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Fundaments of Statistical Inference

Fundaments of Statistical Inference

  • Author: Córdoba Bueno, Miguel; Zamora Saiz, Alfonso
  • Publisher: Dykinson
  • ISBN: 9788491487340
  • eISBN Pdf: 9788413249049
  • Place of publication:  Madrid , Spain
  • Pages: 298
  • Cover
  • Title page
  • Copyright page
  • Summary
  • First part: Probability theory
    • Chapter 1. Statistical Science
      • 1. Introduction
      • 2. Basic concepts
      • 3. Problems solved by Statistics
      • 4. Historical background
    • Chapter 2. Introduction to probabilities
      • 1. Concept of probability
      • 2. Probability axioms
      • 3. Basic properties
      • 4. Conditional probability
      • 5. Classification of events in a sample space
    • Chapter 3. Probability interpretations
      • 1. Laplace interpretation
      • 2. Frequentist interpretation
      • 3. Logical interpretation
      • 4. Subjective interpretation
    • Chapter 4. Fundaments of Bayesian Statistics
      • 1. Prior and posterior probabilities
      • 2. Likelihood function
      • 3. Law of total probability
      • 4. Bayes’ theorem
      • Exercises
    • Chapter 5. Random variables
      • 1. Concept of random variable
      • 2. Probability distribution. Discrete and continuous random variables
      • 3. Cumulative distribution function
      • 4. Probability mass function
      • 5. Probability density function
      • Exercises
    • Chapter 6. Measures of a random variable
      • 1. Measures of central tendency
      • 2. Measures of dispersion
      • 3. Typification of random variables
      • 4. Chebyshev’s inequality
      • 5. Measures of shape
      • Exercises
    • Chapter 7. Discrete distributions
      • 1. Dichotomous distribution
      • 2. Binomial distribution
      • 3. Poisson distribution
      • 4. Multinomial distribution
      • Exercises
    • Chapter 8. Continuous distributions
      • 1. Uniform distribution
      • 2. Normal distribution
      • 3. Chi-squared distribution
      • 4. Student’s t-distribution
      • Exercises
    • Chapter 9. Convergence of random variables
      • 1. Random variables succession and its convergence
      • 2. Types of convergence
      • 3. Laws of large numbers
      • 4. Central limit theorem
      • Exercises
  • Second part: Estimation theory
    • Chapter 10. Sampling theory
      • 1. Introduction to statistical inference
      • 2. Problems solved by statistical inference
      • 3. Sampling basic concepts
      • 4. Types of sampling
      • 5. Simple random sample
    • Chapter 11. Sample statistics
      • 1. Concept of statistic
      • 2. Statistic sample mean
      • 3. Statistic sample variance
      • Exercises
    • Chapter 12. Distributions of statistics
      • 1. Distribution of sample mean
      • 2. Distribution of sample variance
      • 3. Distribution of sample proportion
      • 4. Distribution of difference between sample means
      • 5. Distribution of difference between sample proportions
      • Exercises
    • Chapter 13. Estimators
      • 1. Concept ant types of estimation
      • 2. Unbiased estimators
      • 3. Efficient estimators
      • 4. Consistent estimators
      • 5. Sufficient estimators
      • 6. Invariant estimators
      • 7. Robust estimators
      • Exercises
    • Chapter 14. Confidence intervals
      • 1. Concept of confidence interval
      • 2. Confidence interval for mean
      • 3. Confidence interval for variance
      • 4. Confidence interval for proportion
      • 5. Confidence interval for difference between means
      • 6. Confidence interval for difference between proportions
      • Exercises
  • Third part: Statistical hypothesis testing
    • Chapter 15. Fundaments of statistical hypothesis testing
      • 1. Introduction
      • 2. Statistical hypothesis
      • 3. Types of tests
      • 4. Errors of the first and second kinds
      • 5. Critical region and region of acceptance
    • Chapter 16. Parametric tests
      • 1. Introduction
      • 2. Neyman-Pearson tests
      • 3. Significance tests
      • Exercises
    • Chapter 17. Nonparametric tests
      • 1. Introduction
      • 2. Runs test for randomness hypothesis
      • 3. Shapiro-Wilks test for normality of the population
      • 4. Chi-square goodness-of-fit test
      • 5. Kolmogorov-Smirnov goodness-of-fit test
      • Exercises
      • Fourth part: Multivariate statistics
    • Chapter 18. Factor Analysis
      • 1. Introduction
      • 2. Adequacy of using Factor Analysis
      • 3. Factor matrix
      • 4. Number of factors and interpretation
      • 5. Factor rotation
      • Exercises
    • Chapter 19. Cluster Analysis
      • 1. Introduction
      • 2. Types of data and similarity measures
      • 3. Hierarchical clustering
      • 4. Non-hierarchical clustering
      • Exercises
    • Chapter 20. Discriminant Analysis
      • 1. Introduction
      • 2. Bayes’ rule
      • 3. Discriminant Analysis procedure
      • 4. Misclassification error
      • Exercises
  • Bibliography
  • Appendix
    • 1. Univariate Moments
    • 2. Standard normal distribution tabulated
    • 3. Chi-squared distribution tabulated
    • 4. Student’s t-distribution tabulated
    • 5. Values of lower and upper bounds of critical region in runs test
    • 6. Coefficients of Shapiro-Wilk test
    • 7. Critical values of Shapiro-Wilk test
    • 8. Critical values of Kolmogorov-Smirnov test

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