# Questions tagged [neyman-pearson-lemma]

A theorem stating that likelihood ratio test is the most powerful test of point null hypothesis against point alternative hypothesis. DO NOT use this tag for Neyman-Pearson approach to hypothesis testing, this tag is for the lemma only.

61 questions
Filter by
Sorted by
Tagged with
13 views

61 views

### Can the alternative hypothesis depend on the sample size?

Suppose that we want to test: $$H_0: \theta = 0 \,\,\, vs. \,\,\, H_1:\theta = 1/n,$$ where $n$ is the sample size used to test the hypothesis, and the sample used for this is $X_i \sim f(;\theta)$. ...
29 views

### Understanding the general theory proposed by Neyman & Pearson

I'm reading Neyman & Pearson, 1933, i.e. Neyman and Pearson. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. ...
39 views

### Constant value in Neyman Pearson lemma

To know the k value in Neyman Pearson lemma, do we need to know the alternate hypothesis. To what I understood (from articles like PenStateNotes), we could get value of k using null hypothesis and the ...
51 views

### Hypothesis Testing and Neyman Pearson Lemma

Are there any general steps for hypothesis testing, in terms of what is a one-sided and two-sided test? If the null hypothesis H_o, then there are 3 cases. Is this correct? If H_o:θ=θ_0 3 cases: <...
69 views

601 views

### Proof of Neyman Pearson Lemma

I am trying to understand the proof of Neyman Pearson Lemma as Uniformly Most Powerful test from here (Page 3). It says the following: Let $H_0: \theta = \theta_0$ and $H_a: \theta = \theta_1$. ...
236 views

### Chi-square test for image encryption

I have a cipher image $C$ that has intensity levels between $0-255$. I want to check this cipher image for uniformness. For this, I calculated the Chi-square tests. The $\chi^2=270.2112$ and i know ...
686 views

64 views

### Neyman Pearson Lemma

I've been reading up on Neyman Pearson Lemma but don't understand it to its full extent. Could someone please explain to me how to obtain the most powerful size in a bernoulli distribution?
148 views

### UMP test for a distribution and calculating alpha

My $f(x) = \theta x ^{ (\theta -1)}$ for $0 < x < 1$ and $\theta > 0$. I found that the UMP to test $H_0: \theta = 1 \mbox{ vs } H_a: \theta = \theta_a$ is $\sum(ln(x_i)) \geq c$. I have a ...
36 views

### How to detect signal when threshold is not known for this communication problem?

I am trying to work on a nano scale communication problem. The transmission media is considered to be fluid and the molecules are the one that communicates information from transmitter to receiver. I ...
524 views

2k views

### Best critical region and Neyman-Pearson lemma?

I'm reading an online course and I'm really confused about the Neyman-Pearson lemma. It states From my understanding, does it mean that critical region could be any region like (a,b) and (c,+00)? ...
There are 7 balls in urn. $Q$ of them are white and the rest are black. We have hypothesis $H_0:Q=3$ and $H_1:Q=5$. To test this we draw 2 balls (balls don't come back to the urn - i.e. they are drawn ...