Taylor
  • Member for 10 years
  • Last seen this week
Consistency of Sample Mean in Time Series Data
0 votes

A few years later... here's a solution that does not involve invoking Cesaro's Lemma. It follows from the following result: If $v_n \to \ell$ as $n \to \infty$, then $\bar{v} := n^{-1}\sum_i v_i \to \...

View answer
Sufficient statistic $\sum_{j=1}^{n} |x_{j}|$ for laplace distribution
0 votes

I do not know how to use the factorization theorem You have to write the likelihood as a product of two functions. One function is allowed to have parameters in it, and one is not. The one with the ...

View answer
Modeling a time series of ordered vectors
0 votes

Here's a model: $$ \mathbf{x}(t) = \mathbf{A} \mathbf{x}(t-1) + \mathbf{v}(t) \tag{1} $$ $$ \mathbf{x}^o(t) = g(\mathbf{x}(t)) \tag{2} $$ where $g$ is the ordering function, $\{\mathbf{v}(s)\}_s$ are ...

View answer
What does the pmf of a discrete random variable look like if it can take on the value $\infty$?
Accepted answer
0 votes

If you accept $\{\tau < \infty\} = \bigcup_{k\ge 1} \{\tau = k\}$, then $$ P(\tau < \infty) = \sum_{k=1}^{\infty}P(\tau = k). $$ by countable additivity. To add to the intuition, take ...

View answer
convergence of an average of consistent estimators?
0 votes

By the triangle-inequality \begin{align*} 0 &\le \left|\frac{1}{nm}\sum_{j=1}^m\sum_{i=1}^nX_i^j - E[\mu]\right| \\ &\le \left|\frac{1}{nm}\sum_{j=1}^m\sum_{i=1}^nX_i^j - m^{-1}\sum_{j=1}^m\mu^...

View answer
Meaning of Square Root of Covariance / Precision Matrices
0 votes

Sometimes people are interested in estimating the locations of zeros in the precision matrix for the same reason you describe above. If $M$ is your square root matrix, i.e. $M'M = \Sigma^{-1}$, then ...

View answer
mean and variance of norm of normal random variables
0 votes

Use the polar coordinates transformation if you're good at integrating. Define $$ \left[\begin{array}{c} R \\ \theta \end{array} \right] = \left[\begin{array}{c} \sqrt{X^2 + Y^2} \\ \text{arctan}(\...

View answer
Finding the center of a logistic curve
0 votes

Check out this Wiki page and note that $$ -(5 - 6 x) = -(-6)(x - 5/6).$$

View answer
How to prove nonstationarity of a random walk?
0 votes

First, I think you mean: I know to [dis]prove stationar[it]y it suffices to prove [that] either [the] mean function or [the] autocovariance function is not independent of time. But yeah that's ...

View answer
If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
0 votes

Let $X,Y_1,Y_2,\ldots,Y_{1000} \in \{0,1\}$ denote the true color, and the responses, respectively. "Blue" is coded as a $1$, and vice versa. Assume that $p(x)$ is Bernoulli with parameter $p_x$. ...

View answer
Evaluate integral with Importance sampling method in R
0 votes

Your mean and standard deviation are random. You will never have exactly the right mean (with probability one). Notice how if you run the last portion again, all the numbers change. Maybe you would ...

View answer
Best way to combine MCMC inference with multiple imputation?
-1 votes

I wrote a paper arxiv.org/abs/1907.09090 that describes how the pseudo-marginal approach can impute missing data. 400 covariates sounds tough, though, to be completely honest. Depends on what kind of ...

View answer
1
13 14 15 16
17