Chebyshev s inequality weak law of large numbers central limit theorem statement 2. Distribution of a function of a random variable 4, Bivariate distribution joint marginal and conditional distributions moments covariance correlation.
coefficient 8, Independent random variables and their sums Transformation of two random variables 6. Sampling distributions chi square t F 4, References. 1 A First Course in Probability Ross S, 2 Elementary Probability Theory Chung K L. 3 Introduction to Probability Roussas G, 4 Probability Pitman J. 3 Statistical Methods, Different types of statistical problems and related data analysis 2.
Concept of population sample and statistical inference through examples 2. Summarization of univariate data graphical methods measures of location spread skewness and. kurtosis outliers and robust measures 14, Empirical distribution extension to censored data Kaplan Meier estimate 5. Analysis of discrete and continuous data fitting probability distributions goodness of fit graphical. methods of verifying the fit 10, Concept of estimation point and interval with examples Concept of testing of hypotheses significance. level size power and p value 12, One and two sample t tests paired t test nonparametric tests One and two sample tests for. proportions 12, References, 1 Introductory Statistics Ross S. 2 Statistics Freedman D Pisani R and Purves R, 3 Applied General Statistics Croxton F E and Cowden D J.
4 Statistics A Guide to the Unknown Tanur J M ed, 5 Statistics A New Approach Wallis W A and Roberts H V. 4 Numerical Methods and Optimization, Numerical Methods. Significant digits round off errors Finite computational processes and computational errors Loss of. significant digits 4, Solution of nonlinear equation in one variable Separation of roots and initial approximation 4. Improvement of the initial solution using methods of bisection Regula Falsi and Newton Raphson 10. Fixed point iterative schemes Errors Order of convergence and degree of precision 6. Optimization, Lagrange method of multipliers maxima and minima of differentiable functions 6. Linear programming simplex method dual simplex method sensitivity 12. Unconstrained optimization Newton Quasi Newton method 8. Computational methods of optimization 6, References.
1 Numerical Analysis for Statisticians Lange K, 2 Elementary Numerical Analysis An Algorithmic Approach Conte S D and de Boor C. 3 Operations Research An Introduction Taha H A, 4 Optimization Lange K. 5 Introduction to Packages R S and SAS, Introduction to packages overview of packages data handling input output operations 10. Basic programming data types arrays loops etc functions and graphics 10. Introduction to SAS programming 10, Statistical computations data summary and graphical display of data basic statistics 8. Simulations from probability distributions comparisons of distributions Q Q and P P plots 10. Matrix computations basic operations finding determinant inverse eigen roots and eigen vectors of. a matrix matrix decomposition solving system of equations 8. References, 1 A Handbook of Statistical Analysis using R Everitt B S and Hothorn T.
2 A Handbook of Statistical Analysis using SAS Der Geoff Everitt B S. 3 Modern Applied Statistics with S PLUS Venables W N and Ripley B D. 4 Numerical Analysis for Statisticians Lange K, Semester II. 1 Computer Intensive Statistical Methods, Statistical inference likelihood based Bayesian 10. Categorical data analysis contingency tables measures of association test of independence 4. Principal component analysis 3, Simulation acceptance rejection sampling importance sampling 6. Introduction to discrete time Markov chains finite state space and countable state space Markov chain. Monte Carlo MCMC methods and simulation of Markov chains applications in statistics of the. MCMC methods 20, Histogram and kernel smoothing density estimation nonparametric regression 9. Bootstrap and resampling 6, Illustration of the methodology with real data.
References, 1 Computational Statistics Gentle J E, 2 Computational Statistics Givens G H and Hoeting J A. 3 Statistical Computing Kennedy W J and Gentle J E. 4 Handbook of Computational Statistics Gentle J E Hardle W and Mori Y. 5 Statistical Computing Existing Methods Recent Developments Basu A and Kundu D. 6 Resampling Methods A Practical Guide to Data Analysis Good P I. 7 Simulation and Monte Carlo Method Rubinstein R Y. 8 Smoothing Methods in Statistics Simonoff J S, 2 Regression Time Series. Regression, Classical Linear Regression Model 2 OLS method of estimation tests of hypotheses 6. Use of dummy variables in regression 1 residuals and fitted values 3 Variable selection 3. Validation of assumptions using graphical techniques 7. Logistic regression odds ratio concordance discordance measures 7. Illustration of the methodology with real data, References. 1 Introduction to Linear Regression Analysis Montgomery D C Peck E and Vinning G. 2 Regression Analysis by Examples Chatterjee S and Hadi G. 3 Applied Linear Regression Weisberg S, 4 Applied Regression Analysis Draper N R and Smith H.
5 Applied Logistic Regresson Hosmer D W and Lemeshow S. Time series, Exploratory analysis and graphical display trend seasonal and cyclical components Smoothing. exponential and MA 6, Stationary Time Series AR MA and ARMA models Box Jenkins correlogram analysis ACF and. PACF choice of AR and MA orders 10, Non Stationary Time Series introduction to ARIMA model deterministic and stochastic trends. introduction to ARCH models 6, Forecasting basic tools using exponential smoothing and Box Jenkins method Residual analysis 6. Illustration of the methodology with real data, References.
1 Introduction to Time Series and Forecasting Brockwell P and Davis R A. 2 Analysis of Time Series Chatfield C, 3 Time Series Analysis and Its Applications with R Shumway R H and Stoffer D S. 4 Intro to Time Series Analysis Forecasting Montgomery D C Jennings C L Kulachi M. 5 Forecasting Methods and Applications Makridakis S G Wheelwright S C and Hyndman R J. 3 Statistical Machine Learning Statistical Finance. Statistical Machine Learning, Unsupervised learning clustering procedures hierarchical and non hierarchical association. Supervised learning Linear discriminant analysis Bayesian classifier nearest neighbor classifier Tree. based classification methods predictive modeling using decision trees Entropy based. classifier 12, Support vector machine Boosting and adaptive boosting algorithm 6. Assessment and model selection bias variance trade off training error rate criteria of selection AIC. BIC cross validation 4, Applications in information retrieval and text analysis Illustration of the methodology with real data. References, 1 The Elements of Statistical Learning data Mining Inference and Prediction.
Hastie T Tibshirani J H and Friedman J H, 2 Data Mining Concepts and Techniques Han J and Kamber M. 3 Machine Learning Mitchell T M, 4 Statistical and Machine Learning Data Mining Ratner B. 5 Classification and Regression Trees Breiman L et al. Statistical Finance, Derivatives forward and future contracts Markets prices arbitrage Complete market market risk and. credit risks in the use of derivatives 4, Options markets properties of stock option prices American and European options 4. Binomial model One step and two step models Risk neutral valuation 4. Volatility value at risk 4, Behaviour of stock prices Conditional expectation and properties 6.
Options on stock indices currencies and futures Some exotic equity and foreign. exchange derivatives Interest rate derivatives 8, Illustration of the methodology with real data. References, 1 Options Futures and other derivatives Hull John. 2 Financial Calculus Baxter M and Rennie A, 3 Risk Neutral Valuation Bingham N and Keisel R. 4 Clinical Trials Actuarial Methods, Clinical Trials. Introduction to clinical trials bias and random error in clinical studies conduct of clinical trials. selection of subjects ethical issues outcome measures protocols 6. Different Phases comparative and controlled trials random allocation 4. Design of clinical trials parallel group designs crossover designs symmetric designs adaptive designs. group sequential designs 8, Design of phase I II and III trials 4.
Bioequivalence trials 3, Power and sample size determination 3. Illustration of the methodology with real data, References. 1 Clinical Trials A Practical Approach Pocock S, 2 Fundamentals of Clinical Trials Friedman L M Furburg C and Demets D L. 3 Clinical Trials A Methodological Perspective Piantadosi S. 4 The Design and Analysis of Sequential Clinical Trials Whitehead J. Actuarial Methods, General Insurance Loss models parametric estimation 3 Re insurance and deductibles 2. Collective and individual risk models for aggregate loss 4 No Claims Discount systems 3 Ruin. theory statement of the problem 2, Life Insurance Introduction to survival analysis 1.
Complete and curtate future lives force of mortality and hazard rate 2. Life tables 3 Present values of insurances and annuities 6 Premium 2. Illustration of the methodology with real data, References. 1 Statistical and Probabilistic Methods in Actuarial Science Boland P J. 2 Loss Models From Data to Decisions Klugman S A Panier H H Wilmot G E. 3 Statistical Methods 4 Numerical Methods and Optimization 5 Introduction to Packages R S and SAS SEMESTER II 1 Computer Intensive Statistical methods 2 Regression amp Time Series 3 Statistical Machine Learning amp Statistical Finance 4 Clinical Trials amp Actuarial Methods 5 Project 1 1 Brief Syllabi of Courses Semester I 1 Basic

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