Motivation: Goodness of Fit Testing for a Gaussian Distribution 1 ponto possível (classificado) Let X1,..., X, be iid random variables with continuous cdf F. Let {N (μ,0²)}ER,²> denote the family of all Gaussian distributions. We want to test whether or not FE {N (1,0²)}ER,²>0 Let denote the cdf of N (#4, 2). We formulate the null and alternative hypotheses HoF H₁F = 14,0 for some μER,² > 0 for any μER,² > 0. Motivated by the Kolmogorov-Smirnov test, you define a test-statistic using the sample mean and sample variance 2: Tn sup√√F (t) | tER Assume that the null hypothesis is true. Is it true that (d) T sup B (z)| 11-00 zЄ[0,1] where B (x) is a Brownian bridge? (Refer to the slides.) True False
Motivation: Goodness of Fit Testing for a Gaussian Distribution 1 ponto possível (classificado) Let X1,..., X, be iid random variables with continuous cdf F. Let {N (μ,0²)}ER,²> denote the family of all Gaussian distributions. We want to test whether or not FE {N (1,0²)}ER,²>0 Let denote the cdf of N (#4, 2). We formulate the null and alternative hypotheses HoF H₁F = 14,0 for some μER,² > 0 for any μER,² > 0. Motivated by the Kolmogorov-Smirnov test, you define a test-statistic using the sample mean and sample variance 2: Tn sup√√F (t) | tER Assume that the null hypothesis is true. Is it true that (d) T sup B (z)| 11-00 zЄ[0,1] where B (x) is a Brownian bridge? (Refer to the slides.) True False
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ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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![Motivation: Goodness of Fit Testing for a Gaussian Distribution
1 ponto possível (classificado)
Let X1,..., X, be iid random variables with continuous cdf F. Let {N (μ,0²)}ER,²> denote the
family of all Gaussian distributions. We want to test whether or not FE {N (1,0²)}ER,²>0
Let denote the cdf of N (#4, 2). We formulate the null and alternative hypotheses
HoF
H₁F
=
14,0
for some μER,² > 0
for any μER,² > 0.
Motivated by the Kolmogorov-Smirnov test, you define a test-statistic using the sample mean and
sample variance 2:
Tn
sup√√F (t) |
tER
Assume that the null hypothesis is true. Is it true that
(d)
T
sup B (z)|
11-00 zЄ[0,1]
where B (x) is a Brownian bridge? (Refer to the slides.)
True
False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc877219b-d7c5-4942-94bb-461bbffa36de%2Fd0fc20b2-853e-4d3f-943d-2776e0adeebd%2F4j3plqi_processed.png&w=3840&q=75)
Transcribed Image Text:Motivation: Goodness of Fit Testing for a Gaussian Distribution
1 ponto possível (classificado)
Let X1,..., X, be iid random variables with continuous cdf F. Let {N (μ,0²)}ER,²> denote the
family of all Gaussian distributions. We want to test whether or not FE {N (1,0²)}ER,²>0
Let denote the cdf of N (#4, 2). We formulate the null and alternative hypotheses
HoF
H₁F
=
14,0
for some μER,² > 0
for any μER,² > 0.
Motivated by the Kolmogorov-Smirnov test, you define a test-statistic using the sample mean and
sample variance 2:
Tn
sup√√F (t) |
tER
Assume that the null hypothesis is true. Is it true that
(d)
T
sup B (z)|
11-00 zЄ[0,1]
where B (x) is a Brownian bridge? (Refer to the slides.)
True
False
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