The estimation tag has no wiki summary.
1
vote
0answers
14 views
Is there a way to estimate the range of fitting coefficients from only the data?
Considering an approximation $f$ for a set of $N$ data points $(x,y)$ using, for example, $M$ radial basis functions at arbitrary sites in the domain
$f_i = \sum_{j=1} ^M c_j\phi(||x_i-x_j||)$
where ...
0
votes
2answers
50 views
Mental Math - Estimating Logarithms
How can we estimate logarithms with different bases? Take $\log_2 10$ ($1\over\log_{10}2$$\approx3.32192809$) for example. If we convert $10$ to binary, we get $1010_2$. So $\log_21010_2$ can clearly ...
0
votes
1answer
33 views
Likelihood of the mean of one random variable with unknown parameters greater than another
Assume we have two random variables $X$ and $Y$ that are gamma distributed (or normally distributed, if it makes the math easier) with unknown parameters. We have samples $x_1,x_2,...,x_m$ and ...
1
vote
2answers
22 views
Expected value of total accumulated lifetime (understanding gap in proof)
Problem:
I understand the first line $E(T) = ...$
However, I don't get the next two steps. I feel like I almost get it.
It's like we are factoring out a $\sum_{j=1}^{20}$ but how did he ...
3
votes
1answer
39 views
Best estimate for random values
Due to work related issues I can't discuss the exact question I want to ask, but I thought of a silly little example that conveys the same idea.
Lets say the number of candy that comes in a package ...
0
votes
1answer
18 views
Approximation question
Cars and buses arrive at a bridge according to the independent Poisson processes at a rate of $3$ cars/minute and $1$ bus/ minute. What is the chance that strictly more buses arrive than cars in a ...
1
vote
3answers
85 views
Let $ X_1,X_2,…,X_n$ be i.i.d. $N(\theta_1, \theta_2)$, please prove that $E[(X_1-\theta_1)^4] = 3\theta_2^2$
If $X_{1}$, $X_{2}$, ..., $X_{n}$ is sampled from $N(\theta_1, \theta_2)$, how can I prove that $E [(X_{1} - \theta_1)^{4}] = 3 \theta_2^{2}$?
I started off this question finding the completely ...
1
vote
0answers
27 views
Cramer-Rao bound for $\chi^2$ distribution parameter estimates.
I've stuck in unpleasant problem with noncentral $\chi^2$ distribution.
I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ is ...
0
votes
0answers
28 views
Numerical calculation of fisher information
I am trying to obtain numerically the fisher information. Given a likelihood function
$$ f(X,\theta),$$
with $X \in [0,1]$.
The fisher information is given by
$$ ...
0
votes
1answer
21 views
Estimate growing graphs
Lets make my scenario not generic just so that i could use particular terms
Say i have a graph of population per year of someplace over some decades
Lets say the graph is like this
How can i ...
0
votes
0answers
43 views
Big Oh Equality
I am stuck on a proof, having encountered this bit I can't figure out:
$$e^{O(1/\log x)}=1+O \left( \frac{1}{\log x} \right)$$.
Why is this?
Thank you very much in advance!
0
votes
1answer
58 views
Non-Linear regression
Imagine that I have a function $ f(x,y) $ to model a physical phenomenon.
I believe that functions is defined by $$ f(x,y) = A*x + B*y + C*x*y$$
I have many values for $ (x,y,f(x,y)) $, how can I ...
1
vote
1answer
50 views
How to establish the estimate?
I consider the inequality as follows: let $a>0,b>0$, and satisfy $$2a^2-b^2\leq C(1+a).\tag{1}$$ If we assume that $b\leq a$, then there exist a constant $C_1>0$ such that $$a\leq ...
0
votes
2answers
32 views
Correlation bound
Let x and y be two random variables such that:
Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An ...
1
vote
1answer
21 views
Interpret the terms in Strang's second lemma
The second lemma of Strang states that for a certain choice of $V_h$, $a$, $u$ and $f$ there exists a $c>0$ such that
$$||u-u_h|| \leq c (\inf_{v\in V_h} ||u-v|| + \sup_{v\in V_h} ...
