# Questions tagged [mathematical-statistics]

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

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### Name of two dimensional-space — feature-space

I have 2 features and want to perform some functions independently on them in two-dimensions. So basically I have 2 two-dimension spaces. How can I name them? Should they be called as feature-space 1 ...
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### Predicting the increase/decrease of number

I have these entries in my database that looks like this: ...
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### percentage of reduction and log transformed

I have the following model: log(Y) = Intercept + beta1 * X + Error -> interpretatoion: "One unit increase in X is associated with a (beta1 * 100) percent increase in Y". And now i wish have ...
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228 views

### (binary) Matrix completion with less known data

Recently, I meet such problems, I call it matrix completion problem. For example, the row denotes the users and the column denotes items. And If one user like the ...
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173 views

### Best way to graph probabilities of feature vectors

I have a lot of feature vectors in the form of: v1=[x0, x1, x2, x3, x4] where x0, x1, and x2 can take binary values. either 0 or 1 x3 and x4 can take values from 0 up to 9 I have a lot of vectors ...
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### Statistical nomenclature: what family does “head” and “tail” - in the sense of data runs belong

If I look at mean, variance, skew and kurtosis they are nth moments. If I look at percentiles, quartiles, and medians they are order statistics. Both work together to make a textbook summary. The ...
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739 views

### Combined standard deviation of geometric series

I have two series of trading profit results. I use the geometric mean to calculate the average in percent (CAGR). I would like to divide it by the standard deviation by combining the two series, but I´...
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33 views

### Predictive analysis based on history

Let me first say that I am a CS person and my knowledge about statistics is quite basic. I am trying to see what predictive analysis to use for a problem I am trying to solve. I will try to make my ...
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288 views

### The way to evaluate the importance of an independent variable in a regression model

In a regression model, like y~( x1, x2, x3). Is there a test or a way to evaluate which independent variable, x1, x2, or x3, is ...
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### Derivative of Marginal df equal to marginal pdf?

I am curious as to when the derivative of a marginal df is equal to the marginal pdf for a (continuous) random variable. As a simple example, let Z = (X,Y) be a continuous random vector and F be the ...
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144 views

### finding probability density function $U=Y-X$

suppose joint probability density function of $X,Y$ is $$f(x,y)=\frac{1}{2}\\ x>0 ,y>0,x+y<2$$how can i find probability density function $U=Y-X$
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51 views

### solving an equation with more than two variable algebrically

I want to solve an equation with Lagrange multiplier. I know elimination method but I need to know this method. I wonder if anyone let me know how to estimate $\mu$ and 3 unknown variables ($\hat A$) ...
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56 views

### Is the following estimator for the normal distribution not asymptotically efficient?

Suppose that we have $X_1,...,X_n$ ~ i.i.d $N(\mu,\sigma^2)$, where $\mu$ is unknown and $\sigma^2 = 1.$ Is the following estimator: $\hat{\mu} = \frac{1}{n-1}\sum{x_i}$ consistent but not ...
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### The distribution of the product of two random variables

X=Normal(0,1) random var. Y=Uniform{-1,1} random var. Show that Z=X.Y is normal random variable. Thanks for your help in advance. I tried to solve it through double integral but it failed to do. ...
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71 views

### Transform moments of a random variable to fit the moments of another

Let's say we have the a set $(X_i,Y_i)$, $i\in I$, $I$ is an arbitray finite set of indexes, and the model $$Y = g(X\beta)$$ Using some method, we obtain the individual first four moments of the ...
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### Statistics usage for customer event

We are preparing one event for our customers and I need to count numbers we need to prepare for this event (I think my question belongs to statistics and it isn't a homework). Inputs: We have 26 ...
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140 views

### Determining if these random variables are independent

Let $X$ and $Y$ be iid $N(0, \sigma^2)$ variables. Show that $X^2+Y^2$ and $X/ \sqrt{X^2 + Y^2}$ are independent. Hint: Compute the joint distribution of the first and the square of the ...
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### Covariance matrix explanation OLS and correcting residuals

I have been wondering, in a couple of books on econometrics I have discovered that they explain many things in regards to the distribution of beta. I therefore have an example and a couple of question ...
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### I do not understand the terminology of $Q_n$

I am trying to understand what looks to be some simple terminology issue, involving $Q_n$ from my book here: Specifically, I do not understand what they mean when they say $m = {n \choose 2}$, and ...
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### Appropriateness of applying a fitted model to a different (but similar) set of predictor variables

I have fitted a model of current species habitat suitability as a function of mean annual temperature (MAT) and precipitation (MAP) by regressing the distribution of known occurrences of a species ...
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### review papers on P-values, adjusted P-values and common statistical tests in bioinformatics

I'm looking for review papers which give comprehensive reviews of P-values, adjusted P-values and common statistical tests in bioinformatics.
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### Categorical Dependent Variable in R

How does one interpret the beta coefficients in R for a model that has a categorical dependent variable that is not binary? For instance, in the hypothetical model below, I would interpret B1 as being ...
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11k views

### Manually Calculating P-Value from F-Test - Does not match up

I am trying to manually calculate P-Value (right tailed) from F-Test to understand it better. Would like to learn how the value obtained from the F-Test. Have obtained the below parameters, ...
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4k views

### Joint PMF for two Geometric distribution variables

I am interested to know how to calculate the joint probability mass function for two independent geometric random variables. Suppose two variables X1 and X2 are independent, such that ...
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### Is the p value in a permutation test the same as the p value in the original test?

This is an extension from my last post. It seems to be too long to discuss there. When testing some null $H$ versus alternative $K$ by a test statistic $U(X)$, the p-value for $U$ on a sample $X$ ...
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### Is there stationarity?

I'm trying to analyze a financial time series, these are the ACF and PACF returns graph. What could I say? Lag–9 and lag–15 are significant? I would say they are not, and there is not weak ...
1answer
51 views

### How to tell if the “clusters” I see in my pair plots are statistically significant or occurring by chance?

I have a data set with one row per subject. Some variables include laboratory parameters for blood chemistry, hematology, etc. I also have some flag variables: any = 1 if the subject experienced an ...
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### How to choose the type of t-test to use for analysis?

I did an A/B test on two different versions of an advert. I have the CTR of both variations of the ads for the last 10 days. I'd like to know what kind of t-test ...