User sonicboom

37 votes

5 answers

14k views

Intuition behind standard deviation

asked Feb 4, 2014 at 11:55

6 votes

1 answer

756 views

Can we go from $X_n = \mu + O_p(n^{-1})$ to $E[X_n] = \mu + O(n^{-1})$?

asked Dec 16, 2020 at 13:57

6 votes

1 answer

540 views

Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the case of multiple regression?

asked Mar 22, 2021 at 18:10

5 votes

0 answers

644 views

What conditions are needed for $a_n = O_p(n^d) \implies E[a_n] = O(n^d)$?

asked Dec 17, 2020 at 11:05

5 votes

4 answers

1k views

Conditional variance - $Var(X + U | X) = Var(U)$?

asked Aug 5, 2014 at 20:46

4 votes

1 answer

6k views

Covariance and power spectral density of a signal?

asked Oct 28, 2016 at 12:10

4 votes

3 answers

226 views

Are the estimated linear regression coefficients still normally distributed if one of the predictors is a factor variable?

asked Nov 3, 2020 at 10:17

4 votes

1 answer

109 views

Is $\left\{(\mathbf{X_n}^T\mathbf{X_n}/n)^{-1}\right\}_{n=1}^\infty$ uniformly integrable (UI)? What assumptions make it UI?

asked Dec 10, 2020 at 12:44

3 votes

1 answer

404 views

Rate of convergence of $\hat Q_{xx}^{-1} = \left(\frac{\mathbf{X}^T \mathbf{X}}{n}\right)^{-1}$ to the probability limit?

asked Dec 11, 2020 at 16:52

3 votes

1 answer

353 views

Do all moments of a random variable need to be well controlled for a valid 2nd order Taylor approximation, or is the third moment sufficient?

asked Mar 1, 2021 at 17:22

3 votes

3 answers

151 views

Likelihood ratio test to determine if average number of accidents has dropped?

asked Aug 5, 2014 at 18:05

2 votes

0 answers

113 views

As $n \to \infty$, can we 'ignore' a matrix in an expectation that does not depend on $n$?

asked Mar 31, 2021 at 21:14

2 votes

1 answer

166 views

$E[(\beta_n-\beta)^2|\mathbf{X}]=\sigma^2(\mathbf{X}^T\mathbf{X})^{-1}$, what about $E[(\beta_n-\beta)^k|\mathbf{X}]$ for $k=3,4$?

asked Dec 14, 2020 at 11:26

2 votes

1 answer

261 views

Validity of approximating a covariance matrix by making use of a probability limit?

asked Dec 4, 2020 at 11:12

2 votes

1 answer

340 views

$E(X_1| \overline X ) = \overline X$, the sample mean

asked Jun 27, 2014 at 18:55

1 vote

1 answer

92 views

Does $\hat \theta_n=\theta+O_p\bigg(\dfrac{1}{\sqrt{n}}\bigg)$ imply that $p_{\hat \theta_n X}(x)=p_{\theta X}(x)+O_p\bigg(\dfrac{1}{\sqrt{n}}\bigg)$?

asked Oct 25, 2020 at 18:03

1 vote

0 answers

35 views

If $E[|X_n|] = O(n)$ is $E[|X_n|^2] = O(n^2)$?

asked Apr 9, 2021 at 10:04

1 vote

0 answers

33 views

Does $E[\hat \Sigma^{-1}] \to \Sigma^{-1}$ still hold for samples drawn from a non-normal population?

asked Mar 19, 2021 at 13:23

1 vote

0 answers

185 views

Is it possible to convert a pdf obtained with density() to an ecdf?

asked Jan 9, 2021 at 21:46

0 votes

0 answers

34 views

Accepting vs failing to accept the null hypothesis? [duplicate]

asked Jun 3, 2021 at 13:29

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20 Questions

Intuition behind standard deviation

Can we go from $X_n = \mu + O_p(n^{-1})$ to $E[X_n] = \mu + O(n^{-1})$?

Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the case of multiple regression?

What conditions are needed for $a_n = O_p(n^d) \implies E[a_n] = O(n^d)$?

Conditional variance - $Var(X + U | X) = Var(U)$?

Covariance and power spectral density of a signal?

Are the estimated linear regression coefficients still normally distributed if one of the predictors is a factor variable?

Is $\left\{(\mathbf{X_n}^T\mathbf{X_n}/n)^{-1}\right\}_{n=1}^\infty$ uniformly integrable (UI)? What assumptions make it UI?

Rate of convergence of $\hat Q_{xx}^{-1} = \left(\frac{\mathbf{X}^T \mathbf{X}}{n}\right)^{-1}$ to the probability limit?

Do all moments of a random variable need to be well controlled for a valid 2nd order Taylor approximation, or is the third moment sufficient?

Likelihood ratio test to determine if average number of accidents has dropped?

As $n \to \infty$, can we 'ignore' a matrix in an expectation that does not depend on $n$?

$E[(\beta_n-\beta)^2|\mathbf{X}]=\sigma^2(\mathbf{X}^T\mathbf{X})^{-1}$, what about $E[(\beta_n-\beta)^k|\mathbf{X}]$ for $k=3,4$?

Validity of approximating a covariance matrix by making use of a probability limit?

$E(X_1| \overline X ) = \overline X$, the sample mean

Does $\hat \theta_n=\theta+O_p\bigg(\dfrac{1}{\sqrt{n}}\bigg)$ imply that $p_{\hat \theta_n X}(x)=p_{\theta X}(x)+O_p\bigg(\dfrac{1}{\sqrt{n}}\bigg)$?

If $E[|X_n|] = O(n)$ is $E[|X_n|^2] = O(n^2)$?

Does $E[\hat \Sigma^{-1}] \to \Sigma^{-1}$ still hold for samples drawn from a non-normal population?

Is it possible to convert a pdf obtained with density() to an ecdf?

Accepting vs failing to accept the null hypothesis? [duplicate]