AD-703 (C) RGPV B.Tech
Advanced Statistical Analytics (ASA)
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Syllabus, notes and important questions for AD-703 (C)
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Syllabus units
Topics as the official RGPV syllabus lists them.
Unit 1 Introduction 9 topics
- Population and Sample
- Random Sampling from finite population ($\text{SRSWR}$ and $\text{SRSWOR}$)
- Parameter and Statistic
- Sampling distribution of a statistic in the context of a finite population
- Sampling distribution of sample mean and sample proportion while sampling from a finite population
- Random sampling from an infinite population
- Sampling distribution of sample mean and sample variance when the sample is drawn from a Normal distribution
- Problems on sampling distributions of statistics from finite and infinite populations
- Statement of Lyapunov–Lévy Central Limit Theorem ($\text{CLT}$) and its applications
Unit 2 Correlation, Regression Analysis and ANOVA 16 topics
- Correlation
- Scatter diagram
- Karl Pearson’s coefficient of correlation
- Spearman’s rank correlation coefficient
- Methods of least squares
- Simple Linear Regression (SLR) model
- SLR assumptions and prediction
- Multiple Linear Regression (MLR)
- MLR assumptions and prediction
- Polynomial Regression
- Logistic Regression
- Poisson Regression
- Non‑Linear Regression
- Analysis of Variance (One‑way \& Two‑way)
- Analysis of Covariance
- Multivariate Analysis of Variance
Unit 3 Testing of Hypothesis 9 topics
- Null and alternative hypothesis
- Testing procedure (critical region)
- Type I and Type II errors
- Level of significance \& power of a test
- $p$‑value for symmetric null distribution
- Tests for mean and proportion (single‑sample, two‑sample; exact \& large‑sample)
- Tests for variance (single‑sample and two‑sample)
- Tests for mean and correlation coefficient for paired samples (exact \& large‑sample)
- One‑way analysis of variance
Unit 4 Parametric Point Estimation 11 topics
- Problem of point estimation
- Criteria of a good estimator
- Unbiasedness
- Consistency
- Efficiency
- Sufficiency
- Minimum variance and unbiasedness (small sample)
- Method of moments
- Method of maximum likelihood
- Consistency \& efficiency (large sample)
- Interval estimation: confidence intervals of mean and proportion in large samples
Unit 5 Bayesian Statistics 7 topics
- Introduction to Bayesian inference
- Bayesian parameter estimation
- Markov Chain Monte Carlo (MCMC) methods
- Bayesian hierarchical models
- Survival analysis
- Causal inference
- High‑dimensional data analysis