Questions tagged [statistics]
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.
37,374
questions
5
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Expected value of the stopping time of a moving window
Let $\xi_i$ be iid random variables with $\mathbb{E}[\xi_i]=0$, and define:
$$S_{(k)} = \sum_{i=1}^N \xi_{i+k}$$
Now, define:
$$\tau = \min \left\{ k : S_{(k)} \notin (a,b) \right\}$$
How can I find $\...
- 1,911
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14
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Finding the pivot distribution
Let it be X volume sample $n$ from the logistic distribution, with density $f(x;\theta,\sigma)=\frac{e^{-\frac{x-\theta}{\sigma}}}{\sigma(1+e^{-\frac{x-\theta}{\sigma}})^{2}}$, $x\in R$ where are both ...
0
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Does the invariance property hold for consistent estimators within an indicator function?
Let $X_{n}$ denote a sequence of random variables. Then, $X_{n} = c + o_\text{P}(1)$ for some constant $c$ if, for all $\epsilon > 0$, $$\Pr\left(\left|X_{n} - c \right| \geq \epsilon \right) \to 0$...
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-2
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1
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Unbiased estimate of parameter [closed]
Let it be (X, Y) sample from a distribution with density $f(x, y; \theta)=e^{-\theta x-\frac{y}{\theta}}$, $x>0$, $y>0$, $\theta>0$.
Let it be $\tilde{T_{n}}=a_{n}T_{n}$, wherein $a_{n}$ the ...
0
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0
answers
14
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Sample complexity bounds of $L_S(h)$
Fix $\mathscr{H} \subset \mathscr{Y}^\mathscr{X}$ and a loss $\ell : \hat{Y} \times Y \to [0,1]$. Fix $S \in (\mathscr{X} \times \mathscr{Y})^{2m}$. Assume for now that $S$ is not random. Suppose we ...
- 41
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Can two hypothesis tests with opposing null hypothesis be compared to each other?
Suppose I have an estimator $\hat{\beta}$ for some parameter $\beta_0$ and I have two hypothesis tests
$$
H_0^{(1)}:\hat{\beta}=\beta_0\quad\text{versus}\quad H_1^{(1)}:\hat{\beta}\neq\beta_0
$$
and
$$...
- 362
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14
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Finding Appropriate Formulas/Methods for Finding Correlation.
I want to find the correlation between birth rate (per 1000 people) and unemployment rate in a country from 2000 to 2022 and give suggestions for solving the birth rate declining problem. I know this ...
0
votes
1
answer
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How to sidestep of undifferentiability of Frobenius norm at 0 in the numerical analysis?
I am currently doing the l-bfgs-b optimization algorithm. I have my objective function. I also need to get the gradient of the objective function. Some part of my objective function is Frobenius norm ...
- 17
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Uniform random variables with distribution over [1, 4]
2.4.2 Let W~Uniform[1 4]. Compute each of the following.
(b) P(W >= 2)
(c) P(W^2 <= 9)
For b, I was thinking P(2<=w<=4)= (4-2)/(4-1) = 2/3.
For c, I was thinking since w^2 <= 9, P(1<=...
- 1
1
vote
1
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Co-ordinate ascent update for $B$
I want to solve the optimization problem by getting the update step for:
$\tilde{B} = \arg \max_{B} \{-\text{tr}(M^{T}M \Omega) + \sum_{j=1}^{p} \sum_{k=1}^{q} \text{pen}(\beta_{jk}|\theta)\}$ where $...
- 719
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41
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Optimal matching of Bernoulli random variables
Let $Z_1$, ..., $Z_n$ be a sequence of independent Bernoulli random variables such that
for all $i\in\left\{1,..,n\right\}$ $Z_i\sim\mathcal{B}(p_i)$ where $p_i < 1/2$.
Define $l(x_{1:n}, y_{1:n}) =...
- 175
-1
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0
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17
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Manual Calculations for STL Decomposition [closed]
Does anyone know how to manually perform calculations using STL Decomposition? I have this data:
Date
Count
2017-01-31
68
2017-02-28
59
2017-03-31
75
2017-04-30
71
2017-05-31
70
2017-06-30
68
...
3
votes
0
answers
33
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The sufficient statistic and unbiased estimator of normal variance
Suppose we have a normal distribution with mean $\theta_1$ and variance $\theta_2$.
I know that $\frac{1}{n-1}\sum_{i=1}^n (X_i-\bar{X})^2$ is an unbaised estimator of $\theta_2$ and has a variance $2\...
- 2,013
1
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1
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66
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Integral of a Function Defined on a Point
Let $(\mathcal{X}, F_{\mathcal{X}}, \nu)$ be a $\sigma$-finite measure space and fix $y_0 \in \mathbb{R}^n$. We suppose that $g : \mathcal{X} \times \mathbb{R}^n \to \mathbb{R}$ is a product space ...
- 2,436
0
votes
0
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38
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Probability that random variables with multinomial distribution have a common divisor greater than 1
Consider an election in which $k$ candidates compete: Let $N_{i}$ denote the number of votes for candidate $i$ in the election.
How can we reasonably estimate the probability that the number of votes ...
- 8,330