A First Course on Statistical Inference
Preface
Welcome
Contributions
License
Citation
Course overview
Scripts
1
Preliminaries
1.1
Random experiments
1.2
Probability definitions
1.3
Random variables
Exercises
2
Introduction to statistical inference
2.1
Basic definitions
2.2
Sampling distributions in normal populations
2.2.1
Sampling distribution of the sample mean
2.2.2
Sampling distribution of the sample variance
2.2.3
Student’s
\(t\)
distribution
2.2.4
Snedecor’s
\(\mathcal{F}\)
distribution
2.3
The Central Limit Theorem
Appendix
Exercises
3
Point estimation
3.1
Unbiased estimators
3.2
Invariant estimators
3.3
Consistent estimators
3.4
Sufficient statistics
3.5
Minimal sufficient statistics
3.6
Uniformly minimum-variance unbiased estimators
3.7
Efficient estimators
3.8
Robust estimators
Exercises
4
Estimation methods
4.1
Method of moments
4.2
Maximum likelihood
Exercises
5
Confidence intervals
5.1
The pivotal quantity method
5.2
Confidence intervals for normal populations
5.2.1
Confidence interval for
\(\mu\)
with known
\(\sigma^2\)
5.2.2
Confidence interval for
\(\mu\)
with unknown
\(\sigma^2\)
5.2.3
Confidence interval for
\(\sigma^2\)
5.2.4
Confidence interval for the difference of means with know variances
5.2.5
Confidence interval for the difference of means, with unknown and equal variances
5.2.6
Confidence interval for the ratio of variances
5.3
Asymptotic confidence intervals
5.3.1
Confidence interval asymptotic for a mean
5.3.2
Confidence interval asymptotic for a proportion
Exercises
6
Hypothesis tests
6.1
Introduction
6.2
Tests on a normal population
6.2.1
Tests about
\(\mu\)
6.2.2
Tests about
\(\sigma^2\)
6.3
Tests on two normal populations
6.3.1
Equality of means
6.3.2
Equality of variances
6.4
Asymptotic tests
6.5
\(p\)
-value of a test
6.6
Power of a test and Neyman–Pearson’s Lemma
6.7
The likelihood ratio test
Exercises
ISBN 978-84-09-29679-8
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A First Course on Statistical Inference
Chapter 2
Introduction to statistical inference