Questions tagged [estimation]
This tag is too general; please provide a more specific tag. For questions about the properties of specific estimators, use [estimators] tag instead.
2,876
questions
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7 views
Standard Errors of ECDF with Potential Model Fit Error
I have data and a proposed likelihood. I used MLE to fit the likelihood, but it is a very complicated likelihood and there is some estimation error of the model. The likelihood may be correct, but ...
0
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0answers
18 views
Effect of scaling data on ARMA coefficients [duplicate]
For numerical stability, I thought it might be a good idea to scale my data before feeding them into an ARMA GARCH model. I have gone through a few older posts and understand the affect scaling ...
0
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1answer
35 views
How comparing two confidence intervals
Let's assume I have to point estimates with 95%-CI. The source can be from a simple computation of two samples or from a complex regression analysis. For example: odds ratio
(1) 2.0 (95%-CI: 1.4-2.9)
...
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0answers
29 views
LARS package in R with specific lambda value
I am trying to use the LARS package in R to obtain a Lasso estimate of the sparse coefficient vector, say $\hat{\beta}_{\text{sparse}}$, as opposed to a coefficient path. In other words, I am not ...
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19 views
Question about maximum likelihood estimation [closed]
The question is
Using the asymptotic theory of the MLE, find the limiting distribution of the MLE. Then I need to use it, form an asymptotic two-sided 1−α confidence interval for θ.
I already got ...
0
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1answer
15 views
Estimate parameters for a distribution based on user input
Background
I have a server which is accessed by a different amount of the users at the same time. It is natural from the users to experience some delay in the communications based on how many people ...
1
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0answers
34 views
ARMA GARCH fitting
I've made a few posts regarding a manual ARMA GARCH implementation and I have made some great progress. However, I am still shy of a working program as I am obtaining some rather large forecasts. I've ...
0
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0answers
21 views
SIR: parameter estimation and optimization here (R)
From here https://ourworldindata.org/coronavirus/country/israel I have extracted the Covid Data for Israel, with some manipulations, I have obtained the plot of the daily new infections in Israel
If I ...
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0answers
10 views
covariance estimation method comparison
There seem to be a bunch of ways to estimate the covariance and precision matrices (in sklearn there are several, including MinCovDet and graphical lasso, but also including primitive (which does not ...
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0answers
18 views
Can I take the mean of multiple estimates in a regression, and does that make sense?
I have dataset with 10.000 observations from 100 countries and a variable problem_measure that measures the degree to which something is a problem.
The variable <...
3
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0answers
94 views
+100
Estimating $f(\mathbb{E}[X])$ with a guaranteed error performance
Given "black-box" sample access to a random variable $X$**, are there results that give an algorithm that approximates $f(\mathbb{E}[X])$ with a user-specified error bound, ideally using as ...
1
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0answers
5 views
Are consecutive zeros across multiple dimensions in multivariate time series a problem when estimating VARMA models?
I want to estimate a VARMA model for a 14-dimensional multivariate time series (Fig. 1, 2). The goal is to investigate how the trajectory of my alleged output time series (messages per hour; Fig. 1, ...
0
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1answer
38 views
Issues Manually Implementing ARMA GARCH
I have been working on manually implementing an ARMA GARCH (1,1) model but have been running into a few issues, namely a very large forecasted variance. I am hoping by outlining my process someone can ...
0
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2answers
47 views
Approach to maximum likelihood in logistic model
My question is very easy and probably banal, but I can't understand this concept and I found nothing on internet.
Consider a logistic/logit model, for example with 3 covariates. We want to test the ...
0
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0answers
4 views
R: Estimation using nls() in Poisson - INAR(1)
This is a Poisson-INAR(1) that I want to use for my data.
My purpose is to find estimation of rho_{i,t} and lambda_{i,t} using nls().
But I cannot figure how it can works for my model.
Any suggestion ...
0
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0answers
18 views
Pitfalls of maximizing the likelihood
I have some data (y, X) of length N and covariate matrix X has 2 columns. I know my true model is y = 10 + X1 + noise, so my true beta is [1, 0], one covariate is irrelevant. I now want to estimate ...
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0answers
9 views
Coefficients estimation via covarinace matrices in linear regression
In linear regression I know the OLS-estimator $\beta = (X'X)^{-1}X'y $, but if the number of possible regressors $p$ is high, e.g. higher than the number of observations $N$, this is not a feasible ...
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0answers
13 views
how does arima calculate phi, theta and some more
this is my first question i have ever asked on here, so sorry if its asked somewhere else.
I made a random test dataset containing values: 10,4,8,5,6,4,7,8, and i tried an SARIMA(1,0,1)(1,0,1) and i ...
1
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1answer
50 views
Constraints on GARCH parameters
I have been working on a manual implementation of ARMA GARCH (1,1) with:
$$\sigma_{t}^2 = \omega + \alpha\epsilon_{t-1}^2 + \beta\sigma_{t-1}^2$$
and estimating parameters through MLE. However, my ...
0
votes
1answer
23 views
Where do the error terms come from in ARMA?
I understand ARMA is a linear combination of lagged data points and lagged errors, but I am unclear on its implementation once parameters have been identified. Now suppose I have an ARMA model and ...
0
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2answers
65 views
A riddle about estimating the number of errors in a book
There is a riddle which I heard a while ago and haven't came up with a satisfying approach yet.
Say a book is written by person $A$, two other people, $B$ and $C$ review the text and each of them find ...
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0answers
33 views
Score Function for Sparse Mean Gaussian?
The Sparse Mean Gaussian model can be described by $ X \sim \mathcal{N}(\theta, \sigma^2 I_d)$ where $ \vert\vert\theta\vert\vert_{0} = s$ where $d$ is the dimension of the random variable, and $s$ ...
1
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1answer
58 views
Minibatch Weighted Sampling for estimating log(q_z) for disentangled representation based on ELBO loss in VAE
I'm reading the paper "Isolating Sources of Disentanglement in VAEs" https://arxiv.org/pdf/1802.04942.pdf. Assuming $p(n)$ is a uniform distribution and that we have a model to get $q(z|n)$ ...
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0answers
25 views
Fitting ARMA GARCH
I am interested in fitting an ARMA GARCH model by hand (that is without the use of a package such as rugarch), but am unclear on how the parameters are estimated. I have read that one should use MLE, ...
8
votes
1answer
275 views
What distribution do OLS estimators follow when dependent variable is not normally distributed?
I understand that when $Y$ is normally distributed, then OLS yields the same estimators as maximum likelihood, which implies that the estimators are sufficient and will be approximately normally ...
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0answers
19 views
MMSE estimation from Rayleigh distribution [closed]
Let $X$, $Y_1$, $Y_2$ be independent Gaussian zero-mean, unit-variance random variables, and let $R = \sqrt{Y_1 ^2 + Y_2 ^ 2}$. Determine $E[Y_1 \mid R]$.
I know that $R$ is from the Rayleigh ...
0
votes
1answer
37 views
sum of binomial with normal distribution estimation [closed]
Let
$$Y=X+V$$
where $X$ and $V$ are independent random variables, $V$ is Gaussian with mean zero and
variance unity, and $X$ takes the values $\pm 1$ with equal probability. Show that $X = \tanh(Y)$.
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0answers
11 views
Orthogonality Check in MMSE
We want to estimate non-random parameter $x_0$ based on the following measurements: $\\$
$z_i = x_0 * exp(-t_i) + v_i$ where $t_i$ is a constant, $v_i$ is white noise with zero mean and variance $\...
0
votes
1answer
23 views
Monte Carlo Approximation of a Normalizing Constant [duplicate]
I know that one can approximate expectations of a function with respect to a pdf as such
$$
\mathbb{E}_{p(x)}[\phi(x)] = \int \phi(x) p(x) dx \approx \frac{1}{N}\sum_{i=1}^N \phi(x^{(i)}) \qquad\qquad ...
0
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0answers
10 views
Cramer-Rao Lower Bound for biased sample variance
Given the estimator
$$ \hat{\sigma}^2 = \frac{1}{n}\sum_i (\bar{x} - x_i)^2 $$
where $x_i$ are normally distributed with $\mu = 1$ and $\sigma = 3$,
I simulated 10000 times an estimator and computed ...
0
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0answers
12 views
Estimator of a function that is about the square of the mean and variance
Give some tuples $T=(x_1,y_1$),($x_2,y_2$)...($x_N,y_N$)
$x_i\in[1,c],y_i\in[1,h],x_i,y_i$ both are integers.
$n_i=\sum_{j=1}^{N}{1(y_j=i)}$
$\mu_i=\frac{\sum_{j=1}^{N}{x_j*1(y_j=i)}}{n_i}$
$\sigma_i^...
0
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0answers
39 views
Maximum likelihood ratio test detection of signal + noise where signal is non-random exponential pulse, noise is gaussian
Let n(t) be a one sided Gaussian white noise sequence, independent, unit variance, and discrete:
f(nk) = (sqrt(2/pi)*exp(-nk^2))/2
where nk is the sample value, and we sample at time t = kT.
We ...
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0answers
37 views
Maximum Likelihood estimator and one application for real life
I am studying maximum likelihood estimators (MLE) right now. I am trying to do a little article about how to apply maximum likelihood estimators to one real life problem.
But I see that MLE mostly is ...
0
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0answers
10 views
minimum distance estimation
I need to set up a minimum distance estimator for the uniform distribution $U[0,\theta]$ and take the $\mathcal{X}^{2}$ statistic as distance
https://en.wikipedia.org/wiki/Minimum-distance_estimation
$...
1
vote
1answer
55 views
Modern statistics (with a focus on hypothesis testing) textbooks balanced in terms of rigor and the applied aspect
I work as a data scientist at a product-oriented company. I guess I will not surprise anyone on this website that it's getting more and more popular for companies with enough data and resources to ...
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0answers
15 views
Dummy variables and chow test: which model to chose
I have this model:
Yi=Beta0+Beta1X1+Beta2Di+Beta3(Di*Xi)+Ei
(where Di is Dummy)
Now, with the Chow Test I want to understand if it is desirable do estimate two ...
0
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0answers
6 views
estimating transformation of linear function non-parametrically
Suppose I have a regression model as follows
$$Y_i = f(X_i + \varepsilon_i), $$
where $\varepsilon_i$ is standard normally distributed. I want to estimate function $f(\cdot)$ non parmetrically. I ...
1
vote
1answer
31 views
Is it harder to estimate the variance of a Gaussian compared to its mean?
In various ML talks I keep hearing that variance estimation is harder than mean estimation but I never really get why the above statement is correct. Is there a theoretical argument or a published ...
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0answers
31 views
Homework Problem Consistancy of Estimator
We have to show:
Let $\theta_0$ be a k-dim vector. Show, that the following statements are equivalent:
(1) $\hat{\theta}_n$ is consistent for $\theta_0$.
(2) For each component $i= 1,...,k$: $\hat{\...
9
votes
1answer
165 views
Why do we multiply log likelihood times -2 when conducting MLE?
When we are performing maximum likelihood estimation (MLE) to estimate parameters, the fit function is often to -2 * LL, rather than just LL. I also see this "-2LL" term expressed as "...
0
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0answers
9 views
Should there be a transpose in calculating the parameters of SVM
I am trying to code SVM from scratch using a small toy problem that involves five support vector values. In the code below, there are 5 support vectors arbitrary chosen and denoted by the variables <...
0
votes
1answer
22 views
Link between Maximum Likelihood and Maximum Probability [duplicate]
How can I see that the maximum likelihood approach finds the parameter values of the probability distribution that maximize the probability of the observed sample?
Maximum likelihood is not the ...
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0answers
12 views
Confusion about Maximum likelihood estimation [duplicate]
How can I see that the maximum likelihood approach finds the parameter values of the probability distribution that maximize the probability of the observed sample?
Maximum likelihood is not the ...
0
votes
0answers
21 views
Point estimation of parameters
Let $\theta$ be a parameter with values in $\Theta$ that should be estimated by some given data $X$.
The corresponding estimate is denoted as $\hat\theta = \hat\theta(X)$.
Several times I read that ...
1
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0answers
23 views
What-If Scenario Regression Modelling
I'm pondering a scenario involving some insurance data but this could be relevant in many fields. The idea is that I have a total count of some event. Let's imagine this count is the # of attorney ...
0
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1answer
14 views
Non-adversarial robustness
One measure of an estimator's robustness is the breakdown point, which tells us how many adversarial observations are necessary to make the estimator useless.
However, is there a notion of non-...
0
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0answers
4 views
Creating Proxy variable to minimise estimation error
As part of my econometrics project, I am investigating wage structures for female workers. The econometric model I am using follows the Mincer earnings function. The dataset available includes ...
1
vote
1answer
25 views
Non linear regression on 2D features space using SVR failed
I try to estimate the execution time of some application based on the mCPUs (fraction of physical CPU) used for the run and the overall size of input data that the application is processing.
The data ...
1
vote
1answer
50 views
Did I correctly apply the factorisation theorem in this example?
Suppose that we have a density $f(x,\theta)=c(\theta)\psi(x)\unicode{x1D7D9}(x \in]\theta,\theta+1[)$ and the random variable $\mathbf{X}=(X_1,\ldots,X_n)$ are independently identically distributed ...
7
votes
2answers
110 views
variance estimation using order statistics
I have four largest samples drawn from a distribution of N i.i.d Gaussian R.V. with standard deviation (Sigma) where sigma is unknown. N is known to be between 50-200. Mean is given to be 0.
How do ...
