Inference, in a statistical context, refers to drawing conclusions from data containing an element of randomness introduced by e.g. measurement error, sampling variation, or assignment of experimental treatments. A common inferential paradigm is drawing conclusions about population parameters from ...

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Statistical validity of association rules with low support

We have data sample with 10,000 observations. We are using association analysis to find segments with low support (< 4%) and high(er) confidence. Our rules are always in such way that on the right ...
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16 views

Estimating equation for power divergences

The inference based on minimizing the power divergence $$D_{\lambda}(g\|f) = \frac{1}{\lambda - 1} \log \int g^{\lambda} f^{1-\lambda} dx$$ is known to be robust against outliers for $\lambda <1$. ...
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1answer
18 views

Fisher's LSD test

When we calculate Fisher's LSD test, why do we use Mean Square of Error which is the variance of all groups (pooled variance), as a variance of each individual group mean? In the denominator it's: ...
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14 views

What is the intuition behind asymptotic normality of a parameter vector

I'm studying statistical inference and am trying to understand what it means for the estimate of a parameter vector to be asymptotically normal. I can understand the univariate version of this but ...
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1answer
75 views

How do frequentists guess a distribution?

With competing hypotheses such as testing if a coin is fair, frequentists and Bayesians have their own approaches. What about for coming up with a distribution? In An Essay towards solving a Problem ...
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64 views

Calculating Standard Error of Standard Deviation

Following this post , I think first I need to be theoretically sound . In my theory class , I learnt that inverse of information matrix is the variance-covariance matrix of estimates . To find the ...
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16 views

How is the confidence interval of variance component calculated?

How is the confidence interval of variance component calculated ? As far I know , confidence interval of variance is calculated as : ...
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2answers
18 views

Why OLS F Statistic close to one when there is no relationship?

I might be missing something obvious here. In linear regression, F statistic is defined as (explained variance / p) / mean squared error, where p is number of independent variables. When there is no ...
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34 views

Why are the Wald standard errors often very poor estimates of the uncertainty of variances?

As from this post as @Ben Bolker pointed out that : .. note that these (as often pointed out by Doug Bates) the Wald standard errors are often very poor estimates of the uncertainty of variances, ...
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18 views

Wald confidence interval

Are Wald Type confidence interval and confidence interval based on asymptotic standard normal distribution synonymous ? Can you please give me some reference ?
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1answer
37 views

Applying Lehmann-Scheffe Theorem to an example

Let me state the theorem first: Let $T$ be a sufficient and complete statistic for the statistical model $\mathcal{P}$ and let $\tilde{\gamma}_1$ be an unbiased estimator for the parameter ...
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18 views

Finding a sufficient statistic for a rectangular distribution

Iam trying to use this theorem for the problem below: a statistic is sufficient for $\mathcal{P} = \{P_{\theta}: \theta \in \Theta \}$ iff there exist nonnegative functions $g(\cdot; \theta)$ and ...
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1answer
15 views

Confidence measure/statistic for inferring a category with random independent sampling

Suppose there's a group of dogs and a set of people A,B,C,D. If I know that, in this hypothetical scenario, the person who owns the dog is the person who walks it ...
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10 views

Interpreting Tukey test for significant differences

Hi I have 38 categories and I have their means. I want to see if the differences in means are significantly different. I ran an anova and the p-value is <2e-16. Then I wanted to investigate ...
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1answer
50 views

A question about a Theorem about MLE

I have a question about a proof (about MLE) but let me firstly give you appropriate context. An estimator T is called maximum likelihood estimator of $\theta$, if: ...
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0answers
6 views

Inference from the posterior predictive distribution [duplicate]

I want to use Bayesian model to predict the values of signal in the future. The process is like: a. 1000 observations are given. First 800 consecutive observations are training data, and 200 ...
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1answer
49 views

$T$ is sufficient for $\mathcal{P}$, sufficient for $\theta$ , sufficient for $F$

The definition which is given in my book about sufficiency is: A Statistic $T$ is said to be sufficient for the statistical model $ \mathcal{P}= \{P_{\theta} : \theta \in \Theta \}$ of ...
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1answer
49 views

plot ROC curve from glm model using gaussian model

I have some data (322 x 4) that looks like that ...
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1answer
45 views

What is similarities and difference between statistical inference and hypothesis testing?

What is similarities and difference between statistical inference and hypothesis testing? I am confused between those
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1answer
19 views

transitive property in statistical comparisons

I want to know if the exposure to a given dose of a toxic chemical alters the concentration of a given substance in blood in my animals. I make this super general, bear with me, because I think this ...
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4answers
83 views

$\chi^2$ tabulated value

I noticed that the critical $\chi^2$ value increases as the degrees of freedom increase in a $\chi^2$ table. Why is that?
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1answer
38 views

Statistical Significance

Our teacher told us If a test is rejected at 1% level of significance , then it will be rejected at 5% , 10% level of significance . I don't understand how does the rejection at 1% level of ...
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11 views

Find maximum joint distribution in bayesian network that is not singly connected

I am puzzled the last days because i am trying to find the maximum of a joint distribution represented by a bayesian network. My network is not singly connected. Let's assume that my distribution is ...
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99 views

Karlin-Rubin theorem and exponential family

Let $X_1,...X_n$ a random sample of $X$ with density $$f(x;\alpha,\beta)=\frac{\alpha}{x^{\alpha+1}}\beta^\alpha I_{[\beta,\infty]}(x)\space\alpha>0,\beta>0$$ with $\beta$ known. Find ...
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1answer
31 views

Is there a method to form a CI based on an MLE which is not the mean

I know how to find confidence intervals for parameters based on sample means. I want to know whether there exists a method for finding confidence intervals based on MLE's which are not sample means. ...
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1answer
52 views

$E_{\theta_1}[\ell(\theta_2;X)] $

I am faced with the following in my "Statistical inference book" $E_{\theta_1}[\ell(\theta_2;X)] $ where $\ell(\theta_2;X)$ (loglikelihood) is $\log [P(\theta_2;X)]$, X is a random variable. What ...
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1answer
87 views

Ways to find a UMP test

I'm studying for my final exams and the subject of proof will basically test hypotheses, I will try to summarize here my doubts. For found the UMP test the ways are 1) Use Neyman–Pearson lemma ...
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51 views

How to combine normal distributions to have a mixture with specified kurtosis

I want to generate random samples from Normal Distributions $N(\mu_i,\sigma_i)$ by fixing kurtosis parameters ($\beta$s), as I need to simulate data by varying $\beta$ for my problem. I am trying to ...
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1answer
32 views

Multiple comparisons with normality tests

Suppose I do $1000$ normality tests, and set $\alpha = 0.05$. When testing for normality, should I correct for multiple comparisons? So if $p>\frac{0.05}{1000}$, I should keep the null hypothesis ...
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2answers
40 views

How to choose the sample size for a pilot study for making a power analysis?

Suppose one would like to test some new hypothesis, for which there are no previous data available. To estimate the needed sample size, one should do a power analysis. Since there are no previous data ...
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1answer
46 views

Neyman-Pearson Lemma and hypothesis-testing

Consider testing $H_0:\theta=\theta_0$ vs $H_1:\theta=\theta_1$, where the pdf or pmf corresponding to $\theta_i$ is $f(x|\theta_i)$, $i=0,1$ using a test with rejection region R that satisfies ...
2
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1answer
42 views

Likelihood ratio for normal distribution with known variance

Let $X_1,...,X_n$ random sample of $X$~$N(\mu,\sigma^2)$ with known $\sigma^2$.Take $a=.05$ find the expression for power function of the likelihood-ratio test $$H_0:\mu\leq 0\space vs\space ...
2
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1answer
57 views

Likelihood-ratio test

I was studying on this subject and I got some questions. Lets take the test $$H_0:\theta\in\Theta_0 \space vs\space H_1:\theta\in\Theta_0^c$$ where $\Theta$ is the parametric space and ...
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1answer
53 views

Testing for Significance - Should t-test be used or paired t-test

Let's say there are 100 stock exchanges on which I trade stocks and the cost of me trading has the averages below ...
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8 views

How to compute Potentials in Junction Tree from Set Chain using LS also?

I was going through the original LS algorithm paper. I was not able to compute the potentials from the set chains shown on the page 171 (Table 3). Apart from that, I was able to compute all the ...
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1answer
44 views

Maximum Likelihood, normal distribution

Let $Z$~$N(\mu,\sigma^2+1)$, find the maximum likelihood estimator for $\mu$ and $\sigma^2$. I did but I want to check that this right actually ...
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11 views

sadists package/ Sum of (non-central) chi-squares to a power

I try use "sadists" package in R to compute quantiles and probabilities on sum of non-central chi-squares distribution, but there are some issues in this package. I give an example: wts = ...
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0answers
51 views

chi square test for large data sets

I use the Chi-square test for feature selection. I use it only when all entries in the contingency table are greater then 5. Is that the correct approach statistically? What happens for example, if ...
3
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1answer
37 views

Confidence interval for exponential distribution

Let $X_1,...,X_n$ random sample of $X$~$exp(\theta)$. i) Find a exact confidence interval for $\theta$ with coefficient of confidence equal to $\gamma$ ii)Find a asymptotic confidence ...
3
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0answers
33 views

Sampling distribution of sample trimmed (truncated) mean

It is elementary probability theory that the sample mean of an i.i.d. sample follows normal distribution, if the background distribution is normal. But what about the trimmed mean? Is there any result ...
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2answers
63 views

Find the confidence interval, uniform distribution

Let $X_1,..,X_n$ a random sample of $X$~$U[-\theta,\theta]$, $\theta>0$. Find the confidence interval for $\theta$. I'm trying to find a pivotal quantity with the maximum and minimum, but I ...
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34 views

Sufficient Statistic for non-exponential family distribution

Question: Let $X_1,X_2,....X_n$ be an iid sample from $N(\theta , 4 \theta^2 )$. I want to show that this model is not a member of the exponential family and to find a sufficient statistic for ...
3
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2answers
99 views

Difference of two squared normal dependent variables

I need to find the distribution of the random variable $Z$ $Z = \frac{(X - \mu_0)^2}{\sigma_0^2} - \frac{(X - \mu_1)^2}{\sigma_1^2}$, where $X \sim \mathcal{N}(\mu_0, \sigma_0)$. We can find the ...
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0answers
21 views

Testing if means are different and reporting on that usng R t.test

Lets say I have the 4 means that are the average response time for some variable: Response Time A .12 B .16 C .65 D -.35 I want to test ...
2
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2answers
76 views

Lagrange multipliers and confidence interval

Suppose $X_1,...X_n$ is a random sample from $X$~$N(\mu,\sigma^2)$, with $\sigma^2$ unknow. If $$[\overline{X}+z_{a_2}\frac{\sigma}{\sqrt{n}};\overline{X}-z_{a_1}\frac{\sigma}{\sqrt{n}}]$$ ...
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0answers
22 views

Marginal likelihood and coordinate ascent

When updating posterior distributions in Bayesian inference using coordinate ascent, is the marginal likelihood of the data guaranteed to increase after each update?
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1answer
45 views

Recommended Books on Advanced Statistical Inference [duplicate]

Can anyone suggest a nice book on advanced classical statistical inference? Thanks.
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1answer
136 views

How to extrapolate my sample results to population

We have tested randomly selected bacteria ($k = 198$) for antibiotic resistance over a period of 3 years (total isolates $n = 444$) and observed $117$ resistant strains. I would like to extrapolate ...
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13 views

How do I model chapter-verse references?

Context: I am part of an 8-person group in which each person posts a Bible verse every day. For those who don't know, that is of the format "Psalm 30:1" where first we reference the chapter, then the ...
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40 views

Inference with sample statistics

If I have mean and std deviation for two samples, can I comment on if the difference is statistically significant.