Questions tagged [estimation]

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15 views

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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9 views

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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28 views

How to interpret this kernel regression results?

I tried to do some kernel estimate of second order derivative. In my experiment, $y_i=z_{1i}+z_{1i}z_{2i}^3+e_i$, where $E(y_i|z_{1i},z_{2i})=z_{1i}+z_{1i}z_{2i}^3$. I'm interested in estimating $\...
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29 views

Bayesian estimator not converging

I am trying to run a simple experiment using python. I have a binomial distribution (n = 100, p = 0.6). I am trying to estimate the proportion p of this binom distribution using a Beta(1, 1) as a ...
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21 views

How to compare two estimates?

I have determined the volume of multiple objects via two different methods. I would like to express, per object, something like the percent error: $\delta = \frac{|V - V_{approx}|}{V} \cdot 100$ ...
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66 views

Saddle point method used to calculate the inverse Fourier transform

Here I want to find the asymptotic behavior of the following integral $$f(x,t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\exp(-ikx)*\exp(t(1-\exp(-|k|^\beta)))dk,~~~~~~~Eq~1$$ where $x$ goes to infinity. ...
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1answer
99 views

ARMA(p,q) estimation

In some statistical notes, it is written that it is possible to estimate ARMA(p,q) from the two-step regression, i.e. first is to fit AR and estimate the errors and then to use these errors in the ...
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1answer
29 views

Why do the mean and proportion measurements take the spotlight in estimation?

Based on information I have read and from this website, sampling distributions do exist for statistic variants of measurements other than the mean. Sample ranges, maxima, minima, variance and ...
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16 views

When is mutual information difficult or easy to estimate compared to correlation?

I came across the following statement about covariance/correlation vs mutual information, Covariance can be calculated directly from a data sample without the need to actually know the probability ...
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1answer
27 views

Does entropy have less estimation error than mean and variance estimates?

Estimating the mean or expected value of a continuous random variable's (r.v.) empirical distribution is known to be difficult, moreso than estimating the variance. Estimates of the mean and variance ...
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2answers
41 views

Estimate Unique Number of Visitors

Is there a way to estimate the number of unique monthly visitors to a site based on a limited sample of one week of data? I have information about when a given user visited the site. This isn't as ...
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455 views

how to interpret the results of a GARCH model fit R/python

I have got the following output from a gjrGARCH model, and I need help to interpret it in order to decide whether it is already a good model and proceed with the forecast. ...
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52 views

Taking Expectation Over Inverse Sum of Indicator Functions?

I'm working with a zero inflated Poisson distribution that has the following pmf: $$f(y|w,\lambda)=wI[y=0]+(1-w)\frac{e^{-\lambda}\lambda^{y}}{y!}$$ I would like to find the expectation of the ...
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98 views

How to estimate the intensity rate $\lambda$ of a Cox Process

In a Cox Process, or doubly stochastic Poisson process, the intensity rate itself is a stochastic process that varies across space or time. Let us assume that the intensity rate has the following form ...
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1answer
14 views

Variance Estimator Change if we know Population Mean? (Normal dist. example)

For a normal distribution $N(\mu, \sigma^2)$ a commonly used unbiased and consistent estimator of variance is $$\hat \sigma^2=\frac{\sum_ix_i^2 + n(\bar x)^2}{n-1}=\frac{\sum_i(x_i-\bar x)^2}{n-1}$$ ...
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33 views

Derivation of maximum likelihood estimation of Gaussian mixture model

I want to derive the following formula. The meaning of each expression is as follows It's easy to solve with Kronecker's delta.
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8 views

Optimize Interval

I am working on modelling a process that follows a normal distribution with the following specifications If the processes output (parts) is too short (< 17.55) ...
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33 views

What is the similarity and difference between signal recovery and parameter estimation?

As per inferential approach both are estimation problem. But, in signal recovery, we estimate our input signal from the measured (noisy or noise free) observations. And, in parameter estimation, we ...
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17 views

Estimate cumulative sum of a population from sample distribution parameters?

I have a sample of data containing entities, and counts. What is being counted doesn't really matter, so let's say it's bananas. Each entity in my sample has x bananas. Now, let's say that I have a ...
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1answer
69 views

How do zeroes impact regression estimates?

Assume I am estimating a simple cross-sectional regression model. What happens if a large portion of the cross sections consists of zeros only? That is, both the dependent and the independent ...
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2answers
282 views

How to find the 95% confidence interval when there is outliers?

I know how to find the 95% confidence interval for normal distributions. But how to find it when there is outliers? Question: The health-care costs, in thousands of dollars for 20 males aged 75 or ...
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10 views

Statistical Analysis over different samples - Prediction for the number of objects

This may be a really simple question but here's my problem: I have different boxes with soil (wet sandy kind) and big stones in it. Each box is around 10kg and I want to estimate the number of big ...
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34 views

Why does the sample mean work as an estimator when we know data is not iid?

Let's say I know that height effects weight. To be more precise, let $H_i$ and $W_i$ be the heights and weights of person $i$ respectively. Let's say the true relationship between these variables is ...
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95 views

linear minimum mean squared error estimate under Gaussian prior

I am learning estimation theory through Steven M.Kay's book Fundamentals Of Statistical Signal Processing--Estimation Theory. In the ...
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1answer
54 views

How to estimate cut off percentiles to classify cost per metric?

I work at an ad agency and one of our key performance metrics is what we call "cost per outcome". Right now I have advertisements grouped by type of advertisement, lets say type "A"...
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1answer
26 views

Interpretation of OLS: Scale dependent variable by independent variable instead of including it in the regression model

How does the interpretation on the coefficient of X in this OLS model: Y(Profit in €) = b0 + b1 X + b2 X2 (Firm Size in €) + e change if I rewrite the model as Y(Profit in €) / X2(Firm Size in €) = b0 ...
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2answers
40 views

Doubt in derivation of expectation of sample variance

I am studying statistics on my own. Please help me in understanding following Here in evaluation of expectation $E[\frac{(n-1)S^2}{\sigma^2}]$, why $\sigma^2$(population variance) is treated as ...
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22 views

Advantages of using panel data structure when estimating causal effects consistently

What are the main advantages of using panel data structure compared to the pure cross-sectional data when we want to estimate causal effect of some phenomenon consistently? I know what the general ...
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2answers
47 views

Estimating pi with a Gaussian darts player

It's well known that if you draw a square of 2x2 units side, and inside you draw a circle with a radius 1, and then randomly throw darts/count raindrops/etc. etc. that fall within the square, you can ...
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29 views

Random coefficients and fixed effects

In a nonlinear model, for each time $t\in\{1,..,T\}$ and product $ j\in \{1,..,J_t\} $ individual $i \in \{1,...,I_{t}\} $ chooses an amount $y_{i,j,t}$ modeled as $ q_{i,j,t} = \frac{1}{\tau_j k_{j,t}...
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14 views

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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1answer
135 views

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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1answer
40 views

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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24 views

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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32 views

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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5 views

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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0answers
19 views

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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68 views

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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1answer
142 views

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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1answer
78 views

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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0answers
19 views

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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214 views

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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45 views

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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1answer
123 views

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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1answer
34 views

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 ...
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29 views

How is the reproductive number R being calculated?

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 ...
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1answer
60 views

Point estimator for product of independent RVs

Let $X$ and $Y$ be two independent random variables. Given an (iid) random sample of size $n$ of $X$ and a random sample of size $n$ of $Y$, what is a good way to estimate the mean of their product, $...
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30 views

ADAM First and Second Moments

I'm trying to understand why ADAM uses the gradient and the gradient squared respectively as estimators the first and second moments. I was assuming that the random variable we were estimating was the ...
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2answers
498 views

Maximum likelihood estimator of $\theta$ for uniform distribution [closed]

I know that , For Uniformly Distributed random variables $X_1,X_2,\dots,X_n$ $\in \mathcal{R}$, the p.d.f is given by: $f(x_i) = 1/θ$ ; if $0≤x_i≤θ$ $f(x) = 0$ ; otherwise If the uniformly distributed ...

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