Language: Russian
Pages: 67
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;
Sampling method......Page 2
Sampling D.F.......Page 3
Moments estimation......Page 4
Convergence of estimators......Page 5
Big sample size......Page 8
Exercises......Page 9
Point estimation......Page 11
Moments method......Page 12
Maximum Likelihood method......Page 14
Exercises......Page 16
Mean square comparison......Page 18
Uniqueness of best estimate......Page 19
Acymptotically Gaussian estimates......Page 21
Asymptotical Gaussian estimates vs CLT......Page 22
Functions of sums......Page 23
Exercises......Page 24
Regular and non-regular distributions......Page 26
Rao-Cramer inequality......Page 27
RC inequality and efficient estimates......Page 29
Exercises......Page 32
Confidence estimation......Page 33
Exercises......Page 36
Gamma distr.......Page 37
Chi-squared distr.......Page 38
Student distr.......Page 39
Gaussian samples and rotation......Page 40
Confidence interval for Gaussian samples......Page 42
Exercises......Page 43
Hypotheses......Page 44
Two simple hypotheses......Page 45
Test comparison......Page 46
Most powerful test......Page 47
Proof of Neyman-Pearson Lemma......Page 49
Exercises......Page 52
Goodness-of-fit tests......Page 53
Pearson's chi-squared test......Page 54
Parametric hypothesis: Person's chi-squared test.......Page 56
Test of dependency......Page 57
Means equality testing: Gaussian samples......Page 58
Means testing with known variance......Page 59
Testing using confidence intervals......Page 60
Mean Square Method......Page 62
General Linear Regression......Page 63
Normal Equation......Page 64
Mean square esimates......Page 65
Matrix choosing......Page 66
Exercises......Page 67
