0
votes
1answer
263 views

Asymptotic normal distribution via the central limit theorem

I have a sample $n = 100$ with two "successes" (Two kids having a disease among 100). So we obviously have a binomial distribution. First I had to compute the maximum likelihood (ML) estimator ...
0
votes
0answers
189 views

Test to compare large and small datasets

I send Alice and Bob out to record people's eye colour (blue, brown, green, other). Alice does a great job and writes down the eye colour of 2000 people. Bob only records the eye colour of 20 people. ...
0
votes
0answers
35 views

discrete survival analysis reorganise data

I cannot figure out how I will reorganize and run my data for discrete survival analysis. I have 1169 farms repeated from 2001 to 2010 and I measure years in low income but poverty is not death. So ...
2
votes
1answer
1k views

Chi Squared Results in R and Python

Based on this answer, Python requires expected values in a chi square test to be absolute frequencies. Consider the following in Python: ...
7
votes
1answer
5k views

How to interpret negative ACF (autocorrelation function)?

So I plotted the ACF/PACF of oil returns and was expecting to see some positive autocorrelation but to my surprise I only get negative significant autocorrelation. How should I interpret the above ...
0
votes
1answer
133 views

Simple OLS with two samples

I want to obtain an unbiased estimator for $b_1$ in a simple regression like that: $Y_i = B_0 + B_1X_i + u_i$ when I have two samples, always same size for Y and X, but once the sample size is l and ...
1
vote
1answer
130 views

Reporting operative effect in paired t test

I just want to make sure I have something clear in my head. When I calculate the effect size for a paired samples t-test after obtaining a significant result, I simply take the mean of the differences ...
1
vote
2answers
373 views

Overlapping time series: is there any better way to visualize them?

I have this time series dataset: The graph shows trend lines for 7 stock prices. They are very close and overlapping, but you will be able to get an idea that trend lines are layered (i.e. brown ...
0
votes
1answer
403 views

Best subset selection

My statistical learning text claims that for best subset selection, 2^p total models must be fit through regression if for p covariates, we fit p choose k models at each k, k = 1,...,p. I interpret ...
2
votes
1answer
120 views

Sign of the unnormalized log likelihood in Ising model

Here is a section of Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy I don't understand in (19.18) why there is a negative sign. For me, $\log ...
3
votes
1answer
384 views

Are $\mathbb{F}_2$-linear combinations of random variables in an i.i.d. Bernoulli process again an i.i.d. Bernoulli process?

I'm having trouble understanding how certain combinations of random variables can correlate. The problem is as follows: I have a binary $m \times n$ matrix $A$ of full rank (over the finite field ...
2
votes
0answers
628 views

Correlation coefficient between two arrays of 2D points?

I have two arrays of 2D points and I need to estimate their correlation. What formula should I use? Thank you. Example of arrays: X: [[1,5],[2,5],[1,7],[4,1]] Y: [[3,4],[1,6],[4,6],[4,3]]
5
votes
1answer
418 views

machine learning applications in number theory

is there any research into or applications of machine learning in number theory? am also looking for (leading examples of) statistical/empirical analysis of number theory questions. also ...
1
vote
0answers
581 views

obtaining Standard Errors in maximum likelihood estimation

I am trying to obtain the standard errors of my maximum likelihood model, I am having trouble to fix the error message: ...
4
votes
1answer
93 views

Finding the expected value of two normal random variables

Suppose $a_1 = b + c_1$ and $a_2 = 2b + c_2$ where $b, c_1, c_2$ are all $N(0,1)$ Find $E[b|a_1,a_2]$ My attempt: As $E[b] = 0$, I assume $E[b|a_1, a_2] = 0$. Is this a logical assumption?
5
votes
2answers
232 views

Expected value of $Ye^X$ where $X \sim U(0,1)$ and $Y \sim U(0,1)$

I am trying to find the expected value of $Z$ where $Z = Y\cdot e^X$ where $Y \sim U(0,1)$ and $X \sim U(0,1)$. My attempt so far: $$F_Z(z) = P(Ye^X \le z) = \int \int_{Ye^X \le z} f(x,y)\, dxdy$$ ...
2
votes
1answer
85 views

Directed Graph to Regression Help

So I have this directed graph (above) Each arrow represents a causal link. Is it possible to calculate the affect of X on Z, where all variables are observed except U and W. If so, what would the ...
3
votes
1answer
148 views

Slope of a Regression

Given this chart, how do you determine the slope of the regression Y on F?
0
votes
1answer
474 views

Pearson's correlation for time series requires normally distributed data?

In order to use Pearson's correlation to measure the similarity of two time series, is normal distribution of both time series a necessary condition?
6
votes
2answers
373 views

Why is standard error sometimes used for “error bands” in plots?

It seems that often what someone really wants to plot is a confidence interval of some kind, but using SE for this purpose I think only ends up comprising something like a 68% confidence band. ...
5
votes
2answers
197 views

Cumulative Distribution Function Inequality (Discrete Distributions)

Let a discrete Random Variable $T$ have CDF $F_T(T)$. Could you please help me understand why $$ P \left[ F_T (T) \leq a_1 \right] \leq a_1 $$ I know that the result holds with equality for the ...
0
votes
1answer
173 views

Sample size and correct choice of test in g*power

I am new to g*power and have a question about which test I have to choose and how to interpret the given sample size. I have 2 measurements (pre / post), one control-group and one intervention-group. ...
1
vote
1answer
117 views

Does it matter if I use correlations or regression coefficients to suggest areas to focus on to improve overall customer satisfaction?

I am working with customer satisfaction data where the dependent variable is "Overall satisfaction" and the independent variables are satisfaction with various areas such as customer support, delivery ...
2
votes
1answer
51 views

Similarity of new element x with the training set X

Suppose we have trained a model (function, algorithm) $M$ which gives prediction to a new sample $x$ not observed in the training set, $M(x)$. It is natural to assume that the quality of prediction ...
2
votes
1answer
701 views

overall effects of categorical variables

I'm doing a Poisson regression in Stata, so the dependent variable is a count variable and I have some categorical predictors. If A is a categorical variable with, for example, 4 levels, in the ...
2
votes
1answer
3k views

Does stand-alone dummy variables in linear regression models make sense?

Dummy (or binary) variables ($X_2$) can be used in linear regression models to help explaining a possible group effect that a continuous predictor variable ($X_1$) might present in explaining the ...
2
votes
1answer
219 views

How to test for randomness in bins with small N?

I observe a series of crime incidents linked by modus operandi or some other peculiar characteristic of the crime (e.g. cutting catalytic converters from underneath vehicles). I would like to know if ...
1
vote
0answers
73 views
1
vote
0answers
81 views

need name, reference, and/or study for the following variable reduction procedure in regression

I have seen the following commonly used: 1. fit a model with all variables, 2. in a single reduction step, remove from the model all variables at once that do not fit some criteria (p-value, ...
1
vote
0answers
361 views

Sample from Wishart distribution with inverse Scale matrix

I tried to model precision matrix in a hierarchical Bayesian setup with Wishart prior given d.f. and inverse scale matrix, and matrix normal likelihood, since it's a conjugate prior, my posterior on ...
0
votes
0answers
79 views

Hidden Markov Model speech recognition

What if have N audio signals of different length and for each we know corresponding sentence. How we can train classifer for audio signals->sentence ? And maybe Hidden Markov Model can be used here? ...
2
votes
4answers
234 views

Are there statistical techniques that investigate such relationships …?

If we have data set, X and Y variable. Say, we do correlation analysis and get some correlation coefficient. Besides, we find an important fact after observing their relationship: That is, the scatter ...
4
votes
1answer
1k views

Relation between autocorrelation function and periodogram in time series analysis

I was wondering if anyone could give me some insight on the relation between the ACF and the periodogram of a time series. I have a bunch of timeseries and their ACF's and periodograms are typically ...
4
votes
0answers
726 views

How to calculate spatial correlation between two variables?

I have a dataset of point coordinates of individuals and different variables of these individuals. I want to calculate if the spatial distribution of a certain variable is correlated to the spatial ...
0
votes
0answers
59 views

Leave-out data approach to get intervals for predictive performance of a regression model

When measuring predictive performance of a regression model, I am thinking about using repeated data splitting (or leave-out data at random) instead of using bootstrapping. By "repeated data ...
2
votes
1answer
979 views

When doing systematic sampling, what should be done if the sampling interval (i.e. the skip) is not an integer?

Let: population size $=N$; sample size $=n$; sampling interval $=\frac{N}{n} = k$, which can be non-integer; and $r=$ random starting point, which can be non-integer, $0 < r < k$. ...
1
vote
2answers
109 views

How can I get the prior of a random variable that's a function of a random variable in Bayesian data analysis?

I have a model which includes the following priors: $\lambda_C \rightarrow \dfrac{1}{\sigma_C^2}$ and $\sigma \sim \text{uniform}(0,500)$ Where $\sigma$ is the standard deviation and $\lambda_C$ ...
1
vote
1answer
106 views

Translating R lme comand to mathematical equation

I would appreciate if someone could help me in translating the following R command into a mathematical equation: ...
5
votes
1answer
183 views

What is the intuition behind (M)ANCOVA and when/why should one use it?

As per my understanding here's the what/why/when of the following hypotheses tests in a crude sense: t-test: Used when comparing means between two samples ANOVA (one way): Used when you have one ...
0
votes
1answer
50 views

How should I approach modeling these subjective probability estimates?

In my data about 1000 people have made estimates of the probability of 100 unique events. On average people forecast on about 50 events, but some forecast on all of events and some on only a few. ...
5
votes
0answers
115 views

Entropy of Inverse-Wishart distribution

What is the entropy of the Inverse-Wishart distribution? I need just a reference, but derivation (e.g. using inverse property) would be interesting too.
1
vote
0answers
61 views

Display Correct Poisson Calculation

I'm having difficulty calculating the desired result (i.e. 0.0723) on my calculator. Here is what I have tried: ...
0
votes
2answers
87 views

1-d extension of 2-d variance? [closed]

A random variable X={X1..Xm} and Var(X) is the mXm variance-covariance matrix. Is there an accepted 1-d statistic like variance that may be extracted from the sample variance of data representing a ...
0
votes
0answers
33 views

error of the mean in presence of background

Suppose I have a normal distribution, $N[\mu,\sigma]$, and I have a sample of size $n$. It is well know that the error (std deviation) of the mean is $\sigma/\sqrt{n}$. Now suppose that my ...
8
votes
1answer
296 views

regarding conditional independence and its graphical representation

When studying covariance selection, I once read the following example. With respect to the following model: Its covariance and inverse covariance matrix are given as follows, I do not understand ...
1
vote
0answers
127 views

Challenging Likelihood Ratio Test

Derive Likelihood Ratio Test of size $\alpha$. H$_0$: $\theta=\theta_0$ H$_1$:$\theta \neq \theta_0$ \begin{equation} {f}(x,\theta , c) = \theta(x-c)^{\theta-1} \ {c<x<c+1} \end{equation} I ...
0
votes
0answers
347 views

Regression estimate of a non-negative variable

I have to estimate linear weight $\beta$ for regression $Y \sim \mathbf{X}$, where $Y$ are non-negative samples. If I perform vanilla regression (lets assume ridge regression) it will find $\beta$ ...
0
votes
1answer
308 views

Maximum Likelihood for shifted Geometric Distribution

Really struggling with this please help. Find MLE for p and c \begin{equation} \ {f}(x,p,c) = (1-p)^{x-c}p \end{equation} x=c,c+1,c+2,..... p is between 0 and 1 c is element of the integers I am ...
2
votes
2answers
2k views

Chi Square Test for Independence in R and Python

Consider the following R code and output: ...
2
votes
1answer
425 views

What is the best way to analyze data if your experimental design changes while running the experiment?

I imagine this is a somewhat common situation in practice. I am thinking mainly in terms of preclinical drug trials. 1) During the course of the study a new technique is learned or some time/money is ...

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