Exercises of Statistical Inference E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2023

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics: estimation theory hypothesis testing and verification linear regression Initial theoretical hints are also presented to make the performance of the exercises understood.

Leseprobe

Simone Malacrida

Exercises of Statistical Inference

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Exercises of Statistical Inference”

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

“Exercises of Statistical Inference”

“Exercises of Statistical Inference”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

estimation theory

hypothesis testing and verification

linear regression

Initial theoretical hints are also presented to make the performance of the exercises understood.

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

––––––––

INTRODUCTION

––––––––

I – THEORETICAL OUTLINE

Introduction

Estimation theory

Hypothesis testing

Regression

Bayesian inference

––––––––

II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 21

Exercise 22

Exercise 23

Exercise 24

Exercise 25

Exercise 26

Exercise27

INTRODUCTION

INTRODUCTION

In this exercise book, some examples of calculations related to statistical inference are carried out.

Furthermore, the main theorems used both in estimation theory and in hypothesis testing are presented.

The study of statistics, in fact, does not stop at the properties of continuous and discrete probability distributions, but expands into inference sectors, applying the statistical concepts of estimation, mean, variance, regression and hypothesis testing when in the presence of particular tests.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is presented in this workbook is generally addressed in advanced statistics courses at university level.

I

THEORETICAL OUTLINE

THEORETICAL OUTLINE

Introduction

––––––––

Statistical inference falls into two broad areas of interest: estimation theory and hypothesis testing.

At the basis of both areas is sampling understood as the choice of the sample of the statistical population: it can be random, probabilistic, reasoned or convenient.

The sampling methods depend on the probability distribution and on the random variables just described.

––––––––

Estimation theory

––––––––

The estimation theory allows to estimate parameters starting from measured data through a deterministic function called estimator.

There are various properties that characterize the quality of an estimator including correctness, consistency, efficiency, sufficiency, and completeness.

A correct estimator is a function that has an expected value equal to the quantity to be estimated, vice versa it is called biased.

The difference between the expected value of the estimator and that of the sample is called bias , if this difference is zero as the sample tends to infinity then the estimator is said to be asymptotically correct.