Statistiek: an introductory course in mathematical statistics

Textbook: Mathematical statistics and data analysis, John A. Rice, 3d edition (with CD).

Grading system: homework 30% (earning at least 80% of points is considered as a 100% performance), the midterm test (deeltentamen 1) counts for 30%, and the final exam (deeltentamen 2) for 40%. Herkansing covers the whole course.

  • 14.09.2010. pages 199-214. Distinction of ordered/unordered samples, with/without replacement.

    Inleveropgaven: 1,4,6,7 on pp.239-240 (0.5 points each); prove Corollary B on p 212 (0.5 point)

    The homework is to be returned in the class 21.09.2010

  • 21.09.2010. section 7.3.3, mean squared error of estimator, consistency, section 8.4

    Inleveropgaven: Ch7: 8 (1 point), 9 (1 point), 16 (0.5 points), Ch8: 3 (1 point), 4a,b (1 point)

    The homework is to be returned in the class 28.09.2010

  • 28.09.2010. Sections 8.5, 8.5.1, 8.5.2 including complete formulation and proof of Theorem A. Theorem B (without proof), and two formulas for the Fisher information (Lemma A).

    Inleveropgaven: Ch8: 16ab (1 point), 18ab (1 point), 23 (0.5 point), 27ab (1 point)

    The homework is to be returned in the class 04.10.2010

  • 05.10.2010. Sections 8.7, about a half of Section 8.5.3, Bayesian approach, Example E of Section 3.5

    Inleveropgaven: Ch8: 4e (1 point), 5d (1 point), 6bc (0.5 point each question), 7bcd (0.5 point each question);

    Assume uniform[0,1] prior for the unknown probability of a head. A coin is tossed 100 times, with 60 of the tosses being heads. What is the probability that the next toss will be head? (1 point)

    The homework is to be returned in the class 20.10.2010

  • 19.10.2010. Section 8.8, criterion for the minimal sufficient statistic

    Inleveropgaven from Ch8: 68 (1 point), 69 (0.5 point), 71 find the minimal sufficient statistic (1 point), 72 (0.5 point), 73 (1 point), 74 (0.5point).

    The homework is to be returned in the class 26.10.2010

  • The midterm test is scheduled for 09-11-2010, 17.00 - 20.00, EDUC MU

  • 26.10.2010. Sections 9.1, 9.2, 9.4

    Inleveropgaven from Ch9: 17 (1 point), 18 (1 point), 19 (1 point), 20 (1 point)

    The homework is to be returned in the class 02.11.2010

  • 2.11.2010. Sections 9.5 (with proof in the case of simple hypothesis using local CLT), 9.3, 9.2.1

  • 16.11.2010. A rigorous result on the chi-square test from Section 9.5. The chi-square test for goodness of fit of discrete distributions, and applications to continuous distributions. Order statistics (see pages 352-353), empirical distribution function (pages 378-380). Glivenko-Cantelli theorem. Kolmogorov-Smirnov statistic and test for goodness of fit.

    Inleveropgaven:

    1. (0.5 point) Construct a test for H_0: \mu=\mu_0 vs H_1:mu\noteq \mu_0. Here \mu is the mean of normal distribution, whose variance \sigma^2 is unknown.

    2. (1 point) Consider a sample of n values from distribution function F with density f. Derive a formula for the density of the k-th order statistic.

    From Section 9.11: Problems 1 (0.5 point), 3 (1 point), 7 (1 point), 8 (0.5 point)

  • The lecture room has changed! In this block we have HC on Dinsdag 13.15 - 15.00 in MIN 012, WC on Dinsdag 15.15 - 17.00 in MIN 208.

  • 23.11.2010. pp 420-423, 426, 427, distribution of ranks for iid sample, 435-441.

    Inleveropgaven from section 11.6 (to be returned on December 7)

    10 (0.5 point), 11 (0.5 point), 14 (1 point), 19 (1 point), 24 (0.5 point)

  • 30.11.2010. sections 11.2.3 (finished), 11.2.4
  • 7.12.2010 Sections 11.3; 11.3.1; 11.3.2 (and normal approximation to W_+); 12.2.1

    Inleveropgaven (from section 11.6) 23 (1.5 point) ; 27 (1 point); 33 (1 point)

    In problem 23(b) you may use order statistics of samples to construct first confidence intervals for the medians of F and G, then use the intervals to derive a confidence interval for \Delta, with significance level at least \alpha.

  • 14.12.2010 Sections 14.1, 14.2, 14.3, 14.4.2

    Inleveropgaven (from section 14.9) 18 (1 point); 21 (1 point); 23 (1 point), 31 (1 point)

  • 21.12.2010 The least-square estimate as projection, the Gauss-Markov theorem, Section 14.4.3, Section 14.4.5 page 578, F-test of significance

  • Next Werkcollege is on 11.01.2011 in MIN 012 at 13:15-15:00.