Questions tagged [estimation]

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Parameter estimation for basis function model in Elements of Statistical Learning (ESL)

In the book Elements of Statistical Learning, section 2.8.3 describes Basis Functions, citing an example of a radial basis function as $f_{\theta}(x) = \sum_{m=1}^M \beta_M \sigma(\alpha_m'x + b_m)$, ...
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Estimating Joint Probabilities from Marginal Probabilities

Given 2 categorical variables and their marginal probabilities of variable C. What is a good simple way of estimating the joint probabilities? Let C be a Boolean T/F survey variable. For example: ...
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what metrics to use to estimate accuracy of range prediction?

I trained a model that predicts customer's income given the features: age, declared income , overdue total amount active credit limit, total credit limit Metrics used: NIRDM - not in range distance ...
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VAR($p$) estimation

I am bit stumped by this result. Source: Remark on page 46 of Multivariate Time Series Analysis by Rsay. ... one can obtain the GLS estimate of a VAR($p$) model equation by equation. That is, one can ...
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Monte Carlo standard error for a sum

Suppose that I want to compute $E[X+Y]$ using Monte Carlo simulation and compute the standard error. (Note: $X,Y$ are not necessarily independent) The standard way to do this is to Consider the ...
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relationship between the confusion matrix of a detector and the variance of an estimator

Say I have a detector with a confusion matrix. Also, I am interested in the estimation of the number of the detected cases $(\hat{N})$ rather than in the parameters given by the confusion matrix. For ...
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29 views

Question about estimating the standard error of the regression- notation and intuition

in a standard linear regression frame work: $y_{i}=\beta x_i + \epsilon_i$ when calculating standard errors, we find an unbiased and consistent estimator of $var(\hat{\beta})$. Assume spherical errors....
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While simulating the value of a double integral , why do we need to draw different samples everytime?

Suppose I want to simulate the value of the integral $\int_{0}^{1} \int_{2}^{3} 2xy \ dx dy$ using Monte Carlo methods. So, now, I draw a random sample from $U_1,U_2,...,U_n$ from $U(0,1)$ and for ...
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Asymptotic distribution after replacing quantities by consisent estimators

Suppose that we wish to estimate $T(\theta_1,\theta_2)$, a continuous function of several parameters. Suppose that we know the asymptotic distribution when $\theta_1$ is replaced by an estimator $\hat{...
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SEM: can GLS estimation be used under severe nonnormality?

In Randall E. Schumacher's and Richard E. Lomax's book "Beginer guide to SEM", the writers keep saying that if non-normality is sensed, where you can't use ML, you can go for GLS/ADF/WLS. ...
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In SEM, what is the difference between ADF and WLS estimation methods?

In some books both WLS and ADF are considered different methods. In other books, they acknowledge that ADF = WLS, so they are used interchangeably throughout the book. How solve this confusion?
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How to estimate population statistics for each category?

I have data from a simple random sample having n elements which I’m using as an unbiased estimate for my population statistics (mean). My population can be divided into k categories, and I know the ...
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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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Estimating population mean and standard error

I have data about the average monthly money spent by students at a school. The survey was conducted in several classes and the following results were obtained. a) Suppose that in the school there are ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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
72 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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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
29 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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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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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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54 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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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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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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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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18 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
70 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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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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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
23 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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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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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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34 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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77 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
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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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25 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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