• Rezultati Niso Bili Najdeni

Assume that the parameters µ and Σ are unknown

N/A
N/A
Info
Prenesi
Protected

Academic year: 2022

Share "Assume that the parameters µ and Σ are unknown"

Copied!
1
0
0

Nalaganje.... (ogled polnega besedila zdaj)

Prenesite zdaj ( 1 Strani )

Celotno besedilo

(1)

Correlation test for multivariate normal distribution Assume that the data x1,x2, . . . ,xn are an i.i.d. sample from the multi- variate normal distribution of the form

X1 ∼N

µ(1)

µ(2)

,

Σ11 Σ12

Σ21 Σ22

.

Assume that the parameters µ and Σ are unknown. Assume the following theorem:

If A(p×p) is a given symmetric positive definite matrix then the positive definite matrix Σthat maximizes the expression

1

det(Σ)n/2 ·exp

−1

2Tr Σ−1A

is the matrix

Σ= 1 nA. The testing problem is

H0: Σ12 = 0 versus H1: Σ12 6= 0.

a. Find the maximum likelihood estimates of µ and Σ in the uncon- strained case.

b. Find the maximum likelihood estimates ofµand Σin the constrained case.

c. Write the likelihood ratio statistic for the testing problem as explicitly as possible.

d. What can you say about the distribution of the likelihood ratio statis- tic?

1

Reference

Prenesite zdaj ( PDF - 1 Strani - 86.71 KB )

POVEZANI DOKUMENTI

The Role of Minority Education in the Expansion of the Functions of Hungarian Landscape Houses

– Traditional language training education, in which the language of in- struction is Hungarian; instruction of the minority language and litera- ture shall be conducted within

Border as Method: Impact of the Covid-19 Pandemic on the Border Area between Italy and Slovenia and on the Slovene Minority in Italy

Efforts to curb the Covid-19 pandemic in the border area between Italy and Slovenia (the article focuses on the first wave of the pandemic in spring 2020 and the period until

Bridging the Gap Between the Politics of Recognition and the Politics of Language Service Delivery in Ontario and Wales

A single statutory guideline (section 9 of the Act) for all public bodies in Wales deals with the following: a bilingual scheme; approach to service provision (in line with

New Speakers in the Context of the Minority Languages in Europe and the Revitalisation Efforts

If the number of native speakers is still relatively high (for example, Gaelic, Breton, Occitan), in addition to fruitful coexistence with revitalizing activists, they may

What kind of involvement for national minorities in the political decision-making process? : an overview of the case of the Slovenes in Italy

Several elected representatives of the Slovene national community can be found in provincial and municipal councils of the provinces of Trieste (Trst), Gorizia (Gorica) and

Linguistic landscape as a mirror : the case of the Slovene minority in Italy

Therefore, the linguistic landscape is mainly monolingual - Italian only - and when multilingual signs are used Slovene is not necessarily included, which again might be a clear

The identification and definition of the minority community as an ideological construct : the case of Slovenians in Italy

We can see from the texts that the term mother tongue always occurs in one possible combination of meanings that derive from the above-mentioned options (the language that

The legal protection of national and linguistic minorities in the Region of Friuli Venezia Giulia : a comparison of the three regional laws for the "Slovene linguistic minority", for the "Friulian language" and for the "German-Speaking minorities"

The comparison of the three regional laws is based on the texts of Regional Norms Concerning the Protection of Slovene Linguistic Minority (Law 26/2007), Regional Norms Concerning