# Questions tagged [mathematical-statistics]

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

4,073 questions
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For completeness, assume $C$ is an Archimedean copula with some generator function $\varphi$, which is usually assumed to have nice properties. It is known that $$C(u_1, u_2, \ldots, u_n)=\varphi^{-1}... 0answers 33 views ### Likelihood of Gamma Distribution I'm studying bayesian stats on my own and came across the following problem on Coursera. Can anyone help me understand how to work through this? x_{i}\stackrel {iid}{\sim} Beta(\alpha,\beta), i=1....... 0answers 9 views ### R^square for a pre-determined linear regression I would like to produce the R^square goodness-of-fit statistics for a predictive model. I have the base data (10, 000 number of x-values) which are the true values given by an analytic/deterministic ... 0answers 19 views ### A/B test : Is there a way interpreting factor “A” group is greater than factor “B” group? Plz.. understand my lack of English skills.. T.T I have a problem dealing with statistical hypothesis testing. To be specific, we have two special delivery method like (new) : method "A", (old) : ... 0answers 17 views ### About the power spectrum and confidence upper limit For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate. ... 2answers 63 views ### Is “geometric mean” the same as “the first moment of the lognormal distribution”? I would like to compare the results of two studies, one reporting "geometric mean diameter" and the other one reporting "the first moment of the lognormal size distribution". I am not sure whether the ... 1answer 37 views ### How to justify using Beta distribution as a prior distribution in the following problem Let \theta be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in 2017 with a n volunteers who ask people this question until they obtain yes ... 1answer 63 views ### Finding the MVUE from two independent random samples Suppose we have a random sample X_1, X_2, \ldots, X_n from exponential~(β >0) \text{i.e. }f(x\mid β) = {1/β} ~e^{−x/β} and a random sample~Y_1, Y_2, \ldots, Y_n from exponential~(⍺ >0)... 2answers 59 views ### What would p(a,b|a) be equal to? What is p(a,b|a) equal to in conditional probability? Any sort of breakdown as to why it might be equal to p(b|a) would be helpful (if it is true in all cases). My reasoning for asking this question ... 0answers 29 views ### Finding the limit of a quotient of hazard functions Let \lambda_i(t),S_i(t) be the hazard and survival functions of two populations for i=1,2 and satisfy that: \frac{S_2(t)}{1-S_2(t)}=\phi\frac{S_1(t)}{1-S_1(t)} (1) I want to proof that \lim_{t\... 1answer 32 views ### Seeking origin of variance equation In my data science textbook, it says that the variance of a variable Y can be written as: v_y = \frac{1}{n-1} \sum_{k=1}^{n} y_k^{T} y_k, I have never seen variance defined like this before. ... 1answer 66 views ### How to prove that the robust F statistic is asymptotically chi squared distributed? The linear model is$$y_{i}= x_{i}'\beta+u_{i}$$When written in vector notation such that y_{i} is a 1 x 1 matrix of outcomes, x_{i}' is a 1 x k matrix of control variables, \beta ... 0answers 16 views ### What is the preferred way to show that a 3-dimensional function is a copula? I am currently working with 3 dimensions, and have some functions C(u_1, u_2, u_3) for which I need to check whether or not they are a copula. What are all the requirements that I need to check? In ... 1answer 50 views ### Canonical link of Gamma Distribution [duplicate] I wonder why my professor said that Gamma's canonical link is \frac{1}{\mu}. My thoughts are: EDIT: \theta is the canonical parameter. Since$$\mathbb{E}_\theta(Y)=b^{'}(\theta)=-\frac{1}{\theta}...
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I'm reading the paper on Adaptive LASSO estimator (Zou, 2006). In one of the presented numerical simulation examples (Model 0 (Inconsistent lasso path), page 6 (1423)) they claim the following: To ...
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### Covariance of Constrained Maximum Likelihood Estimators

I plan to numerically estimate the parameters of a GLM but with constraints imposed on some of the parameters. In this case, does the general approach of estimating the covariance matrix of my MLE ...
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### Help analyzing data ranked on a scale

So, I thought it would be interesting to try an experiment with my family. I baked 13 different kinds cookies this year, and then told my 8 family members to rank from each cookie from 1-13. Is there ...
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### Intuition behind the no convergence of the variance of sum of random variables

$$Var[\bar{X}] = \sigma^2/n$$ $$Var [\sum{X}_i] = n\sigma^2$$ $$lim_{n \to \infty} Var[\bar{X}] = 0$$ wich means at $\infty$ we will always get the same $\bar{X}$ after every simulation. I ...
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### Bernoulli distribution/ SOME probability/conjugate prior

I would like to know what "SOME probability of seeing tail" means in the second answer here. I.e. how much is it? EDIT: I do not understand how can I see that there is SOME probability of seeing Tail ...
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### how should replications be done for ANOVA? [closed]

I generate my own data (an order list) and with that data I have multiple scenarios which can be performed which give a resulting value. Now I was wondering when I want to do a ANOVA, should I ...
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### How to justify that $(Y_1,Y_2)$ is not bivariate normal without finding its exact distribution?

Suppose $X_1$ and $X_2$ are independent $N(0,1)$ variables. Define $$Y_1=X_1\,\text{sign}(X_2)\quad,\quad Y_2=X_2\,\text{sign}(X_1)$$ I have to show that $(Y_1,Y_2)$ is not bivariate normal ...
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### Math questions in Kalman filter equation derivation

I am interested in data analysis. While my working data (actually it's shopping mall's daily sale) is accumlating, I wish to find some statistical laws underlying business phenomena. I left school for ...
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### Beta distribution and normalization [duplicate]

Here in the 4 pictures in the last answer, is the vertical axe the probability? I.e. it seems to me that it is somewhat unnormalized : it has the value 2 in the 2nd picture and 3 in the 3rd picture. ...
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### Linear regression formula with sum of residuals

The relationship in our model between X and Y is linear $Y = X^T\beta + \epsilon$ For arbitrary test point $x_0$ we have prediction $\hat{y_0} = x_0^{T}\hat{\beta}$. Alternatively this can be ...
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### Is it always a good idea to perform Box-Cox transformation on positive predictors to make it normally distributed?

It is a pretty general question: a counterexample should also help.