1
vote
0answers
110 views

Density function of the max of smallest and largest observation

Consider $n$ independent uniform random variables $X_i \sim U(-\theta,\theta)$, and let $Y_1 = \min(X_1, \ldots, X_n)$ and $Y_n = \max(X_1, \ldots, X_n)$ . What is distribution of $Z = \max ...
3
votes
1answer
1k views

ROC curve and confusion matrix in classifier performance evaluation

I applied two different classifiers against the same validation set. It turns out that classifier A is better than classifier B in terms of ROC curve. However, classifier B is better than classifier ...
0
votes
1answer
119 views

Conditional fixed effects Poisson *with population exposure*

Reading a paper, the authors use a "Conditional fixed effects Poisson with population exposure." I wasn't sure what "population exposure" meant, so I looked it up. It seems like the term comes from ...
0
votes
0answers
146 views

How to rank the elements for use in Spearman rank correlation?

If I have 50 items and I want to compare the top 30. I have several cases to do the ranking , so which one is correct? For simplicity I will replace in the example below 50 items with 5 ( A,B,C,D,E) ...
1
vote
1answer
516 views

How to test which of five proportions based on Likert scales is highest?

I have used a Likert scale in my survey, where respondents answer statements in terms of 1=strongly agree to 5=strongly disagree. There are 5 items measuring a single type of 'need gratification' ...
3
votes
2answers
393 views

Is it possible to calculate variable confidence intervals, conditional on $\hat{Y}$ to address heteroscedasticity?

Estimating confidence intervals for non-normally distributed residuals can be accomplished using bootstrapping procedures, sandwich estimators or quantile regression. But is there a way to calculate ...
2
votes
1answer
140 views

probability distribution of output value with regression tree methods

If I have a regression problem where I try to estimate the value of $y$ as function of $x_1 \dots x_d$: $$ y = f(x_1,\dots,x_d) $$ using a Boosted Regression Tree or a Random Forest Regression, is it ...
2
votes
1answer
501 views

How to perform step() when n < p in R?

I am trying to perform stepwise regression for variable selection in R. In matlab, the stepwisefit function is able to work in ...
5
votes
2answers
1k views

IRT in R: Does anyone know of an IRT item calibration function that can cope with NA's?

I have a dataset that looks like this. ...
1
vote
1answer
79 views

Estimated normal density is fat-tailed?

I wanted to check what is the relative error of an estimated N(0, 1) density function. By relative error I mean: $$\alpha(x) = E \bigg ( \frac{f(x|\hat{\mu}, \hat{\sigma})}{f(x|0,1)} \bigg ) - 1$$ ...
0
votes
0answers
55 views

Appropriate tests for finding a diffference between the scores of two groups of questions

I am testing whether there is difference between the scores of 2 groups of 12 questions on a Likert-scale questionnaire. Each question from one group has a corresponding question in the other group ...
0
votes
0answers
103 views

show the variance of the estimator

I should show that the variance of the least squares estimator in the simple regression model $y_t = b x_t+u_t$ with the variables in deviation form is $\operatorname{Var}(\hat{b}) = ...
2
votes
0answers
171 views

Do I apply delta method correctly?

I'm no mathematician, so please consider the whole explanation as a subject to criticism and optimization. I'm trying to build a model and calculate an estimate of error variance for the following ...
1
vote
2answers
606 views

Should a mixed effects model be used?

This post provides an excellent example of the inner workings of a mixed effects model: http://emhart.github.com/blog/2012/11/16/making-sense-of-random-effects/ In a hypothetical study, I have ...
0
votes
0answers
51 views

How to read the table to get cumulative relative frequencies?

there is a question i can not answer. Suppose the numbers in the following random number table correspond to people arriving for work at a large factory. Let 0,1,and 2 be smokers and 3-9 be ...
5
votes
1answer
371 views

Comparison between MDL and BIC

I'm currently studying Hidden Markov Models. There's a set of observations from which I need to determine the optimal number of states. After having found the maximum likelihood using Baum-Welch, I ...
3
votes
2answers
1k views

Maximum likelihood equivalent to maximum a posterior estimation

When is maximum a posterior (MAP) estimation equivalent to maximum-likelihood (ML) estimation?
3
votes
1answer
347 views

QQ plot is consistent with normality when subgroups are non-normal

I have read that for a one way ANOVA, you should check that the model residuals are normally distributed. If the variance of each group is homogeneous then this implies that the residuals with each ...
0
votes
0answers
162 views

Classification of states in Markov Chain

Question Consider the following transition matrix: ...
1
vote
2answers
610 views

Is a larger beta weight a better predictor than a high t-statistic?

Say there are two variables. Variable A has a higher $\beta$ weight than variable B but variable B has a higher t-statistic than variable A. Can either of these measurements, standardized $\beta$ or ...
2
votes
1answer
2k views

How does one define own intercept in regression model in R?

My case is that I have one continuous DV variable and two categorical IVs containing 11 and 12 different levels (YEAR & MONTH) form 1998 to 2008. Until now I have experimented a lot with ...
0
votes
1answer
133 views

Dumb Bayes theorem question

What's the difference between "probability of H given E" as calculated by Bayes theorem and the "positive predictive value" of E?
1
vote
3answers
626 views

Which test(s) for analyzing yes-no answers for control vs treated conditions

To keep it simple, I have sets of data in which I have a control and a treated sample. The data I obtain is "yes" or "no" (0 or 1) for a particular behaviour. I have 150 data points for each condition ...
2
votes
1answer
336 views

Training Hidden Markov Models for multiple input observations

I'm working with Hidden Markov Models and I have a dataset composed by independent phrases, where each word is an observation. Hence, the best way to adjust my parameters (via Baum-Welch algorithm) is ...
0
votes
1answer
803 views

Estimate beta binomial distribution

I have a dataset as follows: ni-xi 76 48 38 19 20 14 26 29 39 45 38 36 32 34 26 21 23 12 24 18 14 61 35 21 32 20 89 30 34 35 xi 0 0 16 26 1 8 23 19 24 16 16 19 0 0 0 6 8 3 5 9 5 0 34 ...
3
votes
1answer
55 views

ANOVA using day numbers

I am looking at differences in dates of maximum counts of geese at 3 sites in the UK. My data look like these created in R: ...
2
votes
2answers
336 views

Simulating ordinal variables using fitted probit models

I have fitted a probit model for an ordinal response and a number of predictors, using polr function in R. Now I want to use this fitted model in order to sample from the conditional distribution of ...
0
votes
2answers
216 views

How to combine p values? [closed]

I have three datasets A, B and C. A and C can construct a contingency table, and I can get a p value (pValue1) with Fisher's exact test. B and C can construct another contingency table, and I can get ...
0
votes
0answers
551 views

How is mean date calculated?

I was surprised to discover yesterday that various summary statistics can be calculated on dates. Googling has found lots on syntax required to calculate summary statistics on dates, but very little ...
1
vote
2answers
254 views

Multivariate Weighted Linear Regression

Very simple. I am looking for a package that does Multivariate Linear Regression with weights on the observations. Does anyone know of a package that does this? I am shocked that I have not been ...
1
vote
1answer
239 views

Standard deviation of weighted sums of random distributions with weights random but fixed

Let $a,b,c,d$ be independent normally distributed random variables. I'm aware that the following distributions: $$c a + d b$$ $$(c+d)a$$ both have the same standard deviation ($=\sqrt{2}$ if ...
2
votes
1answer
109 views

Explanation of a step in derivation of residuals for R lm diagnostic?

I'm reading Faraway's book (http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf) to try to understand R's lm diagnostic plots. On page 72 of the book is this: I have been trying to understand a ...
3
votes
1answer
576 views
1
vote
1answer
271 views

Poisson regression - dealing with widely different population sizes

I have a dataset of counts (responses to a marketing campaign), collected at the zipcode level. I am trying to use a poisson regression to determine underlying response rate of each zipcode. How do ...
2
votes
1answer
105 views

Relative efficiency of matching versus adjustment to handle confounding effects in highly disproportionate populations

I am reviewing a paper where the authors compare cancer outcomes (binary) between two groups, one having a small sample size of 200 and the other having over 55,000. The authors then claim that, due ...
2
votes
0answers
223 views

How to pick a good threshold for multimodal histograms

I am trying to do multi-modal detection in a vote map (histogram) however, side lobes obviously cause some false peaks. So using mean shift will not do as it will find all of the local maxima. So I ...
2
votes
2answers
904 views

Sampling from the normal-gamma distribution in R

Does anyone know of a way to sample from the normal-gamma bivariate distribution or the normal-inverse-gamma bivariate distribution in R? I could create the distribution myself as a function, but ...
1
vote
0answers
519 views

Providing the actual measured error instead of weights to the lm function in R (or similar linear fit function)

Is there any way to use the linear fit function or R with my own errors instead of the value weights? That is, I have a physical experiment in which we know the errors for each point, for instance: ...
3
votes
1answer
755 views

What does intercept actually mean in a simple linear model?

Given y = a + b*x, does "a" represent simply an intercept or mean y? For y = a + b*ln(x), is there a need to interpret the intercept "a?"
1
vote
1answer
812 views

Formula to generate Critical t-values for t-test (instead of using a look-up array)

I am searching for the formula that will generate the critical values in a t-test instead of using a static critical value table. I am programming in Java and not R so the qt() function is not what ...
0
votes
1answer
137 views

Random geometric graph connectivity

Given N random points uniformly distributed in the unit square, and a distance d, i can generate a matrix in the following format: ...
2
votes
1answer
497 views

Compute the variance of parameter estimates given limited number of samples

I'd like to infer the variance of estimated parameter $\hat\theta$ of the density function of $f(x;\theta)$ given only a limited number of samples $X_1,\cdots,X_n$. Bootstrapping doesn't perform well ...
2
votes
1answer
273 views

Unbalanced Haar Wavelets and R package unbalhaar

I have found the article by Fryzlewicz (2007) and his R package unbalhaar. I do not understand well the outputs of his functions and in particular of the ...
1
vote
1answer
82 views

Finding moments for a theoretical density function

I am working on finding higher order moments for a given theoretical function, to be used in modelling of daily log-returns. The PDF is, $f_r(x) =$ $\begin{cases} \quad ...
1
vote
1answer
590 views

PCA on returns or levels?

I am doing a PCA on a few economic indices (which I standardized) (24 timeseries). When doing the PCA on the values/level of the index, I get rather similar loadings on each index, which I think is ...
1
vote
0answers
87 views

Asymmetric distribution and PCA

Could someone please explain me this reviewer comment: asymmetric distribution could affect Principal Component Analysis results, symmetry of distribution should be tested. Authors should ...
12
votes
2answers
557 views

Coin flipping, decision processes and value of information

Imagine the following setup: You have 2 coins, coin A which is guaranteed to be fair, and coin B which may or may not be fair. You are asked to do 100 coin flips, and your objective is to maximize the ...
0
votes
1answer
81 views

How to prove that test 1 produces more results than test 2?

If I have 2 tests applied on a set of data, both tests either produce a result ( assume = 1) or no result ( NA , assume = 0 ). Is there a way to prove that test 1 produce more results than test 2 with ...
1
vote
0answers
96 views

Doubts about the standardization process that I should perform with a set of variables

I have a set of categorical variables that I need to encode between $[0,1]$ or $[-1,1]$ to solve a problem in which I have to compare their values with metrics like Euclidean Distance or the Dot ...
0
votes
1answer
865 views

Checking confidence intervals on user defined contrast (one-way ANOVA)

Hi is anyone able to help - I am doing this all in R Code: I have run one way analysis on some data and set up 2 contrasts (Liberarts-Finearts and also Engineering-science). I now need to calculate ...

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