Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
7,817
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Rao-Blackwell Theorem
I'm having problems on understanding the Rao-Blackwell theorem. In particular I don't understand why the resulting estimator is the one with minimum variance between ALL unbiased estimators of the ...
2
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Suppose $(X,Y)$ have copula $C(u,v)$, does $(aX,aY)$ have the same copula for $a>0$?
Suppose $(X,Y)$ have copula $c(u,v)$ in the sense of $Pr(X\leq x,Y\leq y)=Pr(F_X(X)\leq F_X(x),F_Y(Y)\leq F_Y(y))=Pr(U\leq u, V\leq v)=c(u,v)$,
where $u\equiv F_X(x)$ and $v\equiv F_Y(y)$ and $c(u,v)$ ...
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Let $X(t)$ be a Gaussian process. Does $\mathbb{E}[X(t)^2 X(s)^2] = \mathbb{E}[X(t)^2 ] \mathbb{E}[X(s)^2 ] + 2 (\mathbb{E}[X(t) X(s)])^2 $?
As the title says, can I apply Isserlis' theorem to $\mathbb{E}[X(t)X(t)X(s)X(s)]$?
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Manual Calculation using STL Decomposition
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
...
4
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2
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452
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Examples of distribution for which first-order condition is not enough for MLE
As stated by the title, I am looking for an example (if any exists) of a distribution for which annulling the gradient of the (log-)likelihood function w.r.t. the parameters is not enough to ensure we ...
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Mathematical Prediction of Linear Mixed Models Random Intercept
Given data $\{(x_{i,j}, y_{i,j})\} \subset \mathbb{R}^2$, with $i = 1, \ldots, k$ classes and $j = 1, \ldots, n_i$. The linear mixed model is:
\begin{equation*}
y_{i,j} = a + b x_{i,j} + u_i + \...
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3
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2
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sample size in chi-squared test
The chi-square test of independence is a type of non-parametric test, but in cases of small sample sizes, the Fisher's exact test should be used instead. My understanding of non-parametric methods is ...
- 101
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Derivative of the Score Function in Fisher Information
I'm studying Fisher Information and am trying to develop an intuitive understanding. Keep in mind I only have bachelor level mathematics background so I would appreciate an answer that is more ...
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Is it possible to compare the output probabilities of two machine learning models? [closed]
Let's suppose I have two classification machine learning models: $\text{Model}_1$ and $\text{Model}_2$. Each of them are not necessarily the same algorithm, and have not been trained necessarily with ...
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Notation to report the measurement of a parameter
The estimation of a parameter ($p$) is customary reported in Physics and other fields with,
$ p = \hat{p} \pm \Delta p$,
where $\hat{p}$ is an estimator, and $[\hat{p} - \Delta p, \hat{p} + \Delta p]$ ...
1
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0
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72
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Unbiased estimator of covariance^2
Assuming that the sample covariance $c_{ij}$ is an unbiased estimator of the true covariance $p_{ij}$, how do we find an unbiased estimator $\Theta$ which follows $\mathbb{E}(\Theta)=p_{ij}^2$?
I made ...
7
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3
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What is meant by the probability of a sample having a value of $x$ is $ng(x)$?
Reading from Wikipedia:
The probability of one sample having a value of $x$ is $n g(x)$.
Assuming that the notation is consistent throughout the page, I would take $g$ to either be the probability ...
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Is $f(a) = EX^{1+a}EX^{-(1+a)}$ non-decreasing?
$X$ is a non-negative random variable and $a$ is a non-negative real number. Define
$$f(a)= EX^{1+a}EX^{-(1+a)}.$$
Is $f(a)$ non-decreasing with $a$?
Original problem: when I read a paper, I encounter ...
- 305
2
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1
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Right continuity of cdf
Before asking, I want to let you know that I realize already there are different proofs for the right continuity of the cdf, however I would like to know if my proof of this is correct, as I assume it ...
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The generalized likelihood ratio test of H0: µ<=µ0 v.s. H1: µ>µ0 with unknown σ [duplicate]
Assume:random samples in N(µ,σ²)
when null hypothesis(H0) is true,
why MLE is min{µ0,X̄} ?
How can get MLE in restricted parameter space(µ<=µ0) ?
please help me
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