# Tagged Questions

For questions about estimation and how and when to estimate correctly

1answer
77 views

### When to we accept a hypothesis when using Wald test statistic? [closed]

Hello I had to test two hypothesis, one hypothesis gave a wald test statistic with value 0.00015 and the other a value of approximately 40. Is it true when I then say that we accept the hypothesis ...
0answers
4 views

### How to computing Wald test in R based on what I have so far?

I have to simulate an AR(1) process with $\rho = 0.5$ and then estimate $\rho$ based on the first 100 $X_T$ values I did this the following way: ...
2answers
23 views

### When does it make sense to build a confidence interval for the mean with known standard deviation?

While estimating with confidence interval the mean value for a population, there are two options: If the standard deviation is known, and If the standard deviation is unknown. But in the first ...
1answer
121 views

### Upper bound for the error on the Fourier series for $e^{x}$

I have been given the following problem: Find the Fourier series for $e^{x}$ over the interval $-\pi \le t \le \pi$. Hence find the upper bound of its error. To spare me typing a huge expression and ...
1answer
60 views

### An asymptotic estimate for density of eigenvalues

this is the screenshot of the useful part of the cited book Let $\{\lambda_n\}$ be constants such that ${\lambda_n}=n^2\pi^2+\int_{0}^{1} q(t)\,dt +c_n \qquad \text{for} \quad n\rightarrow \infty$ ...
1answer
32 views

### problem using MLE on gamma distributed variable

I am making some kind of systematic error(s), while working with maximum likelihood estimations. Could someone please point these out to me? In my last assignment, I tried to find the MLE of $\beta$ ...
1answer
32 views

### Finding number pattern

I have a program which I originally thought was linear, meaning that if I had twice the data, the program would take twice as long to process. I was wrong, and it seems to be somewhat exponential. ...
1answer
16 views

### on a step of a proof of the Levinson density theorem

Let $n(r): \mathbb{R}\rightarrow\mathbb{N}$ be a monotone (increasing) function such that $\int_{1}^{r} \frac{n(u)}{u}du \leq \frac{1}{2}\log (r)+ A$ where $A$ is a certain constant. I should deduce ...
0answers
18 views

### Finding the closest vector to an observation

I have a collection of vectors (a codebook in hand) which are presented within a matrix $A$ $$A = [ a (\theta_1), \, a (\theta_2), \, a (\theta_3), \, a (\theta_4), \,\cdots]$$ We have obtained ...
1answer
42 views

### Estimate of a (integral) function

I should show that function $H(w)=\int_{-\pi}^{\pi}f(x) e^{iwx}dx$, where $f(x)\in L^2(-\pi,\pi)$, is such that $H(re^{i\theta})=O(e^{\pi r |sin(\theta)|})$. Any suggestion?
1answer
18 views

### Required number of simulation runs

I have the following problem: One wants to estimate the expectation of a random variable X. A set of 16 data values (i.e. simulation outputs) is given, and one should determine roughly how many ...
2answers
21 views

### Significant figures addition/subtraction rounding?

I thought you round to the same place as the number with the addend with the least precision. For example, if you had $25.63+ 42.3$ the answer would be rounded to the tens place ($67.9$). However, my ...
1answer
61 views

0answers
16 views

### Least Square solution for approximating a sequence

Suppose I have a sequence of length N $a_1,...,a_N$ I want to approximate this sequence by $k^1,...,k^N$ where $k$ is my variable. What is the least square solution of this? is there a closed ...
1answer
35 views

0answers
25 views

### Variable value estimation for given product/fracture values

I have a data set (time series) with given values for certain fractions xy = x/y (where x,y are not constant over time) Thus, there are following fractions: AB = A/B CB = C/B AD = A/D CD = C/D AE = ...
0answers
40 views

### Method of moment estimator. Deconvolution

The distributions $Y, X, Z$ and $W$ are related as follows: $$Y_1 = X + Z$$ $$Y_2 = X + W,$$ that is $X$ (random variable) is a common factor to the random variables $Y_1$ and $Y_2$, which ...
0answers
11 views

### How to interpret the Quantified properties of estimator?

https://en.wikipedia.org/wiki/Estimator The link provides a very good explanation of the estimator. I am beginner to statistics and inference , so i have some confusion about the quantified properties ...
1answer
30 views

0answers
50 views

### Minimum mean square estimator for closing value of the NYSE

I am attempting to develop an estimator for the closing value of the NYSE $x(n)$ based on previous $N$ closing values, $x(n-1), x(n-2), ... x(n-N)$. I want to find the Minimum Mean-Square estimator ...
1answer
153 views

0answers
24 views

### Establishing consistency

I need to establish the (weak) consistency of an estimator of the mean, $T=a+b\bar{X}$. I tried to apply Chebyshev's inequality, but I couldn't do much because the parameter that subtract in the ...
2answers
68 views

### Confidence interval for sample

I have a sample of size $n=19593$ of count data ...
1answer
34 views

### construct confidence interval from proportions

Suppose you have a population of count data, i.e., $1,2,3, \dots, k$, you have a sample of the population of size $n$, and you have a confidence interval for the proportion of $1$'s , $2$'s,\dots$n$'s ...