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Exercises in Statistical Inference

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Language:  English
Statistical inference is a process of drawing general conclusions from data in a specific sample.
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Statistical inference is a process of drawing general conclusions from data in a specific sample. Typical inferential problems are: Does alternative A give higher return than alternative B? Is drug A more effective than drug B? In both cases solutions are based on observations in a single sample.

To solve inferential problems one has to deal with the problems: (i) How to find the best estimate of an unknown quantity, (ii) How to find an interval that covers the true unknown value and (iii) How to test hypothesis about the value of an unknown quantity. The treatment of these issues can be found in a large amount of statistical textbooks. The present book differs from the latter since it focuses on problem solving and only a minimum of the theory needed is presented.

  1. Introduction
    1. Purpose of this book
    2. Chapter content and plan of the book
    3. Statistical tables, computer programs and calculators
  2. Basic probability and mathematics
    1. Probability distributions of discrete and continuous random variables
    2. Some distributions
    3. Mathematics
    4. Final words
  3. Sampling Distributions
    1. Some exact sampling distributions
    2. Sample moments
    3. Asymptotic and approximate results in sampling theory
    4. Final words
  • Supplementary Exercises, Ch. 3
  1. Point estimation
    1. Concepts
    2. Requirements on estimators
    3. Estimation methods
    4. Final words
  • Supplementary Exercises, Ch. 4
  1. Interval estimation
    1. Concepts
    2. CIs in small samples by means of pivotal statistics
    3. Approximate CIs in large samples based on Central Limit Theorems
    4. Some further topics
    5. Final words
  • Supplementary Exercises, Ch. 5
  1. Hypothesis Testing
    1. Concepts
    2. Methods of finding tests
    3. The power of normally distributed statistics
    4. Adjusted p-values for simultaneous inference
    5. Randomized tests
    6. Final words
  • Supplementary Exercises, Ch. 6
  1. Linear regression
    1. The Gauss-Markov model for simple linear regression
    2. Multiple regression
    3. Random Coefficient models
    4. Final words
  • Supplementary Exercises, Ch.7
  1. Logistic regression for binary outcomes
    1. Examples of logistic regression
    2. Prediction of binary outcomes based on logistic regression
    3. Final Words
  • Supplementary Exercises, Ch. 8
  • Solutions to Supplementary Exercises
  • References

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About the Author

Robert Jonsson

Robert Jonsson got his Ph.D. in Statistics from the Univ. of Gothenburg, Sweden, in 1983. He has been doing research as well as teaching undergraduate and graduate students at Dept. of Statistics (Gothenburg), Nordic School of Public Health (Gothenburg) and Swedish School of Economics (Helsinki, Finland). His researches cover theoretical statistics, medical statistics and econometrics that in turn have given rise to 14 articles in refereed international journals and some dozens of national papers. Teaching experience reaches from basic statistical courses for undergraduates to Ph.D. courses in Statistical Inference, Probability and Stochastic processes.