Questions tagged [estimation]

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47 views

How can i find bias of estimator for specific value?

I have $X_1,...,X_n~ Ber(p)$ with MLE estimator $\hat p$ which is equal to sample mean. I need to find bias of estimator $\hat p(1 - \hat p)$ for $p(1-p)$. I presume $p(1-p)$ is variance of my RVs, so ...
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41 views

What test to use for threshold

I've got a problem where, with my basic knowlegde of statistical tests, I'm not sure how to solve it. I have a dataset with data on the execution of a process. This includes: Time the process lasted ...
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48 views

How to calculate confirmatory factor analysis by hand?

I am trying to learn how confirmatory factor analysis works and the way I learn is best by understanding how the calculations work by hand using a pen, paper, and a calculator, and then replicate this ...
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36 views

Empirical estimation of conditional distribution $Y|X$ at the boundaries of X

I want to estimate conditional distributions of Y | X. Where X contains several continuous covariates. I'm coding in R. I tried several methods so far, but none gives me entirely satisfactory results ...
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28 views

How to solve a negative binomial regression?

From this https://content.wolfram.com/uploads/sites/19/2013/04/Zwilling.pdf : But I don't know how to solve it . I know let the derivative of the function L with respect to $\alpha$ and $\beta$ equal ...
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9 views

Runtime Estimation for Multi-threaded processes with varying loads

This is much more of a computer-related question but I believe this requires statistical knowledge (which I'm not well versed and currently reading on the basics) so i hope you can bear with me. I ...
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2answers
268 views

Regression and the CEF

I recently read in this page (https://www.timlrx.com/2018/02/26/notes-on-regression-approximation-of-the-conditional-expectation-function/#fn1) that: "Regression offers a way of approximating ...
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0answers
13 views

moderate size of the data sample [closed]

It is often that the authors of papers in AI, ML and Statistics write that their methods are proved to perform good for "moderate sample sizes". I saw this statement in very high ranking ...
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22 views

Calculating measurement variance to achieve desired accuracy in estimation

The variables of interest are related by the following multivariate normal distribution: $$\begin{bmatrix} x \\ z_1 \\ z_2\end{bmatrix} \sim \mathcal{N}(\begin{bmatrix} \mu \\ \mu \\ \mu\end{bmatrix}, ...
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1answer
31 views

LMM parameter estimation results differ when compared to OLS estimation

I am using lmer for estimating effect sizes and I am comparing the results with estimations obtained through OLS. I first ran the LMM model with simulated data where the effect sizes are known and I ...
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1answer
38 views

A Question About Cost Estimation With Neural Networks? [closed]

First of all, I just entered the topic of artificial neural networks, I'm sorry if my question sounds ridiculous. I want to estimate social return to education for Argentina using neural networks. But ...
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22 views

how to solve a complex function

My aim is to solve $$-N (\beta \mu )^{\frac{1}{\beta +1}} s^{-\frac{1}{\beta +1}}-\frac{(\beta +2) N}{2 (\beta +1) s}+t=0$$ The above equation is related to $s$ and the other parameters are constants....
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1answer
27 views

PERT pessimistic formula and standard deviation

I've just read the book "Software Estimation" written by Steve McConnell. I have very little knowledge in statistics. The well known PERT formula to estimate the time of a task is: ...
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79 views

Bayesian Regression with ARIMA errors

Is there a framework (e.g. R package) which allows for Bayesian estimation of dynamic regression models with AR(I)MA errors (similar to the frequentist implementation in the ...
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10 views

Truncation in JAGS: limiting the range of other, linked parameters through an error term?

I am trying to estimate model parameters using JAGS. There is an error term err[i] that describes the error of the model fit to the real data.I would like to ...
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1answer
106 views

LOOCV vs. k-fold CV leads to the same results

I build a linear regression model and use it to predict out-of-sample. In this context, I use LOOCV and k-fold CV (5). However, both methods seem to lead to the same results. The only minor difference ...
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19 views

SIR Estimation Finding Cause of Error While Estimating Parameters With Python

Hello I had a question on stackoverflow and one user redirected me to here as this question is more related with statistics. I'm trying to fit SIR Epidemics Spread Model to the current new case data ...
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1answer
34 views

What is the distinction between bias in prediction and parameter estimation?

I am trying to understand the distinction between bias in prediction and parameter estimation. This example in Gelman, Bayesian Data Analysis, 2nd ed. 2004 pp. 255-256 is very confusing to me. Why do ...
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16 views

Self Study: R Lasso Implementation Error

I am trying to implement a the Lasso Estimator in R using the coordiate descent algorithm. A reference to the algorithm can be found here (page 460). Here is my implementation: ...
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0answers
18 views

Notation in “Fast Computation of Multivariate Kernel Estimators” by M. P. Wand

I'm new to kernel estimation methods and I've reading the paper "Fast Computation of Multivariate Kernel Estimators" by M. P. Wand. Particulary on page 434, it says "Let $(X_1, Y_1), ......
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1answer
260 views

autoregressive time series estimation with OLS vs Yule-Walker

$AR(p)\text{: }X_t = \beta_0 + \sum_{i=1}^p \beta_i X_{t-i} + \epsilon_t$ It’s autoregression, so some kind of regression. I can write it in a data frame like I would any other regression. We assume (...
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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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78 views

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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0answers
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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0answers
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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64 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
93 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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0answers
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
40 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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0answers
403 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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0answers
97 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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32 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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0answers
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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0answers
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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0answers
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 ...
4
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1answer
68 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
234 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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0answers
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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0answers
91 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
48 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
25 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
39 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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0answers
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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