Fundaments of Statistical Inference

Córdoba Bueno, Miguel

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  • Editorial: Dykinson
  • ISBN: 978-84-9085-913-1
  • Páginas: 266
  • Dimensiones: 17 cm x 24 cm
  • Fecha de la edición: September 2016
  • Edición: 1ª ed.
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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.

Miguel Córdoba Bueno is professor in Statistics, Financial Mathematics and Decision Theory at Universidad CEU-San Pablo in Madrid. He was also lecturer at Universidad Complutense and Universidad Carlos III in Madrid. He have also working in different enterprises, carrying out several functions, inter alia Deputy General Manager of BBV Interactivos, Business Development Director of Treasury and Capital Markets of BBV, Marketing Director of Investment Banking of BBVA, and Chief Financial Officer of Naturhouse Group, Adquira, Mnemo and Pecunia Cards EDE. He is the author of over fifteen books and numerous articles about Finance and Economics. 


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

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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