Statistics

STATISTICS COURSES

STH 201 : OFFICIAL STATISTICS (OS)

Present official statistical system in India relating to population, agriculture, industrial production, trade and prices, methods of collection of official statistics, their reliability and limitations, principal publications containing such statistics, various official agencies responsible for data collection and their main functions. 

National and International official statistical system Official Statistics : 

(a) Need, Uses, Users, Reliability, Relevance, Limitations, Transparency, its visibility 

(b) Compilation, Collection, Processing, Analysis and Dissemination, Agencies Involved, Methods 

National Statistical Organization: Vision and Mission, NSSO and CSO; roles and responsibilities; Important activities, Publications etc. 

National Statistical Commission: Need, Constitution, its role, functions etc; Legal Acts/ Provisions/ Support for Official Statistics; Important Acts 

Index Numbers: Different Types, Need, Data Collection Mechanism, Periodicity, Agencies Involved, Uses 

Sector Wise Statistics: Agriculture, Health, Education, Women and Child etc. Important Surveys & Census, Indicators, Agencies and Usages etc. 

National Accounts: Definition, Basic Concepts; issues; the Strategy, Collection of Data and Release. 

Population Census: Need, Data Collected, Periodicity, Methods of data collection, dissemination, Agencies involved. 

Misc: Socio Economic Indicators, Gender Awareness/Statistics, Important Surveys and Censuses. 

STH 202 : SAMPLING SURVEY (SS)  

Concept of population and sample, need for sampling, complete enumeration versus sampling, basic concepts in sampling, sampling and Non-sampling error, Methodologies in sample surveys (questionnaires, sampling design and methods followed in field investigation) by NSSO. 

Subjective or purposive sampling, probability sampling or random sampling, simple random sampling with and without replacement, estimation of population mean, population proportions and their standard errors. Stratified random sampling, proportional and optimum allocation, comparison with simple random sampling for fixed sample size. Covariance and Variance Function. 

Ratio, product and regression methods of estimation, estimation of population mean, evaluation of Bias and Variance to the first order of approximation, comparison with simple random sampling. 

Systematic sampling (when population size (N) is an integer multiple of sampling size (n)). Estimation of population mean and standard error of this estimate, comparison with simple random sampling. 

Sampling with probability proportional to size (with and without replacement method), Des Raj and Das estimators for n=2, Horvitz-Thomson’s estimator 

Equal size cluster sampling: estimators of population mean and total and their standard errors, comparison of cluster sampling with SRS in terms of intra-class correlation coefficient. 

Concept of multistage sampling and its application, two-stage sampling with equal number of second stage units, estimation of population mean and total. Double sampling in ratio and regression methods of estimation. 

Concept of Interpenetrating sub-sampling. 

STH 203 : ECONOMETRIC METHODS (EM)

General linear model, ordinary least square and generalized least squares methods of estimation :

Nature of econometrics, the general linear model (GLM) and its extensions, ordinary least squares (OLS) estimation and prediction, generalized least squares (GLS) estimation and prediction, heteroscedastic disturbances, pure and mixed estimation. 

Problem of multi-collinearity, consequences and solutions of multi-collinearity :

multi-collinearity problem, its implications and tools for handling the problem, ridge regression. Linear regression and stochastic regression, instrumental variable estimation, errors in variables, autoregressive linear regression, lagged variables, distributed lag models, estimation of lags by OLS method, Koyck’s geometric lag model.

Autocorrelation and its consequences and tests. Theil BLUS procedure, estimation and prediction

Heteroscedasticity of disturbances and its testing, test for independence of disturbances concept of structure and model for simultaneous equations, problem of identification-rank and order conditions of identifiability, two-stage least sauare method of estimation. 

Simultaneous linear equations model and its generalization, identification problem, restrictions on structural parameters, rank and order conditions. Estimation in simultaneous equations model, recursive systems, 2 SLS estimators, limited information estimators, k-class estimators, 3 SLS estimator, full information maximum likelihood method, prediction and simultaneous confidence intervals. 

STH 204 : APPLIED STATISTICS (AS)

APPLIED STATISTICS 1 (AS-1)

Index Numbers : Commonly used index numbers - Laspeyre’s, Paasche’s and Fisher’s ideal index numbers, cham-base index number, uses and limitations of index numbers, index number of wholesale prices, consumer price, agricultural production and industrial production, test fot index numbers -proportionality, time-reversal, factor-reversal and circular tests.

Price relatives and quantity or volume relatives, Link and chain relatives composition of index numbers; Laspeyre's, Paasches’, Marshal Edgeworth and Fisher index numbers; chain base index number. Construction of index numbers of wholesale and consumer prices, 

Income distribution-Pareto and Engel curves, Concentration curve, 

Methods of estimating national income, Inter-sectoral flows, Interindustry table, Role of CSO. 

Demand Analysis Time Series Analysis: Economic time series, different components, illustration, additive and multiplicative models, determination of trend, seasonal and cyclical fluctuations. 

APPLIED STATISTICS 2 (AS-2)

TIME SERIES : Determination of trend, seasonal and cyclical components, Box-Jenkins method, tests for stationary series, ARIMA models and determination of orders of autoregressive and moving average components, fore-casting. Time-series as discrete parameter stochastic process, auto covariance and autocorrelation functions and their properties. 

EXPLANATORY TIME SERIES : analysis, tests for trend and seasonality, exponential and moving average smoothing. Holt and Winters smoothing, forecasting based on smoothing. Detailed study of the stationary processes: (1) moving average (MA), (2) auto regressive (AR), (3) ARMA and (4) AR integrated MA (ARIMA) models. Box-Jenkins models, choice of AR and MA periods. 

Discussion (without proof) of estimation of mean, auto covariance and autocorrelation functions under large sample theory, estimation of ARIMA model parameters. 

Spectral analysis of weakly stationary process, periodogram and correlogram analyses, computations based on Fourier transform. 

STH 205 : DEMOGRAPHY & VITAL STATISTICS (DVS)

Introduction : Sources of demographic data, census, registration, ad-hoc surveys, Hospital records, Demographic profiles of the Indian Census. 

Life Tables : Complete life table and its main features, Uses of life table. Makehams and Gompertz curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary populations. 

Measurement of Fertility : Crude birth rate, General fertility rate, Age specific birth rate, Total fertility rate, Gross reproduction rate, Net reproduction rate. 

Measurement of Mortality: Crude death rate, Standardized death rates, Age-specific death rates, Infant Mortality rate, Death rate by cause. 

Migration : Internal migration and its measurement, migration models, concept of international migration. Net migration. Intercensal and postcensal estimates. 

Population Projection & Forecasting : Projection method including logistic curve fitting. Decennial population census in India. 

STH 206 : BIO-STATISTICS (BS)

Concept of time, order and random censoring, likelihood in the distributions – exponential, gamma, Weibull, lognormal, Pareto, Linear failure rate, inference for these distribution. 

Life tables, failure rate, mean residual life and their elementary classes and their properties. 

Estimation of survival function – actuarial estimator, Kaplan – Meier estimator, estimation under the assumption of IFR/DFR, tests of exponentiality against non-parametric classes, total time on test. 

Two sample problem – Gehan test, log rank test. Semi-parametric regression for failure rate – Cox’s proportional hazards model with one and several covariates, rank test for the regression coefficient. 

Competing risk model, parametric and non-parametric inference for this model. Introduction to clinical trials: the need and ethics of clinical trials, bias and random error in clinical studies, conduct of clinical trials, overview of Phase I – IV trials, multicenter trials. 

Data management: data definitions, case report forms, database design, data collection systems for good clinical practice. 

Design of clinical trials: parallel vs. cross-over designs, cross-sectional vs. longitudinal designs, review of factorial designs, objectives and endpoints of clinical trials, design of Phase I trials, design of single-stage and multi-stage Phase II trials, design and monitoring of phase III trials with sequential stopping, Reporting and analysis: analysis of categorical outcomes from Phase I – III trials, analysis of survival data from clinical trials. 

STH 207 : STATISTICAL QUALITY CONTROL (SQC)

Statistical process and product control: 

Process and product control, general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and charts, cumulative sum chart. 

Quality of a product, need for quality control, basic concept of process control, process capability and product control, general theory of control charts, causes of variation in quality, control limits, sub grouping summary of out of control criteria, charts for attributes p chart, np chart, c-chart, V chart, charts for variables: R, (  X ,R), (  X ,σ) charts. 

Basic concepts of process monitoring and control; process capability and process optimization. 

General theory and review of control charts for attribute and variable data; O.C. and A.R.L. of control charts; control by gauging; moving average and exponentially weighted moving average charts; Cu-Sum charts using V-masks and decision intervals; Economic design of X-bar chart. 

Acceptance sampling plans for attributes inspection; Single, double, multiple and sequential sampling plans for attributes, and their properties; plans for inspection by variables for one-sided and two sided specification. OC, ASN, AOQ and ATI curves, concepts of producer’s and consumer’s risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of Dodge-Romin tables.

STH 208 : LINEAR INFERENCE & MULTIVARIATE ANALYSIS (LIMA)

Linear statistical models, theory of least squares and analysis of variance, Gauss-Markoff theory, normal equations, least squares estimates and their precision, test of significance and interval estimates based on least squares theory in oneway, two-way and three-way classified data, regression analysis, linear regression, curvilinear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance components, multivariate normal distribution, Mahalanobis’s D2 and Hotelling’s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, principal component analysis. 

Multivariate normal distribution and its properties. Random sampling from multivariate normal distribution. 

Maximum likelihood estimators of parameters, distribution of sample mean vector. Wishart matrix – its distribution and properties, distribution of sample generalized variance, null and non-null distribution of multiple correlation coefficients. 

Hotelling’s T2 and its sampling distribution, application in test on mean vector for one and more multivariate normal population and also on equality of components of a mean vector in multivariate normal population. 

Classification problem: Standards of good classification, procedure of classification based on multivariate normal distributions. Principal components, dimension reduction, canonical variates and canonical correlation — definition, use, estimation and computation. 

STH 209 : DESIGN OF EXPERIMENTS (DOE)

Fixed effects model (two-way classification) random and mixed effects models (two-way classification with equal observation per cell), CRD, RBD, LSD and their analyses, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial experiments and 24 and 32, confounding in factorial experiments, split-plot and simple lattice designs, transformation of data Duncan’s multiple range test. 

Analysis of variance for one way and two way classifications, Need for design of experiments, basic principle of experimental design (randomization, replication and local control), complete analysis and layout of completely randomized design, randomized block design and Latin square design, Missing plot technique. Split Plot Design and Strip Plot Design. Factorial experiments and confounding in 2n and 3n experiments. Analysis of covariance. Analysis of non-orthogonal data. Analysis of missing data.