Mathematical theory of statistics, concerned with formal definitions and general results.

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The derivative of the absolute value |x| [migrated]

I read about the derivative of the absolute value |x|, but why the absolute value is not differentiable at point zero, and when it becomes 1 or -1 {geometrically}? Thanks
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2answers
14 views

Finding levels/subsets that will give certain labels with high probabilty

Assume some 1000 data-points of the following pattern X1 X2 Y 2 B 1 1 C 0 6 A 0 3 B 1 3 C 0 where $X_1 \in \{1, 2, 3, 4, 5, 6\}$, $X_2 \in \{A, B, C\}$ ...
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25 views

Generate $r_i$ following condition $\sum_{i=1}^n |\frac{r_i}{\sigma_i}|^2\leq\chi^2_{n,\alpha}$

How can I generate $r_i$ for $1 \leq i \leq n$, such that $\sum_{i=1}^n |\frac{r_i}{\sigma_i}|^2\leq\chi^2_{n,\alpha}$, where $\sigma_i^2$ is the variance of $r_i$ and, $\chi^2_{n,\alpha}$ is a chi-...
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0answers
14 views

Why is prewhitening important?

I am writing code,geophysical time series processing.First step is to prewhiten values in time domain.Why is this step important? For example,I have found this on sas.com If, as is usually the case, ...
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20 views

How does the symmetric matrix A= X' X is found to be QDQ'? [duplicate]

I am confused of how does the symmetric matrix A= X'X is found to be QDQ' ? where D is the diagonal matrix of A, and Q is orthogonal matrix i.e Q'Q=I identity matrix.
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13 views

Why does this inequality about the false discovery proportion hold?

I am reading an article from Statistics in Medicine ("Tutorial in biostatistics: multiple hypothesis testing in genomics"). For my question it is only relevant to know that $V$ denote the number of ...
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10 views

Jeffreys Interval Calculations and Sample Size

I have a rough understanding of bayesian statistics and of the Jeffrey's Interval/priors. I understand that the Jeffrey's interval takes the form: $$p\mid x \sim \mathrm{Beta}(x + 0.5, n - x + 0.5)$$ ...
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14 views

Statistics Question [on hold]

Researchers conducted a study in which they invited 85 nutrition experts to an ice cream social (Wansink et al., 2006). These experts were randomly given either a 17- or a 34-ounce bowl, and they were ...
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0answers
17 views

Is there a test suitable for the analysis of my data?

I am trying to compare the performance of pipelines. These pipelines have been sorted into two groups, Insulated and Non-Insulated. I have a total of roughly 60 pipes which are a combination of ...
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1answer
21 views

Applying bayesian inference to a time based problem

I have a N*M matrix with N customers and M products. Each row of this matrix is a M dimensional vector like [1 3 4 1 5 ....] where each value represents how many times that customer has chosen this ...
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1answer
62 views

Variance computed using Taylor series does not agree with numerical experiment

I would like to estimate an angle $\theta\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ given the noisy observations of its sine and cosine (this is related to my earlier question). My estimator is ...
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1answer
42 views

Is real analysis necessary for statisticians? [closed]

I'm almost finishing the undergraduate course in Statistics. Is it worth take a course in Real Analysis if I don't intend to do the master's degree? This will help me in something in the labor market ?...
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29 views

Equivalent of standard error for variance?

I would like to know if there is an equivalent formula of standard error for variance or standard deviation, that is, I would like to know how far the variance of my sample is from the real variance ...
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0answers
12 views

How to calculate first order autocovariance in AR(1) process?

For a process describing dividend yield $x_t$, it is assumed to follow a first-order autoregressive process: $ x_t=\delta +\phi x_{t-1} + \eta_t $ where $|\phi|<1$ and $\eta \sim \mathcal{N}(0,\...
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1answer
36 views

How can I know how 'descriptive' my data is?

I'm an undergrad learning about Statistical/Machine Learning and I've implemented and fitted some models now using methods such as Neural Networks and SVM. I've noticed that when testing some datasets ...
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0answers
12 views

Should I include the level variables along with the difference variables in the Error Correctional Model(ECM)?

I am running an ARDL model, I have both levels and difference variables. I know for sure that the difference variables should be included in the ECM but should I include the level variables as well?
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29 views

math statistics [closed]

person a and person b both took the same test. person a got a score of 100 while person b got a score of 75. in order for a counselor to determine whether the difference between their scores was ...
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3answers
527 views

Can I ignore multicolinearity problem if all the regression coefficients are highly significant? [duplicate]

Can I ignore multicolinearity problem if all the regression coefficients are highly significant? My data is large enough (i.e. I have several regression models where each of the data points for them ...
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0answers
25 views

If a sample point comes from the same distribution [duplicate]

In advance, I'm really sorry for having wishy-washy explanation of what I'm trying to do. Basically, I have a sample of numbers (say 4,9,10,11,8,10,5) and I want to know if a number, say 9, is close ...
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0answers
39 views

Find Bayesian estimator with random sample from poisson and prior distribution from exponential distribution

Let $X_{1}$ .....$X_n$ be a random sample from Poisson distribution, prior distribution with parameter $\pi(\lambda) = \beta e^{-\beta\lambda}$. Find Bayesian estimator I couldn't take integration ...
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0answers
12 views

how to write an inverse function of lognormal in R for simulation purpose? [closed]

how to write an inverse function of lognormal in R for simulation purpose? F^(-1) (x)=exp⁡[σφ^(-1) (u)+μ]
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26 views

Invariance to measurements, and invariance to a group of transformations [closed]

Is invariance to measurements(IM) a special case of invariance to a group of transformations(IG)? Any help would be appreciated.
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22 views

How to cancel out the effect of a voter voting again?

I couldn't come up with a better title but here is the problem I have: in a voting system members are allowed to rank a subject as many as they want. The final rank will be calculate based on the ...
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2answers
61 views

Why the inverse of the covariance matrix is equal to the original covariance matrix in Seemingly Unrelated Regression?

In Zellner 1962 p350-351, you may see (2.4) & (2.6), and you can also verify that the Sigma(c)=Sigma(c)^-1. Why the inverse of the covariance matrix is equal to the original covariance matrix in ...
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UMP test for 1-sided hypothesis: Why the focus on the monotonicity in the sufficient statistic, and not in the parameters?

Let's assume that we have $X_1,...,X_n\sim^{iid} Exp(\theta)$. The LRT is of the form $\Lambda(X,\theta_0,\theta_1)=e^{\left(\frac{1}{\theta_0}-\frac{1}{\theta_0}\right)\sum X_i}$. When $\theta_0<\...
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1answer
52 views

Why would you want a smaller critical region when testing large samples?

Is it because when you have a smaller critical region you have a smaller probability of the event happening?
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19 views

PDF from difference of two Weibull distributions

How should I derive a PDF from the difference of a couple of given two parameter Weibull distributions ? The convolution integrals become very difficult to evaluate. PS : The parameters are not ...
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1answer
30 views

Question on Kernel function notation and rationale

Say I have the following kernel function: $$K(u) = \frac{15}{16}(1-u^2)^2\ 1_{(|u|\leq1)}$$ As I understand, $u$ denotes some absolute distance parameter for each observation $x_i$ from a given ...
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0answers
26 views

What is it that you're doing when you do a single t test on one predictor of a multiple regression model?

I hope my interpretation is correct. When you're doing a t-test on a single predictor of a multiple regression model, are you looking at how it behaves while the other coefficients are fixed?
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1answer
15 views

Is it appropriate to exclude outliers in ensemble learning?

While the term 'appropriate' is usually subjective and largely dependent upon the domain that one is talking about, I am here asking whether the exclusion of outliers goes against the principle of ...
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2answers
106 views

Using Markov chains for prediction

i'm new to Markov theory and i'm trying to figure out how to solve the following question. Given the following transitions matrix (A), What is the probability of 5 consecutive Z?
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29 views

Limiting distribution of $\frac{\bar{x}-p}{\frac{pq}{n}}$ from mean of $Bin(1,n)$?

I found some difficulties in here. We know that if $X$ has Binomial distribution with $1$ trial and $p$ success, or what we called $X$~$Bin(1,p)$, we have $\mu=p$ and $\sigma^2=p(1-p)=pq$. From that, ...
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2answers
26 views

Figuring out why the total number of outcomes is $n^k$

I have encountered two problems that are almost identical. Consider this: $12$ basketballs numbered 1 through 12 are thrown at random into 20 boxes. I want to know the total number of possible ...
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0answers
27 views

Number of parameter in a distribution and Accuracy

I have some data sets defining a random variable (already checked). and I tried to fit those data to different distributions. I have found a bunch of distributions that fit and have not been rejected ...
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1answer
45 views

Intuition behind pearson correlation, co-variance and cosine similarity

In this post, the best answer gives excellent mathmetical explanation among pearson correlation, co-variance and cosine similarity. Where I quote here ($\mathbf A $ is the data matrix). If you ...
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1answer
69 views

Covariance of two variables that are products of shared random variables

How to analytically express cov(X,Y), when: X=C*A/(A+B) and Y=C*B/(A+B) Here C, A and B are independent variables with ...
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10 views

Should a cluster randomized trial with multi-level treatment be conducted on one site?

When designing a randomized controlled trial, should a cluster randomized trial with multi-level treatment be conducted at one study site? For example if it is an evaluation of educational materials, ...
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61 views

Distribution of the ratio of two shifted generalized gamma random variable

$X \sim \mathrm{GG}\left(p,d,\theta_{1},\mu\right)$ where $p$ is power, $d$ is shape, $\theta_1$ is scale and $\mu$ is location parameter. Also Consider $Y \sim \mathrm{GG}\left(p,d,\theta_{2},\mu\...
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27 views

How to understand randomness in the training data from bias-variance tradeoff?

The bias-variance decomposition of MSE is $MSE = (\mathbb{E}(\hat{\theta})-\theta)^2 + Var[\hat{\theta}]$. $\mathbb{E}(\hat{\theta})$ can be explained as the average from the randomness in the ...
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1answer
64 views

Formula for Cohort Fertility Rate

I understand the definition of Cohort Fertility Rate as the average number of live births that a woman born in a particular year has had by the end of her reproductive life. But is there a formula to ...
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0answers
15 views

Calculating standard error of estimate by hand

So i have the following $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + e$ where $x_1$ and $x_2$ are dummies. We have 512 observation, 212 of obs have $x_1 = 1$, 345 of obs have $x_2 = 1$ and 84 of obs ...
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0answers
73 views

Using R to create a predictive analysis model [closed]

I'm an intern for a movie studio and my boss has said to use what I know about R and predictive modelling (which is 2 edX courses) and make some sort of predictive model. The data I have available is ...
2
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0answers
42 views

Underfitting : mean and variance demonstration

Consider the following true data generating process (DGP): $$y = x_1\beta_1 + \ldots + x_p \beta_p + \varepsilon = x_{true}' \beta + \varepsilon$$ where $x_i \in {R}^n$, $y \in {R}^n$ and ${E}(\...
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56 views

Different type or regressions (R or matlab) [closed]

I do not know much about regression, and, in order to practise, I need to code this different regressions in R or Matlab, for the next function: $$y=\alpha+\beta_1 x_1+\beta_2 x_2+\epsilon$$ where $...
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12 views

normalization and rescaling definitions are mixed up?

in: https://en.wikipedia.org/wiki/Normalization_(statistics) it's written that rescaling(min_max_scaling) and standarization are types of Normalization what i see in alot of stackoverflow answers is ...
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1answer
99 views
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13 views

Hit rate: How to best compare the data points?

I have Hit rate data (hit rate being "number of transactions"/"number of visitors") weekly and for several years. I want to compare how the hit rate has changed from year to year and my first idea ...
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7 views

Over-represented categories in one sample

Suppose we have a sample with $n$ discrete categories; e.g., in R: ...
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0answers
15 views

how to find a relation between three group of data

I have a piece of data. There are three groups without balancer, apache and HAProxy. Virtual users and Total sample are parameters. Example 1 virtual user makes 7 request such that the throughput of ...