Questions tagged [estimation]
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2,498
questions
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6 views
Formulae to Convert between z Critical Value and Confidence Level [duplicate]
What are the two formulae to convert between the two?
For example, I have a z critical value of 3.00. With what formula can you convert this to ...
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7 views
What's the meaning of estimator standardization?
Just to give some context:
Two different types of alloy (named here A and B) are used to
manufacture experimental specimens of a small tension link to be used
in a certain engineering ...
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0answers
8 views
Posterior of risk ratio as ratio of samples from posteriors of risks
I want to sample from the posterior distribution of a risk ratio. My idea is:
define the posterior of risks $R_A$ and $R_B$) for two subgroups (e.g, exposed and non-exposed) in my data, using Beta(1....
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0answers
5 views
In SPSS, how to obtain a single prediction of the dependent variable for each fixed factor, rather than for each random factor combination?
I have a number of thing-types X and for each type want to obtain a single estimate of its true value Y.
When I have measured the same thing-type several times in the same session and several times ...
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1answer
32 views
Parameter Estimation via MCMC
In general, we use MCMC method to sample from a distribution which is hard to compute. In Bayesian setting, we sample from the posterior distribution of the random parameters defining the underlying ...
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39 views
Finding Average Wait Time From Number of People Waiting
Problem:
We are trying to estimate the average wait time for a process. Only data we have is how many people are in the system at a given time, how many have entered this period, how many exited this ...
1
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1answer
17 views
MAP, MLE and parametrised data
It is often said that maximum likelihood is used to obtain estimates of distrubtion's parameters. However, what is unclear is whether it will produce consistent estimate parameters other than those of ...
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0answers
12 views
constract a 95% confidence interval and deter mine lower and upper limit [closed]
suppose for the entertainment indusrty as a whole it is known that the variance of wages for full time employees are birr 1764 per hour a random sample of 196 employees frm entertainment industry ...
1
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1answer
58 views
Classification vs. Prediction
Recently there has been much discussion of the distinction between classification and prediction.
The main claim as I understand it is that prediction must be a probability - specifically $E[Y|X=x]$, ...
1
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1answer
24 views
Standard deviation in Direct-Sampling
In a computational physics course, I was asked to do direct-sampling for the numerical value of $\pi$
and then I estimated the standard deviation of $\pi$ , ...
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0answers
12 views
Statistical method for estimation of Penetrance
I was thinking on a problem: there is a rare disease, associated with some ultra-rare genomic variant (which means ~ 1 out of millions), and there are estimations of penetrance (how many individuals ...
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15 views
GARCH mean parameter estimation in R (rugarch)
I cannot seem to figure out how rugarch calculates the parameter $\mu$ when fitting a specific model
For example:
...
3
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0answers
27 views
AIC and model selection with multimodel
For a simple example, I am doing a multi-model regression/likelihood estimation.
The data is $(y_1,y_2,x_1,x_2,x_3,x_4,x_5)$. The first model (A) consists with two regressions:
$y_1=e^{a_1x_1}+e^{...
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0answers
18 views
why the sigma(volatility) is so small when useing the maximum likelihood estimation for vasicek model
This is my monthly data(in percentile)-2year japan government bond's yield to marturity from year 2001 to year 2019.And my LL function comes from "Maximum likelihood estimation using price data of the ...
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0answers
13 views
How are SARIMA models (which are non-linear in coefficients) generally estimated?
Very simple question but couldn't find answer to this online.
Taking $(1,0,0)(1,0,0)_{12}$ as an example,
$$(1-\Phi B^{12})(1-\phi B)Y_t=\epsilon_t$$
$$\implies Y_t=\phi Y_{t-1} + \Phi Y_{t-12} - \...
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1answer
18 views
Multiple regression when the dependant variable is unmeasured or hidden
Say I was measuring the individual performance of each of a group of athletes every week. I measure things like running speed, jumping height, grip strength etc.
I want to use these scores with ...
2
votes
1answer
62 views
Convergence of kernel density estimate as the sample size grows
Let $X\sim\text{Normal}(0,1)$ and let $f_X$ be its probability density function. I conducted some numerical experiments in the software Mathematica to estimate $f_X$ via a kernel method. Let $\hat{f}...
0
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1answer
40 views
Constrained MLE
How to write R-code for obtaining MLEs of a ,b and $\theta$ for the density function
\begin{equation}
f(x)=\theta(a+bx)e^{-(ax+\frac{1}{2} b x^2)}\left(1-e^{-(ax+\frac{1}{2} b x^2)}\right)^{\theta-1}
\...
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0answers
29 views
how can I get the P-value for each parameter in vasicek model then do the simulation in Excel? [duplicate]
I use the solver in Excel to estimate the parameter, the out put is b=0.001153,a=0.095516,sigma=0.0013. I follow the steps at https://www.youtube.com/watch?v=X17cpkkwG_4
The method is the Maximium ...
2
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0answers
14 views
Can measuring a linear combination of signals improve SNR?
The system is described as follows:
$y= max(M x + n,0),\quad n|x \sim N(0,\sigma _0^2+\alpha M x)$
With parameters:
$ x\in \mathbb{R}_{q\times1}^+ ,\quad \mathbb{E}[x_i]\approx\sigma_0, \quad M\in[...
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29 views
Why one of my estimated paramater (sigma) of vasicek model is so large in R?
I use the yield to maturity of 2year, 3year, 5year, 7year japan government bond from 1989-2019 as my data (i.e.,the name of my data is vasicdata), they are all daily data, and each year contains 261 ...
4
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0answers
30 views
Is it possible to show that this estimator has minimum variance?
Doing some exercises I stumbled upon this tricky one:
Suppose we have an independent random sample $(X_1, ... , X_n)$ with $X_i \sim Poisson(\lambda)$. Define $\theta = e^{-\lambda}$.
Let $$ \...
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0answers
20 views
Variance estimator that is optimal under absolute loss
Given a random i.i.d. sample from a population with a finite variance $\sigma^2<\infty$, what estimator of $\sigma^2$ is optimal under absolute loss?
$$
\arg\min_{\hat\sigma^{2}\in F}\mathbb{E}(|\...
2
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2answers
40 views
Maximum Likelihood Estimator with exponential noise
So I need a little help with this please. I'm given N measurements of a signal $Y_{i} = A + v_{i}, i = 1,...,N$, where $v_{i}$ is measurement noise with the exponential pdf $f_{v}(v) = e^{-v}, v \geq ...
0
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2answers
47 views
How are $n$ and $Var(\varepsilon)$ affecting to Variance of Estimation of Slope Parameter $\beta_1$ in Simple Linear Regression
Once I have derived the variance of $\hat{\beta_1}$ as:
$\text{Var}(\hat{\beta_1})= \frac{\sigma^2}{\sum(x_i-\overline{x})^2}$
I would like to know how are affecting to this formula:
the size of ...
1
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0answers
26 views
More efficient estimator in this situation?
I am thinking about the following situation (it is an example):
There are N families in a city and we have a simple random sample of size n. In that sample we know that there are $x_{0}$ families with ...
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0answers
27 views
Why do some people say that an asymptotically unbiased estimator “satisfies a strong law of large numbers”?
If $x\in\mathbb R$, an estimator for $x$ is an integrable random variable $X$. We say that $X$ is unbiased if $\operatorname{Bias}(x,X):=x-\operatorname E[X]=0$.
Now, in the context of Markov chain ...
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0answers
40 views
Who performed the first Maximum Likelihood Estimation?
I am very interested in the historical development of statistical theories. Here is the research I've done: I've tried to read two old papers of Fisher. I think the first theory paper on MLE should be ...
18
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5answers
1k views
What regression/estimation is not a MLE?
I just rigorously learned that OLS is a special case of MLE. It surprises me because the popular and "reliable" sources such as researchgate and this do not mention this most important connection ...
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0answers
9 views
Simple worked-out example to compute mutual information between two random variables that are vectors
Here is a simple worked out example to compute MI between two random variables $X,Y\in \mathbb{R}$. This also does a good job.
Suppose now i am dealing with two random vectors $P\in \mathbb{R}^3,\ Q\...
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1answer
41 views
Optimality of Bayesian filtering
In Kalman filter, we can show it's a minimum variance filter, which I believe is due to the linearity of system and the Gaussianity of noise. It comes to me that what is the optimality criterion used ...
1
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2answers
77 views
Estimation of multiple regression model with cross-product terms [closed]
I am studying statistics and I stumbled on the following question. If we have the following model: Y = b0 + b1X1 + b2X2 + b3X3 + b4X1X2 + e with X3=X1-X2, which of the parameters can be estimated and ...
1
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1answer
30 views
Estimating a distribution from sums of samples
I'm trying to figure out the parameters of a distribution from real data, but I only get their sums and counts. For either exponential or normal distributions.
So, I'll get the sum of 27 samples, ...
1
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0answers
7 views
Estimation of population quantile based on mutually exclusive sub-populations?
I have read somewhere that "it's obvious" that the estimator $\hat{q}\%$ where $q\%$ is the q-quantile% of a $X_i iid \tilde{ } Dn$ for some distribution $Dn$ for $...
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0answers
12 views
Count distinct from a bootstrapped sample
I have a dataset of N items, with attribute V which can be repetitive, for example:
...
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0answers
13 views
Checking unbiasedness of an estimator
After finding the method of moments estimator, how do we check for unbiasedness?
For an exponential distribution, I found the method of moments estimator as (theta + 1), the book concluded that ...
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0answers
21 views
Combining estimated model distribution
I estimate separately a univariate model distribution $f_d(x;\widehat{\mu_{d}},\widehat{\sigma_{d}^{2}})$ with data of $d$ day. I have 5 models according with the 5 days of week. The behavior of ...
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0answers
12 views
Using expectation maximization for robust regression
What are the advantages/disadvantages of using EM for robust estimation vs. the robust estimation with Huber or Tukey loss functions?
1
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1answer
29 views
How to identify one-one correspondance in Sufficient Statistics?
The correct answer to the given question is (1),(3) and (4). I understood how 3 and 4 are correct but I could not understand how (1) is also a correct answer.
I know that here $\sum_i X_i$ is a ...
2
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0answers
51 views
Different loss functions for estimation and cross-validation
Assume that the goal is to estimate some parameter $\theta$ (finite or infinite dimensional) based on some data available. Also, assume that there are other nuisance parameters are present in the ...
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0answers
31 views
Efficient online (rolling window) estimation of a GARCH model
I have a time series $x_t$ of length $n$. I would like to model it using rolling window approach with window length (width) $w$:
window $1$: $x_1,\dots,x_w$,
window $2$: $x_2,\dots,x_{w+1}$,
$\dots$,
...
0
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0answers
16 views
Fisher Information with respect to the Standard deviation of Normal distribution
Let $X\sim\mathcal{N}(0,\sigma^2)$ be given. I computed the Fisher Information to be $I(\sigma)=\frac{2}{\sigma^2}$. Note that the Fisher Information for the variance is given by $I(\sigma^2)=\frac{1}{...
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0answers
8 views
Confusion on when you can apply CRLB
I am somewhat confused on when you can apply CRLB when estimating parameters which are not of densities directly.
For example a classic problem is estimating the magnitude, phase and frequency of a ...
0
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1answer
20 views
Non Gaussian QMLE for GARCH(1,1)
What is the difference between QMLE and MLE method to estimate GARCH parameter? Because both maximizes the same log likelihood (?)
I tried to estimate the GARCH(1,1) parameter by using quasi maximum ...
0
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1answer
32 views
MLE $\hat{h(\mu)} = h(\hat{\mu})$ of $h(\mu) = var(Y_1) = \mu^2$
Question: Suppose Y1, · · · , Yn follows an Exponential distribution with $\lambda = \frac{1}{\mu}$. Derive the MLE $\hat{h(\mu)} = h(\hat{µ})$ of $h(µ) = var(Y_1) = µ^2$, and show that $h(\mu)$ is ...
0
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1answer
43 views
Standard error of the $n^n$ bootstrap means
I need to show that the standard error of the $n^n$ bootstrap means is $SE^*(\bar{Y^*}) = \frac{S\sqrt{n-1}}{n}$, where $\bar{Y^*}$ is the sample mean of a randomly drawn bootstrap sample, and $S^2 = \...
1
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0answers
20 views
Data scale for regression analysis
I am working on my PhD thesis.i have dependent variable as daily stock return for many firms and independent variable are inflation, exchange rate etc.
My problem is
1-my dependent variable stock ...
0
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0answers
32 views
Expectation of the k-th order statistic of a standard Gaussian sample
Let $(X_1,\dots,X_n)$ be independent random variables with common distribution $\mathcal{N}(0,1)$. The order statistics satisfy $X_{(1)} \leq X_{(2)} \leq \dots \leq X_{(n)}$. I am interested in the ...
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0answers
10 views
How to estimate population size from repetition in random sampling? [duplicate]
I'm periodically sampling values from what's likely a large population. Millions, let's say. And I'm assuming initially that it's random sampling.
However, it's only workable to collect thousands of ...
4
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0answers
33 views
Dynamic panel data model with AR(2) process in the errors
I set up the following dynamic panel data model:
$$y_{it}=\alpha y_{it-1}+x_{it}^T\beta+v_{it}$$
Additionally, I have the process in the errors:
$$v_{it}=\rho_1u_{it-1}+\rho_2u_{it-2}+\epsilon_{it}$$
...
