Beskjeder

Viktig: Det blir arrangert s?kalt kontinuasjonseksamen i l?pet av januar 2010 (med samme eksamensform som for prim?reksamen av 14. desember, alts? fem timers skriftlig, uten l?rebok, men med anledning til ? ta med ett (1) selvskrevet A4-ark med selvvalgt materiale). De som har sykemeldig for prim?reksamen eller har str?ket p? denne, har anleding til ? ta denne kontinuasjonseksamenen. Jeg vil anbefale dem som viser seg ? ha f?tt en "F" for prim?reksamen ? benytte denne anledningen -- les, repeter og ?v p? det sentrale stoffet, og fokuser p? ? kunne skrive sentrale resonnementer p? en klar m?te.

Viktig: Jeg fikk tilfeldigvis h?re at eksamen er flyttet (ikke i tid, men i rom), fra Store lesesal i VB-bygget, til Undervisningsrom 3 i Biblioteksbygget. Antagelig er denne informasjonen sendt til kandidatene, kanskje pr. StudentWeb (?), og jeg h?per at beskjeden n?r frem:

Avsluttende skriftlig eksamen 14 December at 09:00 (5 hours):

Undervisningsrom 3 Georg Sverdrups hus

The teaching Tue Dec 2 from 9:15 to 11 takes place in B 81.

Since several stk 4010 students have an exam Tue Dec 1, we postpone that week's lecture to Wed Dec 2, 9:15 to perhaps 11:15. A message will be put up here within a day or two about where this lecture will take place.

Note that the "tidligere eksamensoppgaver" site also has some exam sets for the course ST 201, which perhaps may be said to have had a correlation with the stk 4010 course around 0.80. Browse through these exam sets and try to solve as many problems as you can.

Exercises to be dealt with this week: Exam stk 4010 h?st 2005, #1; Exam st 201 1994 #2.

Exercises for Tue Nov 24:

Nils Exercises #52, 53, 54; Exam stk 4010 h?st 2005, #5.

The last part of our curriculum is that of Sections 7.1-7.4 in Lehmann's book, which we focus on Nov 24.

There is now a Version C of the Exercises and Lecture Notes, comprising 68 exercises on 42 pages; please print out a copy for your own convenience. I have included some exam sets I made for the similar course "ST 201" in 1989 and 1995.

Exercises for Tue Nov 17:

Nils Exercises, Nos. 50, 51, 52, 53. (These actually make up the full Exam set, Exercises 1, 2, 3, 4, for the course ST 201, "twenty years ago today", to quote Sgt. Pepper.) For Exercise #53, you may limit the ambition level from "almost sure convergence" to "convergence in probability".

Importantly, the students are generously given the possibility of handing in written solutions to all or any of these four exercises, by Tue Nov 17; Nils will then mark them and provide individual comments.

Nils gives a lecture for KoMiN (Konferanse for Matematikkstudenter i Norge) in Trondheim, Sat November 1: "Stille flyter ikke Don: En statistisk analyse av en krangel mellom to Nobelprisvinnere".

Nils gives a lecture for TENK math coaches at the Fysikkbygget, Blindern, Oslo, Sat November 8: "Matematikk i Andeby".

Exercises for Tue Nov 3:

Nils Exercise 20, 9; Lehmann 1.14, 1.16, 2.12 from Ch 4. (The exponential E(a,b) is defined on page 31.)

Pensum er som f?lger:

A: Alle oppgaver som er gjennomg?tt i l?pet av kursets gang, fra Lehmanns bok og fra Nils' "Exercises and Lecture Notes". Appendiks-oppgavene der, spesifikt A1 til A5, utfyller og supplerer Lehmanns Sections 7.1-7.5.

B: Fra Lehmanns bok:

Ch. 1: Hele. Ch. 2: 2.6 og 2.8 g?r ut. Ch. 3: 3.2 g?r ut. Ch. 4: 4.4 g?r ut. Ch. 5: 5.6 og 5.7 g?r ut. Ch. 7: Sections 1, 2, 3, 5.

Note that Exercises and Lecture Notes now have been updated to a Version B, currently comprising 55 exercises over 34 pages; I have excavated and included some of the exercises I've constructed for similar courses taught in the past. We will not have time to go through all of these, but they serve a purpose as useful material to be exposed to; note, by the way, the long excursion into prime numbers and mathematical number theory in Exercise 19.

Also note the last six pages (comprising exercises A1 to A6); these will be defined as inside the curriculum of the course, and may be seen as an alternative version of Lehmann's Sections 7.1-7.3.

Exercises for Tue Oct 27:

Nils Exercises: what remains of 18, and then 20. After that we start on Exam 2005, Exercise 1.

Note that Exercises and Lecture Notes now have been uploaded to the course website. The current version comprises twenty exercises on eleven pages; please print out a copy for your own convenience.

Exercises for Tue Oct 20:

First, the rest of Exercise 3 from Exam 2007, with the extension that you also develop an approximation for the test's local power function.

Then, as far as we get with Nils Exercises 18 and 20.

Note that Exercise 19 is intended to serve as a "prototype illustration" for the essence of Chapter 3.

Please find, via http://www.math.uio.no/academics/eks/ , the two examination sets for STK 4010 for H?st 2005 and H?st 2007, and print them out for your convenience.

Exercises for Tue Oct 13: All of the H?st 2007 examination set (i.e. Exercises 1, 2, 3).

YES! Jeg m? noe mer presist opplyse om "Young European Statisticians", som arrangerer internasjonale PhD-kurs i "Eurandom", Eindhoven, Nederland, og p? forelesningen 29.9 glemte jeg ? si klart fra at det ikke blir undervisning i stk 4010 tirsdag 6.10, siden jeg alts? (og som nevnt en gang tidligere) gir et kurs for YES den uken.

Eksamensdatoen skrues som nevnt fast til mandag 14.12, og vi kommer tilbake til detaljer senere.

1. We are tentatively fixing the Exam Date for Monday December 14 ("skriftlig eksamen, uten hjelpemidler", possibly with the variation that each student is allowed to bring to the exam a single sheet of his or own notes). If there are no protests, this date will be official & fixed by next week.

2. Exercises for Tue Sept 29:

From Ch 2, Section 5: 8, 10; Section 7: 2, 7. Extra 6: Consider independent Bernoulli trials X1, X2, ... with probabilities p1, p2, ... Work with the explicit moment generating function of Zn = (Sn - mean)/standev, where Sn = X1 + ... + Xn, and give a characterisation of when Zn tends to a N(0,1).

We have started working on Ch 3.

Exercises for Tue Sept 22:

From Ch 2, Section 5: 2, 3, 4, 5, 8, 10.

I intend to use one more hour on Ch 2 material (e.g. Section 7), after which we attack Ch 3.

9/9/9: Exercises for Tue Sept 15:

From Ch 2: The rest of 3.10; then from Section 4: 3, 4, 6, 7; then from Section 5: 2, 3, 4.

From Ch 2, Sections 2.6 and 2.8 are gently pushed out of the curriculum, in order for us to more quickly come to Chs 3 and 4.

Exercises for Tue Sep 8:

Extra 4: Let Y1, ... Yn be i.i.d. from the uniform (0, theta) distribution, and let Mn be the largest of these observations. Find the limit distribution of n (theta - Mn), and use this to form an approximate 95% confidence interval for theta.

Extra 5: Suppose Xn and X are variables taking values in 0, 1, 2, ..., with Pr(Xn = j) = pn(j) and Pr(X = j) = p(j). Show (from the start definition) that Xn tends in distribution to X if and only if pn(j) tends to p(j) for all j. Use this to demonstrate that if Xn is Bin(n, p), with np tending to lambda as n increases, then Xn tends to the Poisson (lambda).

Then, from ELL's exercises for Ch 2: 3.1, 3.2, 3.3, 3.6, 3.7, 3.10, 3.12.

Exercises for Tue Sep 1:

Extra 3: We have shown "the continuity lemma", that Xn to a in probability implies g(Xn) to g(a) in probability, if only g is continuous at the point x = a [cf. Theorem 2.1.4]. Now demonstrate the extended version, where the limit is a random variable X rather than merely a constant a: Xn to X in probability implies g(Xn) to g(X) in probability, if g is continuous (in the region that X falls).

Then, from ELL's exercises for Ch 2: rest of 1.8, then 1.7, 1.9, 2.1, 2.9, 2.10.

Exercises for Tue Aug 25:

Extra 1: Consider Z =(X1 + ... + Xk - k mu)/(sqrt(k)*sigma), where the X's are i.i.d. uniform (0,1), with mu = 1/2 and sigma = sqrt(1/12). Simulate 10^4 such variables for k = 1, and give a histogram; then similarly 10^4 values for k = 2, with a histogram; etc., for k up to say 10. Comment on what is being shown by these histograms.

Extra 2: Simulate 10^4 random variables Xi from the unit exponential distribution, and compute the sequence Z1, Z2, ..., where Zn is the mean of the n first (Xi - mean(Xn))^3. Plot them, and comment on what you find.

Then, from ELL's exercises for Ch 2: Nos. 1.1 to 1.5; 1.8, 1.9.

Welcome to the stk 4010 course -- which starts Tue Aug 18th. On this first day of the course we shall only use two rather than three hours (since we do not have Exercises yet, and since I need to go to a meeting).

The course material will be drawn from E.L. Lehmann's "Elements of Large-Sample Theory" (1999), which you should get hold of, e.g. from the Akademika bookshop. I will also prepare some extraneous lecture notes and exercises during the course. The curriculum will consist of some material from each of the chapters (but not of everything from each chapter).

On Tue Aug 18 I plan to give an overview of sorts over what the course will involve and to what problems its methods may be applied. More regular teaching (i.e. chapter by chapter, and most of the time divided into two hours lectures plus one hour exercises) will then proceed from Tue Aug 25 onwards.

Nils Lid Hjort