# Questions tagged [estimation]

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### Is the cost function fixed or something to be estimated?

Is the cost function or loss function something you fixed before running the optimization algorithm or something you have to estimate such as in the case of regularized regression?
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### Is a non-parametric density estimation required for a bimodal distribution?

How to approach the following two cases is clear, I am mentioning them to set up my question. (Case 1): For data that appears to be a Gaussian distribution, we can assume the distribution is Gaussian ...
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### How to compare estimators for consistency between in-sample and out-of-sample fits?

What general procedures are out there for quantifying how well an estimator (such as for the mean, standard deviation or correlation) of a continuous random variable gives a consistent picture of its ...
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### Estimate parameters in Matlab (multivariate t distribution)

Is there a built-in function in Matlab that estimates parameters of a multivariate t distribution (scale matrix, degrees of freedom). In other words, I have time series of returns for 10 stocks. ...
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### Closed-form likelihood. Why to use Bayesian parameter estimation instead of maximum likelihood? [duplicate]

Given a model with a closed-form likelihood, what are reasons to use Bayesian parameter estimation instead of maximum likelihood? In other words, what are additional estimation results that you can ...
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### What additional data value would keep perfectly constant the variance of the now larger dataset

Playing with the algebra this is easy to figure out for the mean, but I can't solve it for the variance. Please notice it's not about the properties of the variance with regard to systematic ...
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### How to estimate differences between two normal means when variances are tested to be unequal

Let $X_1 X_2...X_n, Y_1 Y_2...Y_n$ be $\sim N(\mu_x$, $\sigma_x^2$), $\sim N(\mu_y, \sigma_y^2$). I want to estimate ($\mu_x - \mu_y$) and have used F-test to see that $\sigma_x^2$ $\neq$ $\sigma_y^2$ ...
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### What is the conventional way of estimating a population parameter?

I was wondering about the correct way to approach the following question (I am quoting the question as it was originally written): Consider a particle residing at x = 1, y = 1 and the particle begins ...
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### selecting sub-groups on one variable before correlating with another

I am wondering what the potential pitfalls are of the following approach. I want to check whether a neural measure is related to a questionnaire measure. I know that this is rarely the case (...
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### Calculate GINI inequality coefficient from IRS SOI data

I am trying to calculate the GINI coefficient from the IRS SOI dataset using the adjusted gross income (AGI) bins provided in the csv. I know this will not be an exact GINI index score, and only a ...
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### Estimation of MA parameters in ARIMA with MLE

I understand that the AR models can be estimated with both OLS and MLE, since all the values of the time series are known. However, I don't understand how the parameters for the MA parts can be ...
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### Estimation of the second moment and square root of the second moment (not variance and standard deviation)

I want to estimate the second moment of a distribution. I know the breakdown of the second moment into the mean-squared and variance: $\mathbb{E}[X^2] = (\mathbb{E}[X])^2 + var(X)$. When I want to ...
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### True population regression line

I am doing an online course and came across this line- "There is a population regression line that joins the mean of the dependent variables". I was stumped by this because if I took the ...
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### Combination of different estimates of the same quantities?

Suppose we have $n$ number of estimates for a parameter, each derived independently. How will one combine these estimates to get a single estimate which has lower variance than each individual ...
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### Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$

Question: Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$ My attempt has been by modifying the answer from this question: The Poisson distribution is a one-...
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### A practical example where maximum likelihood correctly estimates an underlying parameter, but where least squares would fail?

Forgive my very limited understanding. I am trying to learn about maximum likelihood estimation, and how it differs from least-squares estimation. From reading a little, I understand that the two are ...
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### Multivariate GARCH, DCC(1,1) - Autoregressive order

About my question: it is a mix between the assumptions of the model and the implementation. I implemented a DCC(1,1) model for two retrun series (bivariate correlation), with the autoregressive order: ...
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### Bayesian estimation Prior adaptation [closed]

I have a dataset of 1 dimensional 20points as prior information, so assuming prior distribution to be Gaussian distribution we can easily find its variance and mean. Now we will use this prior finding ...
The reproductive number $R(t)$ quantifies the expected number of secondary infections caused by an infected individual at time $t$. Thus, an R number below 1 will be likely to stop a disease like ...