Questions tagged [estimation]

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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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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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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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 <...
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+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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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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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 $s$ ...
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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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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, ...
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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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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 ...
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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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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 $\...
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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 ...
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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 ...
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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^...
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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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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 ...
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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 $...
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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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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 ...
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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 ...
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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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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{\...
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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 "...
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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 <...
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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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 ...

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