Questions tagged [estimation]
This tag is too general; please provide a more specific tag. For questions about the properties of specific estimators, use [estimators] tag instead.
2,925
questions
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5 views
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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1answer
21 views
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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23 views
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 ...
2
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1answer
73 views
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 ...
-4
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0answers
39 views
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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0answers
18 views
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
12 views
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 ...
1
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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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13 views
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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0answers
41 views
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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0answers
9 views
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 ...
4
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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 ...
1
vote
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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0answers
16 views
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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0answers
21 views
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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14 views
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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4 views
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) ...
2
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0answers
18 views
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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0answers
16 views
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 ...
2
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1answer
97 views
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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0answers
65 views
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
$$x \sim N(\mu,\...
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18 views
Why use naive bayes instead of computing probability directly [duplicate]
Situation: In the exam question found below, we are tasked with using the naive bayes assumption to find: $$P[K = 1 | a = 1 \land b = 1 \land c = 0]$$
Problem:
Although I could solve the exercise, I ...
1
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1answer
23 views
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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0answers
20 views
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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0answers
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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0answers
9 views
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 ...
1
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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 ...
4
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1answer
62 views
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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29 views
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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0answers
58 views
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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0answers
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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0answers
31 views
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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0answers
27 views
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 ...
0
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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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0answers
48 views
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,$$
where $e_i$ i.i.d. comes from $N(0,\sigma^2)$; $x_1$, $x_2$ are centralized with mean $0$.
I am only ...
9
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2answers
250 views
How to estimate the variance of correlated observations?
Assume we have n observations $x_i$ (i from 1 to n), each from the a normal distribution with mean 0 and some variance component: $X_i \sim N(0, \sigma^2)$. The random variables $X_i$s have some (let'...
1
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0answers
32 views
number of samples required to estimate mean
I have a dataset consisting of number of times an individual pauses when speaking during a particular recording. I have several recordings per individual (around 10). I ultimately want a measure of ...
0
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1answer
37 views
What is the importance of non-informative prior in Bayesian Inference? [duplicate]
By the name, noninformative prior, the prior distribution doesn't contain any information about the parameter. Then why we use this thing to estimate the parameter by the Bayesian approach?
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0answers
14 views
Posterior distribution shape for Gaussian Likelihood and non-linear model
I have an easy question I can't seem to find the answer to. I'm trying to fit some data to a non-linear model:
$$d_{L}\left(x; H_0, \Omega_{m}, w\right)=\dfrac{c}{H_0}(1+x) \int_{o}^{x} \frac{\mathrm{...
0
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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 $\theta$ ...
2
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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 ...
1
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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 ...
1
vote
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, ...
2
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0answers
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_{\...
3
votes
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 ...
