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Fundaments of Statistical Inference

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  • Córdoba Bueno, Miguel.
  • Zamora Saiz, Alfonso.
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    • Editorial: Dykinson
    • ISBN: 978-84-9148-734-0
    • Páginas: 294
    • Dimensiones: 17 cm x 24 cm
    • Plaza de edición: Madrid , España
    • Encuadernación: Rústica
    • Idiomas: Inglés
    • Fecha de la edición: 2018
    • Edición: 2ª ed.
    Versión en papel:
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    Resumen del libro

    Statistical Science aims to collect all the grouped manifestations of stochastic phenomena, in order to try to know the reality, using a process of systematization and analysis. This knowledge may be total or partial, but in any case it would be necessary to observe, describe and analyse the phenomena, in order to infer the laws that rule them. To do that, we will try to collect all possible information available to know the phenomenon which interests us. Once we analyse this information and know our phenomenon, we will be able to predict reasonably future situations, and consequently to make decisions. This is a textbook which objective is to introduce the students in the basic knowledge of what is the Statistical Inference, and how to use the probabilities to estimate parameters and to test hypothesis. We also include several solved exercises in order to achieve a more practical approach of the different lessons.


    Índice

    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

    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

    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

    Chapter 7. Discrete distributions

    1. Dichotomous distribution

    2. Binomial distribution

    3. Poisson distribution

    4. Multinomial distribution

    Chapter 8. Continuous distributions

    1. Uniform distribution

    2. Normal distribution

    3. Chi-squared distribution

    4. Student’s t-distribution

    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

    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

    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

    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

    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

    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

    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

    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

    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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