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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37 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.
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51 views

Applying the T-test [on hold]

So far I have calculated the sample means $\overline{A} = 0.75$ and $\overline{B} = 2.33$. Using these I computed the sample variances: $S_A^2 \approx \frac{28.805}{9} = 3.2005$ and $S_B^2 = ...
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1answer
26 views

What's my population? Is this Descriptive or Inferential?

I have a list of employees at a company. I want to show some comparison of some demographics (say, %female) of those who have left the company and those who have stayed with the company. However, I ...
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30 views

Rao-Blackwell exponential distribution

Let $X_1,..,X_n$ random sample of $X\sim\text{Exp}(\lambda)$ with $f(x;\lambda)=\frac{1}{\lambda}e^{-\frac{1}{\lambda}x}I_{[0,\infty]}(x)$ i) Find a unbiased estimator of $\lambda$ based ...
2
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1answer
28 views

UMVUE for a function

Let $X_1,...,X_n$ random sample $X$~$Bernoulli(p)$. For $n\geq 4$ show that the product $X_1X_2X_3X_4$ is a unbiased estimator for $p^4$, and use this fact for find the best unbiased estimator of ...
2
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0answers
30 views

Proper test for comparing two means from different distributions? (with limited data)

I have some data on frog weights for a small sample ($n \approx 30$). I need to compare the mean frog weight from this sample $\mu_s$ to the mean of another, much larger sample of frog weights $\mu_r$ ...
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29 views

Confidence interval, lower and upper bound

I am studying on confidence intervals, but I'm still with some doubts Let a random sample $X_1,..,X_n$ with density $f(x;\theta)=\theta e^{-\theta x}I_{[0,\infty]}(x)$. Find a confidence interval for ...
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25 views

Test of confidence intervals?

In one of my assignments I have to "test" if the confidence intervals (CIs) for a set of parameters in a mixed effect model is accurate. I'm asked to simulate from fitted parameters and after that to ...
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1answer
48 views

Testing a power-law hypothesis from the averaged distribution

A way to test the existence of power-law in the distribution is given in the following paper: http://arxiv.org/abs/0706.1062 The gist of the whole procedure is as follows: Let $\textbf{X}$ be the ...
2
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71 views

Confidence interval and probability

Suppose that $T_1$ is $100\gamma$ percent lower confidence limit for $\tau(\theta)$ and $T_2$ is $100\gamma$ percent uper confidence limit for $\tau(\theta)$. Further assume that ...
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1answer
25 views

Confidence Interval, uniform distribution

Let $X_1,...X_n$ random sample from $f(x;\theta)=I_{[\theta-\frac{1}{2};\theta+\frac{1}{2}]}(x)$. i) Show that $(X_{(1)},X_{(n)})$ is a confidence interval for $\theta$.ii) find your ...
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1answer
28 views

UMVUE explanations

Let $X_1,...,X_n$ a random sample where $X$~Poisson$(\theta)$. i)Find UMVUE for $\theta$ ii)Exists UMVUE for $\frac{1}{\theta}$ For i) I found that $T=\overline{X}$ is UMVUE for ...
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0answers
15 views

UMVUE for pareto distribution

Let $X_1,..X_n$ random sample with $f(x;\theta,a)=\frac{\theta}{a}(\frac{a}{x})^{(\theta+1)}I_{(a,\infty)}(x),a>0,\theta>0$. Find the UMVUE for $\theta$ when $a$ is fixed. My attempt ...
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0answers
32 views

What is Frequentist Inference?

Frequentist Inference is defined as (according to the tag wiki) : In the frequentist approach to inference , statistical procedures are assessed by their performance over a hypothetical long run ...
2
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1answer
49 views

I want to take a decision on two gaussian distributions, what approach can I take?

I observe a one dimensional random source, which could be any of two Gaussian distributions with a different set of parameters that do not change over time. They have a the same variance and a ...
2
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1answer
32 views

Cramer-Rao Lower Bound

Let $X_1,..,X_n$ be an iid sample of $N(0,\sigma^2)$. Find an unbiased estimator of $\sigma^2$ and its lower bound. I found that $$\hat{\sigma}^2 = \sum_{i=1}^{n} X_i^2$$ is an unbiased ...
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1answer
14 views

How to scale up mean/variance and confidence interval of clinical trial for whole population

In a clinical trial I have 1000 patients with disease A. Their mean treatment cost is 1000$ per patient with a 95% confidence interval of [900;1100] for example. The whole population of country X is ...
2
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1answer
55 views

Unbiased estimator and sufficient statistics

Let $X_1,..,X_n$ be a random sample of $f(x;\theta)=\theta x^{\theta-1}I_{[0,1]}(x)$ Find a sufficient statistic for $\theta$ and construct a unbiased estimator for $\theta$ as a function ...
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1answer
41 views

is an unbiased estimator better than an efficient estimator?

I've learnt that the efficiency of an estimator, say $\theta$, is defined by $Var(\theta)$. The closer to 0 this value is, the more efficient the estimator is. Let's say I have two estimators: ...
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1answer
65 views

Find a complete sufficient statistic,

Let $X_1,...,X_n$ be iid observations.Find a complete sufficient statistics for i)$f(x|\theta)=\frac{\theta}{(1+x)^{1+\theta}}I_{[0\infty)}(x), \theta>0$ What I did ...
2
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1answer
28 views

Problems due to analyzing variables from different levels at one single level

Please ease the following paragraph from the first chapter , Introduction to Multilevel Analysis , p.3 of the book: Historically , multilevel problems have led to analysis approaches that moved ...
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9 views

In a simple hypothesis vs composite hypothesis test, are the p-values the same?

In a simple hypothesis test, we have something like $H_0 = 5$ and $H_A = 10$ while in a composite hypothesis test we have something like $H_0 = 5$ and $H_A >5$. Since the p-value is defined to be ...
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1answer
20 views

How is the F-Stat in a regression in R calculated [duplicate]

I am running a regression and I'd like to be able to do the calculation to get to the F stat .3062. How is this .3062 calculated? Can you help? ...
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46 views

Evaluating integral to obtain marginal PDF related to Tikhonov Regularization

I am attempting to derive the marginal PDF for an application of the Gibbs Sampler. My joint PDF contains: $P(b,x) = \frac{1}{\sigma^{n}}\exp \left( -\frac{1}{2\sigma^2}\left\lVert ...
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1answer
41 views

Sufficient Statistics, normal distribution

Let X be a single observation from $N(0,\theta)$. $(\theta=\sigma^2)$ a)Is X a sufficient statistics? b)Is |X| a sufficient statistics? What I did ...
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22 views

What are some advanced algorithms in bayesian networks? [closed]

What are some advanced algorithms in bayesian networks? I am familiar with the conventional algorithms of network construction and inference in bayesian networks. What are some algorithms that provide ...
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2answers
28 views

Sampling distributions of sample means

Given a population from which we draw repeated samples of fixed size, say, 'n', my questions is what size is considerable? Is there any lower bound on sample size? Also how many such samples do we ...
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2answers
57 views

multiple regression advice on results

I am testing to see if there is a relationship between my dependent variable Y and any of 4 explanitory variables x1, x2, x3 or x4 First I started by doing simple linear regression and got these ...
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2answers
35 views

Calculating P- value

In ANOVA table , I got $F$-statistic $=330.285$ degrees of freedom (df) due to regression $= 6$ Error degrees of freedom $= 9$ But i don't know how to calculate $p-$value ? I have tried in ...
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1answer
48 views

Identify the distribution

Can anyone tell me which distribution has the density $$f(x)=\frac{x}{\sigma ^2}e^{-\frac{x^2}{\sigma ^2}}I(0,\infty)(x),\sigma >0$$
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1answer
30 views

Why are $M$-estimators NOT scale equivariant?

Consider the following location model. $$ x_i = \mu + u_i, (i = 1,\dots, n), $$ where $u_i$ are $i.i.d.$ with density function $f_0$. Hence, $x_i$ are $i.i.d.$ with density function $f_0(x-\mu)$. It ...
4
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1answer
129 views

Neyman-Pearson lemma

I have read the Neyman-Pearson lemma from the book Introduction to the Theory of Statistics . But I have not understood the lemma . Can anyone please explain me the lemma in plain words ? What ...
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5 views

Analogies between Gaussian Discriminant Analysis and Joint Probability Distribution

Can I say GDA is like a full joint probability distribution over all the feature random variables? I mean, if we are given some random variables, we try to inject some conditional independencies, and ...
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0answers
24 views

Inferences with non-normal data

I have the data of index closing values that I later will use to run some regressions. When examining the data, I find heteroscedastic residuals and that the distribution is non-normal. In fact, it ...
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0answers
10 views

Do I get the HRSEs from my OLS or WLS regression?

I have a multiple regression linear model which I ran a simple OLS test on. I then performed the White test and found that it was heteroskedastic. Then I performed a Weighted Least Squares ...
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1answer
41 views

Time Series Comparison - Correlation and Regression Model

I am trying to see if and how the news for affects the financial markets. I have a time-series for both of them. Should I standardise the series? I have a monthly return on prices from the Dow and a ...
0
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1answer
43 views

Should I use the t-test or the Wilcoxon rank sum test given these qqplots and Shapiro-Wilk stats [duplicate]

I have 4 groups and I want to test if the pairwise difference in means are significantly different. There are 6 pairwise differences. The QQnorm plots of the 4 groups look like this: The ...
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19 views

EM to Variational EM in LDA

Why exactly, when learning hidden variables distribution in LDA(Latent Dirichlet Allocation), one cannot use to the EM (Expectation Maximization) algorithm and have to resort to a variationnal EM ...
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13 views

Finding the underlying pdf by sampling “buckets” of values

The situation I'm looking at a system where I can perform the following trial: $N$ samples are randomly taken from a population of $V$ different values (which can be treated as categorical), ...
2
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0answers
53 views

Combining two probabilistic predictions

I am solving a machine learning task in which I need to predict a label $\tau$ from input $\vec x$. The input $\vec x$ can be considered as two parts $\vec u$ and $\vec v$ ($\vec x$ can be thought of ...
2
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2answers
189 views

Likelihood Ratio for the Bivariate Normal distribution

For a random sample from a Bivariate Normal distribution with $\rho=\frac{1}{2}$ and equal variances, i.e. $\sigma^2_x=\sigma^2_y=\sigma^2$, I would like to derive the Likelihood Ratio Test for the ...
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0answers
8 views

Probabilistc Inference for Hybrid Models

I am looking for a library that can solve (calculate the MAP estimate) of the variables in a probable graphical model in which some variables are discrete and some are continuous. I understand that ...
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0answers
15 views

Process interpretation of confidence intervals?

Frick (1998) explains how statistical inference can be interpreted as making causal claims about processes, without resorting to random sampling and infinite populations. This view seems particularly ...
3
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1answer
76 views

Connection between MLE (Maximum Likelihood Estimation) and introductory Inferential Statistics?

The first thing that one learns in statistics is to use the sample mean, $\hat{X}$, as an unbiased estimate of the population mean, $\mu$; and pretty much the same would be true for the variance, ...
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0answers
14 views

How to calculate the parameter value for a test with Item Response Theory?

Given a set of responses to a test with multiple choice I wish to analyse it with Item Response Theory: wikipedia on IRT. I am planing to use the 3PL (3 parameters) in the Item response function. How ...
1
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3answers
39 views

Inference about parameter $\theta$ be same?

Let $\mathbf x$ be a sample point and $T(\mathbf x)$ be a statistic of $\mathbf x$. Similarly, let $\mathbf y$ be a sample point and $T(\mathbf y)$ be a statistic of $\mathbf y$. In the book ...
2
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1answer
66 views

Example of sample $X_1,X_2,\ldots,X_n$

In the book Statistical Inference by George Casella, it is written that An experimenter uses the information in a sample $X_1,X_2,\ldots,X_n$ to make inferences about an unknown parameter $\theta$. ...
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16 views

Inference problem, potential testing methods

For a person who hasn't studied statistics thoroughly, but instead is only at entry to median level, when facing a hypothesis test/inference problem, how does she/he know all the potentially possible ...
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1answer
35 views

Confidence interval for a function of the MLE

I am studying an old assignment in which I have calculated the MLE for a sample from an exponential distribution. It then gives the formula for the median of an exponential distribution ...
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1answer
65 views

Problem with generalized likelihood ratio test from samples from beta distribution

I was trying to resolve this exercise: This exercise is from the book "Statistical Inference, Second Edition" by Casella and Berger. Checking the solutions manual, I was understanding the solution ...