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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53 views

Predicting the increase/decrease of number

I have these entries in my database that looks like this: ...
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1answer
35 views

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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144 views

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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1answer
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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27 views

Determine a distribution of a gaussian stochastic with different time

I would like to determine the autocorrelation function of a Gaussian stochastic. Let see my problem So my solution is The distribution of $y=x(t_1)-x(t_2)$ is also a Gaussian stochastic with $E[y(...
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132 views

Confusion about nonlinear transformation of gamma and inverse-gamma distributions

I have a question about the variance of a transformed random variable, illustrated by a particular example. Let $X_1, ..., X_n$ and $Y_1, ..., Y_n$ be independent random variables drawn from an ...
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164 views

How to derive this problem with soft-thresholding method?

The problem is defined as $$ \min_{x} \Bigg\{ a{\|x\|}^2+\frac{b}{2}{\|x-c\|}^2 \Bigg\} $$ where $x\in R^{n \times 1}, c \in R^{n \times 1}$ and $a,b$ are scalars. Equations 2.5 to 2.8 of this paper ...
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1answer
33 views

Area below probabilities

Let $p$ be probabilities and $D$ is the real How can I proof that the areas $$\int p \; d F_{p}(p|D=1) = \int (1-p) \; d F_{1-p}(1-p|D=1)$$ are equal. Where $F_{p}$ is the empirical distribution ...
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1answer
40 views

What is $C_{pk}$(test) $-\ C_{pk}$(reference)?

I have a process under test (approximately normal distributed), and I have calculated $C_{pk}$ (a process capability index) for this process. These values are compared to reference values which are of ...
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1answer
1k views

Anomaly detection using exponential weighted moving average

I would like to detect anomaly using exponential weighted moving average. I don't have series of data points. All I have is EMA(t-1) and the data point of the current time(t) DP(t). From these data, ...
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1answer
47 views

Alternatives to absolute error?

Let me explain my scenario in which I need to calculate absolute error. Lets say the X is the actual value. And X' is the value of X with some error 'e'. So X' = X + e'. Lets say i = 1 to 10000. I ...
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1answer
65 views

What statistical model should I use to analyze the likelihood that a single event influenced longitudinal data

I am trying to find a formula, method, or model to use to analyze the likelihood that a specific event influenced some longitudinal data. I am having difficultly figuring out what to search for on ...
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25 views

Probability of a sale in a given month based on past activity including order frequency

The sales history for customer A looks like this: Jan : $500 (4 sales) Feb : $200 (2 sales) Mar : $0 (0 sales) etc.. I want to know: The probability of ...
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140 views

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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1answer
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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1answer
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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75 views

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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1answer
47 views

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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179 views

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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73 views

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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37 views

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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66 views

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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2k views

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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928 views

How to prove that this process is strict stationnary

$W_t$ is strict stationary process and $X_t=g(W_{t-1},W_{t-2},...,W_{t-q})$ where $g$ is a measurable function. Prove that the process $X_t$ is strictly stationary. Remark : to prove that a process $...
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84 views

Difference between two univariate coverage versus bivariate coverage (ellipse)

I am trying to compare coverages from accounting for two outcomes independently and as a pair. I have 2 sets of p values (p1,p2) from 60 simulations say. I am trying to find out how many times is the ...
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2k views

The distribution of the sum of squared normal random variables

I have done some extensive googling and I haven't been successful. Say I have 3 independent random variables that are normally distributed with different means, that is, $X_i \sim \mathcal{N}(\mu_i,\...
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292 views

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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130 views

About sigma algebra (proof of Borel field)

Suppose that the sample space S of some experiment is finite. Show that the collection of all subsets of S satisfies the three conditions required to be called the collection of events: $S \in \beta ...
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901 views

What is the MLE if the variance is heteroskedastic

The normal distribution of MLE is start ${x_1,...,x_n}$ random sample from $\sim\mathcal{N}(\mu,\sigma^2)$ This family of distributions has two parameters: $\theta = (\mu, \sigma)$, so we maximize ...
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64 views

Method of Additional Events for the two-state Markov Process

I'm trying to understand a research paper but am facing a few difficulties, any help would be really appreciated. A three state markov process with transition probabilities for states being: 0 --> ...
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1k views

Autocorrelation of a Bernoulli sequence

I have some doubts about the following exercise: Given the sequence of Bernoulli (0,1/2) independent random variables $x(n)$, $n\ge 1$, determine the average function and autocorrelation (time-delay) ...
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205 views

Multiple categorical Variables and Multiple Hierarchical Counts- how to infer the effects?

I have the following categorical/count data : ...
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571 views

statistical derivation of Pearson correlation of two variables obtained from regression model

I have asked a stat question on math.SE which now I believe should be here. However, I repeat it here. As a newcomer, I would appreciate it if you could excuse me for any mistakes or repeating the ...
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292 views

Integral of survival function

If X is a nonnegative random variable representing the life of a component having distribution function F, and S is the survival ...
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118 views

Comparing two opposite ranked sets of data

Looking for the best formula to compare two sets of numbers Set #1 - Rank: Smaller numbers indicate higher "rank" (Ex: 1 is the best, 1,000,000 is the worst) Set #2 - Number of Items: The more items ...
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664 views

Variance covariance matrix for the inverse of a matrix

Suppose we have a matrix $\mathbf{A}=\begin{bmatrix}a_{11} & a_{12}\\ a_{21} & a_{22} \end{bmatrix}$ and know its variance covariance $\left(4\times4\right)$ matrix. Then how the variance ...
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1answer
38 views

Can I have some help for Statistics/probability theory

Let $\Omega = \{0,1\}^{\mathbb{N}} = \{\alpha=(\alpha_1,\alpha_2,...):\alpha_i \in \{0,1\}\}$ Fact. There exists a $\sigma$-algebra $\mathcal{F}$ such that for every $\beta = (\beta_1,...,\beta_n)\in\...
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1answer
43 views

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 ...
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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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1answer
19 views

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 ...