Questions tagged [estimation]
For questions about estimation and how and when to estimate correctly
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the behavior of the Fourier series partial sum
Consider the Fourier series partial sum $S_n(x)$ as $n \to \infty$ where $S_n(x)$ is the partial sum of the Fourier series representation of a function $f(x)$ defined on a $2\pi$ periodic interval.
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Estimation of Sum of Binomial Coefficients that doesn't Start from Zero
I am having some trouble showing the following estimation:
Let $\mu \in (0, 1)$ be an absolute constant. There exists an absolute constant $\eta \in (0, 1)$ small enough such that the number of ...
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Average Rank versus Ranked Average in Parameter Estimation
I have the following problem:
In a cricket tournament, the eleven batsmen of a team play 100 matches before the final. The runs scored by each are available. Determine the average rank of the batsmen ...
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the sum of $O_p$ --$ O_p(s^2\frac{\log d}{n}+s\sqrt{\frac{\log d}{n}}) $
I read papers in the area of inference for high-dimensional graphical models and these papers always state the convergence rate of the estimator. Using $O_p$ is a good choice.
Maybe I made some ...
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Is there a version of the delta method when taking the derivative of an estimator with respect to time for stochastic processes?
Suppose that $X$ is a stochastic process and $f$ some measurable function. Consider the random variable $S_t=\int_0^tf(X_s)\mathrm{d}s$ and an estimator $\hat{S}_t^n=\sum_{i=1}^{\lfloor t/n\rfloor}f(...
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How might one estimate the number of samples in a uniform distribution given only the sample range?
Let's say we have a fair roulette wheel with 2^256 segments, each printed with a unique integer in the range 0 to 2^256 - 1. Let's say that the wheel is hidden from us and that Trevor spins it ...
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Estimates for incomplete Gamma functions
I want to show that
$$\int_{0}^{\sqrt{n}} \exp(-s^4)s^{n+1} ds - \int_{\sqrt{n}}^{\infty} \exp(-s^4)s^{n+1} ds \geq 0\, \quad \text{for all }n\in\mathbb{N}.$$
These integrals can in fact be written ...
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A vectorial estimate I can't understand.
Let $w\in (0, \kappa], p < 1, p\neq 0, \alpha \in (0, 1), \beta(1-p) -Kp>0, \sigma\in \mathbb{R}^{n\times n}, $invertible, and $ \mu, \eta \in \mathbb{R}^n$.
I want to estimate $|\mathbf u|$, ...
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What is a good way to compute $\Gamma(1/3)$ on a standard pocket calculator?
This question is inspired by this one. The earlier question asks how to calculate a certain integral efficiently with a standard pocket calculator. A fine answer by Travis Willse gives a good result ...
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UMVUE of $\mathbb{P}[X=x_0]$ where $X_1,\cdots,X_n$ is Poisson
I came up with this problem and tried to solve it myself. Please check my solution, I am a bit unsure it is correct because it says the UMVUE for the probability where $x_0>\text{sum of ...
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Evaluate or estimate $\int_{8}^{27}\frac{\mathrm{d}x}{\sqrt{x}-\sqrt[3]{x}}$ without a calculator in a fast way
In a fast way and without a calculator, I need to evaluate the following integral or just estimate it in a way that will lead to the correct answer.
$$\begin{align}\\&
\text{What is the value of}\...
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Observer for LTI system with linear inequality constraints for state
I have searched quite a bit about this topic but only found methods that consider equality constraints.
Consider LTI system
$$
\begin{align}
\frac{d}{dt}x&=Ax+Bu\\
y&=Cx+Du
\end{align}
$$
with ...
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A question about Wiener filter based on Linear Estimation by Kailath
In my linear estimation class based on the textbook Linear Estimation by Kailath, we went through the process of finding LLSE of $\hat{x}(t+\lambda)$ for fixed $\lambda$ given $\{y(\tau)|-\infty<\...
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How to bound $\mu (\{ x \le X : |ψ(x) − x| \ge εx^{1/2} (\log x)^2 \})$ from above?
From the following estimate $$ \int_0^X |ψ(x) − x|^{2k} dx ≪ (ck^2)^k X^{k+1} \tag{1}$$ where $c$ is an absolute constant, I want to prove the following estimate $$ µ ( \{ x \le X : |ψ(x) − x| \ge ...
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Estimates of the derivatives of $\Xi(s)$
The $\Xi$ Function is defined by $\Xi(s)=\xi(\frac{1}{2}+is)$, where $\xi(s)=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$.
This is a problem from my homework: since we can write it ...
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