For questions about estimation and how and when to estimate correctly

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11 views

Estimate average change over time with matlab

I'm trying to use matlab to estimate the average difference in location and height for tectonic plates for a university assignment. Not alot of guidelines or pushes in any direction as how to solve ...
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0answers
33 views

Estimating distribution from two distributions

I have been doing a survey on Family Incomes in India. The income of male and females are denoted by x and y. x and y are strictly positive. Per chance, individual values of y were deleted. I only ...
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1answer
23 views

Stability (wrt parameters) of elliptic partial differential equation

consider the equation $$\mathcal Lu=f \quad \text{in } \Omega $$ With some appropriate boundary condition, $\Omega$ regoular as you like, $ \mathcal L$ to be defined by $$\mathcal Lu=-div(A(x)\...
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0answers
9 views

Estimate Results From a Database

I have some data in an Excel document, from differents projects i've made. Now I would like to use this data in order to estimate the results for new projects with different input values. Each ...
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1answer
42 views

Energy estimate in Evans PDE book

Before Theorem 6 in Chapter 7.4 in Evans' PDE book Evans claims that there exists $\beta > 0$ such that $$ \beta\|u\|_{H^1(\Omega)}^2 \leq B[u,u]\,, \quad \forall u \in H_0^1(\Omega)\,. $$ From how ...
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2answers
29 views

Optimal estimation of the fusion of two measurements

Suppose I have a sensor measuring a quantity $\text R$. For example the sensor could be a radar estimating the range of a target. We can write: $$R(t)=r(t)+\nu_0(t)$$ where $r(t)$ is the real range ...
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1answer
17 views

An issue related to the expectation maximization algorithm for a coin toss experiment

I just read a very nicely written introduction paper for the expectation maximisation algorithm published in Nature biotechnology by Do and Batzoglou (http://www.nature.com/nbt/journal/v26/n8/full/...
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16 views

Error propagation in complex formula

I'm currently trying to use error propagation formulae to calculate an estimate for the error in the following molecular dynamics formula: $C_v^* = \frac{3}{2}\bigg[1-\frac{2}{3NT^{*2}}\big\langle (\...
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1answer
20 views

Predicting values based on given data

num value 8 ? 10 ? 12 24.33 16 22.5 20 22.29 24 22.41 28 22.55 32 ? 36 ? let's say i have the following ...
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1answer
24 views

Estimation for points in a neighbourhood of a root of a polynomial

Let $p(x)$ be a polynomial with complex coefficients and $p(\tilde x)=0$. Choose $\delta>0$ small enough, such that $\tilde x$ is the only root of $p$ in $B_\delta(\tilde x)$. I want to show that ...
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1answer
16 views

Extimate error, payment rate, continous compounded

Give an estimate of the error, when the payment rate $x_m = r P_0 \frac{(1+r/m)^{mT}}{(1+r/m)^{mT}-1}$ (compounding and repayment m times per year) ist approximated bei $x_{\infty}=\frac{r P_0* e^{rt}}...
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1answer
24 views

Can a prediction interval be interpreted as a probability?

Suppose I find a 90% prediction interval for some data distribution. This implies that if I sample large enough data from this distribution, then 90% of such data will lie inside the prediction ...
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12 views

Representation of the optimal filter measure as the measure of a diffusion process

In "Mitter SK, Newton NJ. A Variational Approach to Nonlinear Estimation. SIAM J Control Optim. 2003 Jan;42(5):1813–33", it is shown that the path estimation measure $P_{X|Y}(\cdot,y)$ for the ...
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1answer
18 views

Given the estimator find wheter

X has an uniform distribution on interval $(0,\theta]$ where $\theta$ is a positive parameter Given the estimator: $$T(X_1,X2, \ldots, X_n)=\frac{2}{n} \sum_{i=1}^n X_i$$ Find whether this estimator ...
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1answer
37 views

Bias and variance of estimator

I have the following estimator, $E = 1/\bar{X}$ of $E = 1/\lambda$ where X is exponentially distributed with parameter $\lambda$. I'm trying to find the bias and variance of this estimator. For the ...
3
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1answer
228 views

Estimate of the derivative

Show that if $f(x)=x^2+O(x)$, and $f$ is differentiable with non-decreasing derivative $f'(x)$, then $f'(x)=2x+O(\sqrt{x})$. I know that if $f'$ is not non-decreasing, then the statement is not true....
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2answers
25 views

Estimation of a defined integral

I need to show that $$\left|\int\limits_{0}^{\frac{1}{2}}\frac{(2t-1)^3}{(\sqrt{1+t})^7}dt\right|<\frac{16}{125}$$ Evaluating it would be my last hope, but it wouldn't be easy wither. Is there a ...
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0answers
4 views

Computing the log-likelihood ratio for a large dataset

I have a sparse binary matrix $M$ of size $500k \times N$ where rows are objects and columns are features. $M_{ij} == 1$ if there is an observation of feature $j$ in item $i$. For each object I would ...
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16 views

Numerical Estimation and Integration by Parts

I have hit a roadblock in a project and I wonder if anyone with better quantitative skills (shouldn't be hard to find :p) can lend me a hand. I need to compute the following: $\int^a_bxf(x)dx$ ...
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0answers
35 views

How to estimate probability of a binomial passing a threshold?

Let $X$ be a binomial random variable $X \sim Bi(p, t)$. ($t$ is the number of tosses) Is there a way to estimate $$P(X \ge \alpha t + \beta)$$? I know that I can write the probability exactly but ...
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1answer
37 views

Unbiased Estimator of $\sigma^2$

Let $X_1, X_2, ..., X_n$ be a random distribution such that the mean $\mu = 0$ and the variance $\sigma^2$ is unknown. I'm finding a constant $c$ such that $$U(X) = c \sum^{n-1}_{i = 1}(X_{i+1} - ...
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1answer
46 views

Asymptotic variance of MLE of normal distribution.

I am trying to explicitly calculate (without using the theorem that the asymptotic variance of the MLE is equal to CRLB) the asymptotic variance of the MLE of variance of normal distribution, i.e.: $$\...
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1answer
17 views

Estimation with Hölder condition

Do you have any hints about how to prove (or find a counterexample) that, given $f \in \mathcal{C}^1 ( \mathbb{R}^n \smallsetminus \{ 0 \}) $ such that $$\int_{|x|=r} f(x) \, dS(x) = 0$$ for all $r&...
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4answers
81 views

How to estimate $\sum_{n=1}^{\infty}\frac{(-1)^n}{n^3}$ with error less than $0.01$?

How to estimate $\sum_{n=1}^{\infty}\frac{(-1)^n}{n^3}$ with error less than $0.01$? In order to solve the question, I think we need to write out the terms. So $\sum_{n=1}^{\infty}\frac{(-1)^n}{n^3}...
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0answers
24 views

Parameter estimation - Holt's Two parameter Linear Exponential Smoothing

The reference for the below equations can be found in the Link . Note that $k$ is the timestamp and $i$ is the $i^{th}$ entry of a vector or $(i,i)^{th}$ entry of a matrix, $F$ in this case Equation 1 ...
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1answer
42 views

Simple expected value manipulations (in estimation problem)

Let $\hat{\theta}_{1}$ $\hat{\theta}_{2}$ $\hat{\theta}_{3}$ be three estimators of the parameter $\theta$. E($\hat{\theta}_{1}$) = E($\hat{\theta}_{2}$) = $\theta$, E($\hat{\theta}_{3}$) $\ne$ $\...
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1answer
21 views

Simplifying linear algebra division

So yesterday, I posted a question but it seems I wrote it too confusingly. Now, I will simplified the question so that probably you have some opinion or suggestion. Suppose, I have an function like ...
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2answers
94 views

Earth population growth rate is exponential or logarithmic?

How many points on a monotonically increasing curve is needed to determine if it is exponential or logarithmic? For example can we tell that in the most recent history population is increasing ...
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0answers
16 views

Addition of two estimated means to become new estimated mean

In order to estimate population mean there were conducted two independent questionnaire survey. They have mean estimates $\hat \mu_1$ and $\hat \mu_2$ respective. And their standart deviations are $\...
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1answer
23 views

Estimation Question - London Eye

Good afternoon, I was recently at an assessment center and was asked an estimation question. This was the first one I've ever done so was wondering how everybody else would go about solving the ...
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0answers
16 views

Underestimation of absolute value of integrals

If we have a function for which it is not possible to calculate the definite integral explicitly, we may want to approximate it somehow, for example by giving bounds for its absolute value. There are ...
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0answers
9 views

General approach of MLE for function of parameters.

everyone. Imagine that you have two random variables $X(\theta)$ and $Y(\alpha)$. How to estimate using MLE function of this two parameters $f(\theta,\alpha)$? For example, sum or difference, or ...
2
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1answer
61 views

How to show that $E[E[X\mid Y]\mid Y] = E[X\mid Y]$

I'm reading a little proof about how the estimation error (based on the conditional expectation estimator, $E[X\mid Y]$) has zero expectation, and at one point the author used the equality that the ...
1
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1answer
32 views

Showing $X_{(n)}$ is an unbiased and consistent estimator for $\theta$.

Let $X_1,X_2,\ldots, X_n$ is distributed iid $\mathrm{Uniform}(0, \theta)$ with $\theta$ in being real positive. Show $\frac{n+1}{n}X_{(n)}$ is an unbiased and consistent estimator for $\theta$. I ...
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1answer
122 views

Find a 95% confidence interval of the mean serum cholesterol of patients on the special diet.

A physician who has a group of thirty-eight female patients aged 18 to 24 on a special diet wishes to estimate the effect of the diet on total serum cholesterol. For this group, their average serum ...
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0answers
30 views

Using Log Likelihood to Find Sufficient Statistic

So, I've been given the following problem from Wackerly's Mathematical Statistics with Applications (specifically 9.60). I'm aware of one way to find the solution, but I'd like to know if this works ...
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2answers
50 views

Obtaining exact decimals in bisection method

While studying the bisection for the approximation of roots of non-linear equations I was given the following bound for the error: $|x_n-s| \leq \frac{(b-a)}{2^{n+1}}$ where $x_n$ is the n-th ...
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1answer
24 views

Calculate average time of person in system when ins and outs are roughly equal

I have a system that has people going through a sensor for in, a sensor for out. I'm measuring ins and outs through the day, ...
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0answers
28 views

Weird behaviour of CLT's application to binomial.

I am carrying out the simulations of the following experiment for all $n$ in the set $\{1,2,3,...,100\}$. (0) Set $k=0$. (1) Generate $n$ $Bernoulli(0.9)$ trials. (2) Construct estimate $\hat\theta=...
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1answer
74 views

Show that Cov(T,T')=Var(T) [closed]

Let $X_1,...,X_n$ be a sample, all with mean $\mu$ and $Var(X_i)<\infty$. Let $T(X_1,...,X_n)=\sum_{i=1}^na_iX_i$. If T is the UMVUE of $\mu$ and T' is another linear unbiased estimate of $\mu$, ...
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0answers
119 views

ML estimation for bivariate data.

Consider the random variables $X$ and $Y$ with joint distribution $$F(x,y)=[1-e^{-a_{1}x}]^{\theta}+[1-e^{-a_{2}y}]^{\theta}-[1-e^{-a_{1}x-a_{2}y}]^{\theta},$$ where $a_{1}>0$, $a_{2}>0$, $0<\...
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0answers
27 views

Parabolic interpolation in $k$ dimensions

I know the values of a smooth function of $k$ variables at $3^k$ points on a cube in $k$ dimensions (where $k=2,3$ or $4$). The central value is known to be the largest. I want to estimate the ...
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1answer
30 views

Why is $m(n)\approx\log_2(n)$?

Why is $m(n)\approx\log_2(n)$ ? If $m(n)=\inf\{m:2^{-m}m^{-3/2}\le\frac1n\}$, taking log of $m(n)$ I get $-m(n)-\frac32\log_2(m(n))\le-\log_2(n)$ (This appears in the solution of an exercise in ...
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0answers
13 views

Estimation of binomial probabilities $f(r)$ over $r \in [0,\frac{1}{2}]$

I want to fit a (decreasing) univariate function, \begin{equation} f(r), \end{equation} over $r \in [0,\frac{1}{2}]$ to a series ($r =\frac{1}{100}, \frac{2}{100}, \frac{3}{100} ,\ldots,\frac{1}{2}$) ...
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1answer
10 views

Understanding the steps taken in a calculation of the maximum profile likelihood of a simple ODE, given some data

I'm trying to understand a calculation made in a paper (section 2 from the supplementary contents of ...
1
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1answer
26 views

Estimating confidence Interval for unknown Variance, Normal distribution

I've been stuck with this question for a while: I've learnt how to use t-distribution to estimate CIs for an unknown variance, but I'm unsure how that applies to this situation. Any help would be ...
0
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1answer
56 views

How can I calculate missing values from a table listing of areas and prices? [closed]

I have a set of objects of different sizes (measured in square metres). I know the price of some of them. I want to use the known prices to find the missing prices. Here is the data I have: \begin{...
4
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2answers
46 views

Probability of island having 8 people born with disease, estimate?

The chances of being born with a certain disease are estimated as $1$ in $1200$. What is a good estimate of the chance that an island with $10000$ inhabitants has precisely $8$ people born with that ...
0
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1answer
46 views

Supremum of $\cot(\pi z)$ where $z$ is on circle with radius $n+1/2$

I try to estimate the supremum of $|\cot(\pi z)|$ and where $z=(n+1/2) e^{i t}$, $n\in\mathbb N$ and $t\in[0,2\pi)$. I should be a constant. So far I did by wiriting it in exponential form and ...
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0answers
14 views

Fitting a model to a collection of binomial proportions, based on varying (large) sample sizes.

I have a multi-parameter bivariate function, say $f(i,j)$ that I want to use to predict the entries of a matrix $M(i,j)$, the entries of which are binomial probabilities based on varying sample sizes, ...