Author | Andersen, Erling B. author |
---|---|
Title | Statistics for Economics, Business Administration, and the Social Sciences [electronic resource] / by Erling B. Andersen, Niels-Erik Jensen, Nils Kousgaard |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1987 |
Connect to | http://dx.doi.org/10.1007/978-3-642-95528-0 |
Descript | XII, 440 p. online resource |
1. Introduction -- 1.1. Statistical methods -- 1.2. Examples -- 2. Descriptive Statistics -- 2.1. Data and variables -- 2.2. Description of the observed distribution of a categorical variable -- 2.3. Description of the observed distribution of a quantitative variable -- 2.4. Description of a grouped distribution of a quantitative variable -- 2.5. Linear relationship between two quantitative variables -- 2.6. Multiplicative and additive structures in two-way tables -- 3. Probability Theory -- 3.1. Observations and events -- 3.2. Combinations of events -- 3.3. Relative frequencies and probabilities -- 3.4. The axioms of probability theory -- 3.5. Conditional probabilities -- 3.6. Stochastic independence -- 4. Probability Distributions on the Real Line and Random Variables -- 4.1. Probability distributions on the real line -- 4.2. Random variables -- 4.3. Discrete random variables -- 4.4. Continuous random variables -- 4.5. Transformations -- 4.6. Empirical frequencies and density functions -- 5. Mean Values and Variances -- 5.1. The mean value -- 5.2. The variance -- 5.3. Theorems about mean values and variances -- 5.4. Other moments and distributional measures -- 5.5. Applications of location and dispersion measures -- 6. Special Discrete Distributions -- 6.1. The binomial distribution -- 6.2. The Poisson distribution -- 6.3. The Pascal distribution -- 6.4. The multinomial distribution -- 6.5. The hypergeometric distribution -- 7. Special Continuous Distributions -- 7.1. The normal distribution -- 7.2. The log-normal distribution -- 7.3. The exponential distribution -- 7.4. The Pareto distribution -- 7.5. The gamma distribution -- 7.6. A comparison of six distributions -- 8. Multivariate Distributions -- 8.1. Multi-dimensional random variables -- 8.2. Discrete m-dimensional random variables -- 8.3. Continuous m-dimensional random variables -- 8.4. Marginal distributions -- 8.5. Conditional distributions -- 8.6. Independent random variables -- 8.7. Mean values and variances for sums of random variables -- 8.8. The covariance and the correlation coefficient -- 8.9. The multinomial distribution -- 8.10. The distribution of sums of random variables -- 8.11. The multivariate normal distribution -- 9. The Distribution of Sample Functions and Limit Theorems -- 9.1. Introduction -- 9.2. The distribution of $$\overline {\rm{X}}$$ and S2 for normally distributed random variables -- 9.3. The t-distribution and the F-distribution -- 9.4. The law of large numbers -- 9.5. Limit theorems -- 10. Estimation -- 10.1. The statistical model -- 10.2. Estimation -- 10.3. Maximum likelihood estimation -- 10.4. Unbiased estimators -- 10.5. Consistency -- 10.6. The properties of ML-estimators -- 11. Confidence Intervals -- 11.1. Point estimates and confidence intervals -- 11.2. Confidence intervals -- 11.3. Confidence intervals for the mean value and the variance in the normal distribution -- 11.4. Confidence intervals for the parameters in the binomial distribution and the hypergeometric distribution -- 11.5. Approximate confidence intervals -- 11.6. Concluding remarks -- 12. Testing Statistical Hypotheses -- 12.1. The statistical hypothesis -- 12.2. Significance tests -- 12.3. Construction of tests -- 12.4. Tests in discrete distributions -- 12.5. Conditional tests -- 12.6. Approximate tests -- 12.7. The power of a test -- 12.8. Hypothesis testing and interval estimation -- 13. Models and Tests Related to the Normal Distribution -- 13.1. The u-test -- 13.2. The t-test -- 13.3. The Q-test -- 13.4. The comparison of two independent normally distributed samples -- 13.5. A model for pairwise observations -- 13.6. The model for pairwise observations and the model for two independent samples -- 13.7. The analysis of variance -- 13.8. Distribution free tests -- 14. Simple Linear Regression -- 14.1. Regression analysis -- 14.2. Simple linear regression -- 14.3. Estimation of the parameters -- 14.4. Properties of the LS-estimator -- 14.5. Analysis of variance -- 14.6. Interpretation of the estimated regression parameters and R2 -- 14.7. Examination of the residuals -- 14.8. Predictions -- 14.9. Experimental and non-experimental data -- 14.10. Transformations -- 14.11. Comparison of two regression lines -- 15. Multiple Linear Regression -- 15.1. The multiple linear regression model -- 15.2. Estimation of the parameters -- 15.3. Properties of the LS-estimator -- 15.4. Residual analysis -- 15.5. Hypothesis testing -- 15.6. Case analysis -- 15.7. Collinearity -- 15.8. Predictions -- 16. Heteroscedasticity and Autocorrelation -- 16.1. Heteroscedasticity -- 16.2. Autocorrelation -- 17. Survey Sampling -- 17.1. Introduction -- 17.2. Simple random sampling -- 17.3. Simple random sampling in the binary case -- 17.4. Simple random sampling m the general case -- 17.5. Stratified sampling -- 18. Applications of the Multinomial Distribution -- 18.1. Hypothesis testing in the multinomial distribution -- 18.2. Goodness-of-fit tests of discrete distributions -- 18.3. Goodness-of-fit tests of continuous distributions -- 18.4. Comparison of k Poisson distributions -- 19. Analysis of Contingency Tables -- 19.1. The test of independence -- 19.2. The test of homogeneity -- 19.3. Comparison of binomial distributions -- 19.4. The multiplicative Poisson model -- 19.5. The effect of the sampling procedure -- 19.6. Analysis of the marginals of a two-way table -- 19.7. Three-way contingency tables -- Appendix Table -- Index of Examples with Real Data