UGC NET Statistics — Complete Syllabus
Deep Institute | Coaching by Sudhir Sir
Subject Code: 107
Paper II: Statistics
10 Units
Online & Offline Classes
Unit I
Probability and Distributions
Basic concepts of probability
Conditional probability & Bayes theorem
Independent events
Random variables & distribution functions
Expectation, moments & MGF
Standard discrete & continuous univariate distributions
Jointly distributed random variables
Marginal & conditional distributions
Chebyshev inequality
Sampling distributions & transformation of random variables
Characteristic function & its properties
Modes of convergence of random variables
Weak & strong laws of large numbers
Central Limit Theorems (i.i.d. case)
Unit II
Real Analysis and Matrix Algebra
Finite, countable & uncountable sets
Sequences: convergence, bounded, monotonic, Cauchy criterion
Series: convergence tests, alternating series
Power series & radius of convergence
Functions: limit, continuity, differentiability
Rolle’s theorem, MVT, Taylor’s theorem
Riemann integration & improper integrals
Functions of two variables: partial derivatives, maxima & minima
Lagrange multipliers, double & triple integrals
Vector spaces, rank & nullity, row reduced echelon form
Trace, determinant, inverse of matrix
Gram-Schmidt orthogonalization
Characteristic roots & vectors, Cayley-Hamilton theorem
Positive definite matrices & quadratic forms
Unit III
Sampling Methods and Design of Experiments
Simple random sampling (SRSWR & SRSWOR)
Stratified random sampling
Systematic sampling
Ratio & regression methods of estimation
Cluster sampling (equal & unequal clusters)
Double sampling
Sampling with varying probabilities (PPS)
Nonnegative variance estimation
ANOVA: one-way & two-way classification
Principles of design: replication, randomization, local control
CRD, RBD, LSD & missing plot techniques
Factorial experiments & confounding
Incomplete block designs (BIBD, PBIBD)
Connectedness & orthogonality of block designs
Unit IV
Estimation Theory
Unbiasedness & consistency
Method of moments & MLE
Efficiency & UMVUE
Rao-Cramer lower bound
Sufficiency & factorization theorem
Minimal sufficiency & ancillary statistic
Completeness & Rao-Blackwell theorem
Lehmann-Scheffe theorem & Basu’s theorem
Interval estimation & method of pivoting
Confidence intervals (one & two sample normal)
Large sample confidence intervals
Order statistics & empirical distribution function
Rank correlation: Spearman & Kendall
Unit V
Testing of Hypotheses
Basic concepts of hypothesis testing
Neyman-Pearson lemma
Families with monotone likelihood ratio
UMP, UMPU & UMPI tests
Likelihood ratio tests (one & two sample)
Wald’s SPRT, OC & ASN functions
Chi-square tests: goodness of fit, independence, homogeneity
Sign test & Wilcoxon signed rank test
Mann-Whitney U-test
Linear rank tests for location & scale problems
Kruskal-Wallis test
Unit VI
Linear Estimation, Regression Analysis and Econometrics
Simple & multiple linear regression
Gauss-Markov model
Least squares & MLE in regression
Testing of regression parameters
Generalized & weighted least squares
Indicator/dummy variables
Multicollinearity, heteroscedasticity, autocorrelation
Durbin-Watson test
Logistic regression models
Restricted regression estimation
Errors in variable model & instrumental variable estimator
Simultaneous equations model & identification problem
Two-stage least squares & k-class estimator
Unit VII
Time Series
Time series data & descriptive measures
ACVF, ACF & PACF, correlogram
Strong & weak stationarity, ergodicity
General linear process & Wold decomposition
MA, AR & ARMA processes
Stationarity & invertibility conditions
Yule-Walker equations
Identification, estimation & order selection of ARMA models
Forecasting with stationary & invertible processes
Non-stationary series & random walk
ARIMA (p,d,q) models & parameter estimation
Spectral representation & spectral density
Periodogram analysis
Unit VIII
Multivariate Analysis
Multivariate normal distribution & properties
Estimation of mean vector & covariance matrix
Distribution of sample mean vector
Wishart distribution & properties
Simple, partial & multiple correlation coefficients
Inference for parameters (related tests)
Test of hypothesis for mean vector (Hotelling’s T²)
Discriminant analysis
Principal component analysis (PCA)
Canonical correlation analysis
Unit IX
Stochastic Processes
Markov chains (finite & countable state space)
Classification of states
Chapman-Kolmogorov equations
Limiting behaviour of n-step transition probabilities
Stationary distribution
Gambler’s ruin problem
Simple random walk
Poisson process
Inter-arrival & waiting time distributions
Birth and death processes
M/M/1 queues
Unit X
Indian Statistical System and Research Methodology
Ministry of Statistics & Programme Implementation (MoSPI)
National Statistical Commission
National Statistics Office (NSO)
Census & large sample surveys
Contributions of P C Mahalanobis
Contributions of P V Sukhatme, R C Bose, S N Roy, C R Rao
R as a calculator, functions & matrix operations
Built-in functions, missing data & logical operators
Conditional executions & loops in R
Data management: sequences, sorting, strings, lists, factors
Data frames, input/output, graphics & plots in R
Basics of programming, scripts & functions in R