Questions tagged [estimation]

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The difference between total error, prediction error and fitted error via residual

Consider a regression model $Y=E(Y|X)+Prediction \ Error$ i.e $Prediction \ error = Y-E(Y|X)$. Now, define an estimate of the regression function $E(Y|X)=\hat{Y}+ Fitted \ error$ i.e. Fitted error = $...
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Rationale behind ignoring the "denomintator" in Bayes Rule [duplicate]

In the context of MCMC sampling, we often say that the posterior distribution is only proportional to the numerator of Bayes Law. We tend to say that the "denominator" (i.e. the normalizing ...
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The Role of Summary Statistics

I am reading about this algorithm called "ABC" (Approximate Bayesian Computation). https://cran.r-project.org/web/packages/abc/vignettes/abcvignette.pdf (page 3) Over here, it makes mention ...
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Bayesian MAP Estimates

Suppose you have a simple linear regression problem (y = bo + b1x) and you decide to use Bayesian Estimation to estimate the value pf bo and b1. Using Bayesian Estimation, you obtain a list of ...
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Please help me to solve my problem... It's urgent [closed]

It's about the probability/estimation section questions. I send the jpg format of the question. In the photo above is the exercise I have to solve. I am in my first year at Statistics and the ...
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20 views

Least square estimation and nonlinear model

Suppoese X is the attribute and Y is the response as random variables. We observe (X,Y) jointly as a bi-variate normal variable, then least square estimation of Y as a regression function ...
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Logistic regression: Determining the effect of a variable when it is only a part of an interaction term [closed]

If you have a logistic regression model forced through the origin with dependent variable Y and predictors A and A:B, how can you determine the effect of B on A? In R, your model would look something ...
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25 views

Interpretation of logistic regression - interaction between predictors

Context: Workbook question for my high-school statistics subject An experiment was conducted where 30 parasitic worms of each sex were poisoned at each of five dosages, and the number of deaths were ...
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1answer
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Seeking a good model for extrapolation

I have two parallel data sets. Set #1 is from the federal government, showing for instance, the following data for 2010 number of food processing firms in county for 2010: 74 total number of employees ...
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1answer
53 views

How does computing the bias of model parameters make sense?

I've been studying statistics recently and was thinking about the fact that computing the expectation of a random variable $E(X)$ only really makes sense if $X$ is a random variable defined over a ...
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Compressed sensing [closed]

I have sensors in a train station which depicts pedestrians in some arbitrary spots. I want to reconstruct the whole state(pedestrian distribution in the station) using compressed sensing. I need some ...
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Is it possibe to find an estimator for variance of interest using least squared estimation in a linear model?

In a linear model, maximum likelihood estimation (MLE) provides estimator for both mean of insterest and variance of interest, but least squared estimation (LSE) just provides estimator for the mean ...
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Likelihood vs quasi-likelihood and restricted likelihood

I understand that the purpose of likelihood is to serve as an estimation mechanism that returns the model parameters which would most likely re-produce the observed data (given some model or ...
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1answer
208 views

Coming up with a better estimator for this quantity

I have data from the following generative process: $$ Z \sim F(z)\\ p = g(Z)\\ X \sim \text{Bernoulli}(p) $$ Where $F(z)$ is an unknown distribution on $[-10^5, 10^5] \cap \mathbb{Z}$, and $g$ is an ...
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1answer
25 views

Multiple linear regression: true effect and variable specific variation

I intend to simulate a population with a single outcome variable and multiple explanatory variables, some of which do have a true effect on the outcome variable and some of which do not. The idea is ...
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Sample size calculation when using estimation statistics?

Estimation statistics has been proposed as an alternative to traditional hypothesis testing in numerous fields in biomedical science using frequentist statistics and estimation has also been ...
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Pivoting a discrete cdf? A method for interval estimation

I am studying the following theorem from "Inferential Statistic" by Casella. With reference to the picture below, there were some mistakes in the proof, which I corrected using a pencil : ...
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Estimator for a particular statistic involving Order Statistic

Let$ X_{1}, X_{2}, \cdots, X_{n} $ be a random sample from a continuous life distribution $ F $ be with survival function $ \bar{F},$ density $ f $ and finite mean $ \mu. $ While doing some ...
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1answer
29 views

Dividing data set based on the Dependent Variable, for interpretation of the coefficients

I have a data set that has as DV the preference of spatial reproduced audio files (OLE) and as IVs the preference of only their content and the sensation of envelopment. All the variables are ...
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How to analyse effect of the combination of two ordinal variables on an interval variable?

So, I got a data set of scientific journals and I want to find out if "interdisciplinary" journals (so that journals have a good relative reputation specifically in economics and history) ...
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Problem Implementing MLE Estimation in bbmle Package (for R) [migrated]

I am trying to verify the MLEs obtained for $\alpha$, $\beta$ and $\lambda$ for the Logistic-Lomax distribution in the paper entitled A Study of Logistic-Lomax Distribution by Zubair et al when using ...
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Estimate KL divergence between an unknown distribution and a known one

I am looking for a method to estimate KL divergence between a set of samples (presumably obtained from a continuous distribution) and a known, explicit distribution. I could find some algorithms for ...
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1answer
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Better understanding Maximum Likelihood parameter estimation

Suppose I am trying to model the dependence of a variable $B$ on another variable $A$ by a function $B=f(A;k)$, where $k$ is a parameter, whose value I would like to estimate. Given $n$ observations $\...
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Estimating conditional probability when events are sampled

Suppose I have many people who eat different fruits (apples, oranges, bananas &c): ...
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1answer
30 views

estimate multivariate normal parameters

Suppose that I have "a realization" of random vector $x=(x_1,\cdots,x_N)$ where $N$ is sufficiently large $N>100$. I know that random vector is joint normally distributed $$x \sim N(\mu,\...
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Why use naive bayes instead of computing probability directly [duplicate]

Situation: In the exam question found below, we are tasked with using the naive bayes assumption to find: $$P[K = 1 | a = 1 \land b = 1 \land c = 0]$$ Problem: Although I could solve the exercise, I ...
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Estimate the Image Using Multi Many Realizations of Its Convolution with a Known Filters Using Wiener Filter

Suppose we have a corrupted image $Y = H*X + \epsilon$ that is formed by taking an image $X$, convolving it with a point-spread function $H$, and adding gaussian noise $\epsilon$. Then we know that ...
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Estimating Joint Probability of non-i.i.d., dependent, Bernouli trials

A joint probability space of $n$ bernouli trials has $2^n$ parameters (one probability for each configuration of T/F). I want to estimate the distribution using a subset of the necessary knowns. ...
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6 views

Generate a misspecified covariance matrix depending on a relative error measure

I am not sure if this question belongs to stackoverflow or here, but I think it is more statistics related. I want to do a simulation study where I want to investigate the robustness of a certain ...
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Estimating rate of convergence from MSE

Given that I have calculated values for the MSE for differing values of $n$ and the estimator $\hat{\theta}$. Is it possible to calculate the rate of convergence, $O_p(n^{-r})$, of this estimator by ...
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2answers
54 views

Confidence Interval - Revisit [duplicate]

I've read in many articles about Confidence Interval as below One such article link: https://www.statisticssolutions.com/misconceptions-about-confidence-intervals/ [FALSE] - There is a 95% chance ...
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1answer
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Is there a way to use partial information about the distribution to estimate better?

I learned college statistics but only at the undergraduate level. I feel like it's hard to apply what I learned to real-life situations, unlike self-contained problem sets. Here's what I'm trying to ...
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Expectation of next value conditioned on previous sample

I've been studying for my estimation class, and I can't wrap my head around the lecturers notes. The question is about empirical bayes credibility models, but my confusion boils down to this: Consider ...
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Joint distribution of estimator and true parameter

Suppose we have probability distributions parameterized by $\theta$, and we have an estimator $\hat{\Theta}$ for $\theta$. Denote a fixed particular value of $\hat{\Theta}$ by the lower-case variable $...
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19 views

Estimation of coefficients of variables x when the sum of the x is equal to y

I'm a new beginner in learning statistics, and I have an issue with the estimation of coefficients. To begin with, let's suppose I have 3 observations and 4 explanatory variables: First observation: y=...
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graphical lasso with known precision matrix structure

I wonder if there is a way to estimate the precision matrix when certain elements are restricted to be zero? Suppose data are from $N(\mu,\Omega)$, where $\Omega=V^{-1}$, i.e. the precision matrix. ...
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Estimate the mean, variance and correlation separately to make off-diagonal elements of covariance matrix "identically distributed"?

I have a $d$-dimensional data with $n$ observations. So the matrix for the dataset is $d\times n$. One possible way to fit the data is to assume that each column is a random sample from a multivariate ...
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1answer
26 views

Estimator of failure by cause j at time t

I am reading Dirk Moore's Applied Survival Analysis Using R page 124. Let $S(t)$ be cumulative survival curve of population facing cause of death due to a set of cause $\{1,2,\dots,n\}$ where $1,2,\...
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Differences between least-squares estimate and weighted least-squares estimate when I focus on only one coefficient in a multiple linear regression?

Suppose we have $n$ samples from the following linear model: $$y=x_1 \beta_1+x_2 \beta_2 + e,$$ where $e_i$ i.i.d. comes from $N(0,\sigma^2)$; $x_1$, $x_2$ are centralized with mean $0$. I am only ...
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How to estimate the variance of correlated observations?

Assume we have n observations $x_i$ (i from 1 to n), each from the a normal distribution with mean 0 and some variance component: $X_i \sim N(0, \sigma^2)$. The random variables $X_i$s have some (let'...
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32 views

number of samples required to estimate mean

I have a dataset consisting of number of times an individual pauses when speaking during a particular recording. I have several recordings per individual (around 10). I ultimately want a measure of ...
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1answer
37 views

What is the importance of non-informative prior in Bayesian Inference? [duplicate]

By the name, noninformative prior, the prior distribution doesn't contain any information about the parameter. Then why we use this thing to estimate the parameter by the Bayesian approach?
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Posterior distribution shape for Gaussian Likelihood and non-linear model

I have an easy question I can't seem to find the answer to. I'm trying to fit some data to a non-linear model: $$d_{L}\left(x; H_0, \Omega_{m}, w\right)=\dfrac{c}{H_0}(1+x) \int_{o}^{x} \frac{\mathrm{...
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1answer
44 views

Is the Hodges-Lehmann estimator 'optimal' for estimating the location parameter of Logistic distribution?

Is the Hodges-Lehmann estimator $\hat\theta_{HL}=\operatorname{median}\limits_{1\le i\le j\le n}\left\{\frac{X_i+X_j}{2}\right\}$ in some sense 'optimal' for estimating the location parameter $\theta$ ...
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1answer
60 views

Bayesian and Markovian Networks: How do we obtain the probabilities at each node in a Bayesian or Markovian network

I just have a very basic 2 part question about Bayesian and Markovian networks. I suppose my confusion stems by trying to learn about these things through blog posts and videos, and not being able to ...
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1answer
66 views

Posterior calculation on binomial distribution using quadratic loss function

Que Let x be a binomial variate with parameters n and p (0<p<1). using a quadratic error loss function and a priori distribution of p as $ \pi(p) $ = 1, obtain the bayes' estimate for p. Hey ...
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3answers
52 views

Unbaised estimator of $\ e^{- 2 \lambda } $ is t(x) = $ \ (-1)^x $

Prove that Unbaised estimator of $\ e^{- 2 \lambda } $ is t(x) = $ \ (-1)^x $ , when x follows poisson distribution with parameter $\lambda $ Sorry to ask the direct question but I need a starting ...
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1answer
24 views

Infectious Outbreak and the Foundation of Epidemiology

There was an infectious outbreak that was responsible for the foundation of epidemiology, it was the cholera outbreak that affected London between 1846 and 1860, which, in order to be resolved, ...
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29 views

MCMC not constraining parameters correctly [closed]

I have to fit a model to some data and I was wondering how to interpret the results I get from the Bayesian parameter inference performed using emcee. Model #1 has 3 parameters: $h_0,\Omega_m,\Omega_{\...
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1answer
34 views

Finding the finite correction factor for the margin of error

I have the following question in exercise 5.3.21 in Mathematical Statistics and Application by Hogg, that asks to redefine the Margin of error equation to cover the case where a finite correction ...

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