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.
111 questions from the last 365 days
2
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0
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30
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Marginal empirical distribution from joint sample
I have a quite 'simple' doubt that would like to clear.
Suppose I have a heiarchical model where data is sampled in the following manner:
Sample $U_i$ from $P_U$
Sample $X_i$ from $P_{X|U_i}$
In ...
3
votes
2
answers
48
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Given the total cost of many graph walks, how to estimate the cost of each edge?
I have a real-world problem in which I have a collection of nodes and their edges. This collection is composed of hundreds of nodes and thousands of connections. Then I have about 10 K datapoints each ...
- 133
0
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0
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11
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Variance estimation from dependent data
I would like to estimate the variance of a zero-mean normal distribution, $x_n \sim \mathcal{N}(0, \sigma^2)$, from data of the form $y_n = u_n x_n$ where the input $u_n \in [u_{\min}, u_{\max}]$ can ...
- 1
4
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1
answer
68
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How do machine learning topics fit into a traditional undergraduate statistics course on estimation?
I'm recently teaching an undergraduate introduction to statistics course, but as required by program director, need to add some machine learning materials to it. I'm wondering what is the appropriate ...
- 3,028
0
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0
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13
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Importance sampling with relative weight from two histograms
I have two datasets of real values, $X = (x_1, \dots, x_N)$ and $Y = (y_1, \dots, y_M)$. Here $Y$ is a subset of $X$. These data points can be regarded as samples from some unknown densities, $x\sim p(...
- 4,552
6
votes
1
answer
211
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Calculate the mean and variance of a stochastic process?
I was introduced to the Polya Urn problem in statistics (a problem where we draw a ball from an urn and place another ball back of the same color). These are the formulas for the mean and variance of ...
- 121
2
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0
answers
33
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How Are The Initial Value of Conditional Variance Calculated in rugarch Package?
I am trying to verify the calculations of my zero-mean GARCH(1,1) model using the rugarch library. At first I thought the initial first value of the conditional ...
1
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0
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20
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Time Series Analysis - AR model
I am new to the subject and trying to learn and equip well into the topic. I got a problem to solve and it only contains the model equation - {Generic AR(N) model} modelled using the equation: v[k] + ...
6
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2
answers
574
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Why Gaussian Process Regression (GPR) is non-parametric?
Given that Gaussian Process (GP) regression relies on a kernel with specific hyperparameters that control the relationships and smoothness between points, can GP regression truly be considered a non-...
- 315
0
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0
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23
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False interpretation of 95% confidence interval? [duplicate]
Disclaimer: I come from a science background and recently started a Master's degree in Statistics, so my current statistical knowledge comes from introductory university courses and the occassional ...
0
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0
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17
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A practical way to understand subgaussian parameter
I am currently assuming that the random variable $X$ I am working with is subgaussian with parameter $\sigma^2$. I have simulated data, but I would like to know how to use the generated data to ...
- 113
1
vote
1
answer
43
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Unbiased Variance MLE Distribution
If you take $10000$ samples from a normal distribution, the unbiased variance MLE (with Bessel's correction) is
$$\hat{\sigma}^2 = \frac{1}{9999}\sum_i (x_i - \hat{\mu})$$
Apparently the distribution ...
- 503
0
votes
0
answers
10
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How to find the estimate of the correlation between Beta_1 hat and Beta_3 hat
I am studying multiple linear regression and am working on finding the estimate of the correlation between Beta_1 hat and Beta_3 hat.
Given the regression model y = B_0 + Beta_1x_1 + Beta_2x_2 + ...
1
vote
1
answer
45
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Cross-fitting seems to always reduce asymptotic variance for estimators converging slower than $\sqrt{n}$ - how can this be true?
Setup: Imagine the situation where you for a fixed value of your covariates have a regression estimator $\tilde{f}$ based on $n$ i.i.d. observations which is asymptotically normal with convergence ...
6
votes
1
answer
243
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Variance of MLE's in mixture distribution
I am studying mixture models, and I am interested in calculating the variance of the estimators using maximum likelihood. How is the variance calculated in this case? I already implemented the EM ...
- 281
0
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0
answers
12
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Control the estimation error measured by induced matrix $L_1$ norm
when I use the lasso-type method to estimate a matrix, such as $A$, column by column, I observe that in the numerical experiments the estimation error $\|\hat{A}-A\|_{L_1}=\underset{1\le j \le p}{\max}...
- 209
4
votes
1
answer
78
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Intuition behind the weighting matrix of a GMM estimator
I'm trying to fully understand the GMM estimator. I hope you can clarify my doubts.
Suppose that $y_i$ is described by the following DGP:
\begin{equation}
y_i = x'_{i} \beta + \epsilon_i
\end{equation}...
- 333
1
vote
1
answer
28
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Calculating mean variance between double determined measurement of random variable
I have two sets of data, measuring a varible that changes at random (concentration of a gas). The measurement are double determined, providing two data points for each measurement.
I would like to ...
William
5
votes
2
answers
151
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Estimate probability value is greater than x from an unknown distribution
Lets say that we have a population of N items that has a value from 0 to 6000.
Let's say that the mean of the population is $\mu$.
We do not know the distribution of the items.
We extract a item from ...
- 719
2
votes
1
answer
132
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Widespread inconsistency in maximum likelihood estimation approach to logistic regression
I have found some widespread inconsistency in how the loss function of logistic regression is derived through the maximum likelihood estimation approach.
In the logistic regression model, we assume ...
- 1,630
1
vote
0
answers
36
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Max Likelihood of GBM with 2 Markov States
Consider the stochastic process
$$dX_t = \mu_{\epsilon_t}X_tdt + \sigma_{\epsilon_t}X_tdW_t$$
where $W_t$ is a standard Brownian motion. The process $X_t$ is a geometric Brownian motion (GBM) whose ...
- 387
0
votes
1
answer
35
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Error in derivation of variance of $\beta_1$ in SLR [duplicate]
I'm trying to derive the variance of the slope parameter for a simple linear regression in the following way, however I'm running into an issue I don't know how to resolve. Define $y_i=\beta_0+\beta_1\...
- 181
3
votes
1
answer
406
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Why is "unbiased" estimator more important than min-error estimator?
According to Edwin Jaynes (Chapter 17 of his book Probability Theory: the Logic of Science), the mean squared error of an estimator consists of bias term and variance term, that is:
$$L =E[(\beta - \...
- 471
3
votes
1
answer
61
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Can someone explain why ancillary statistic is needed in "orthodox statistics"?
I am reading Jaynes' Probability Theory: the Logic of Science. In Chapter 8 Jaynes discusses the issue of ancillary statistic in "orthodox" setting, where he says that ancillary statistic ...
- 43
3
votes
2
answers
97
views
Likelihood from forecast::Arima vs. manual replication
I am trying to replicate some results from forecast::Arima in R. I am particularly interested in the likelihood that I would like to use for some likelihood ratio ...
- 69.5k
0
votes
0
answers
32
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Asymptotic properties of estimators for general time series model
my question concerns the asymptotic properties of estimators in time series analysis. In particular I am interested in the behavior of the estimators for time series NOT being an ARMA time series. So ...
- 273
1
vote
0
answers
33
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Estimate standard deviation and get a confidence probability
I have no background in statistics so please be nice. With my little knowledge, I also did not find any similar posts or at least posts that I could understand.
Here is my problem, I have a variety of ...
- 11
0
votes
0
answers
14
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Estimating the parameter of Weibull accelerated failure time regression model
The parameters of Weibull AFT regression model are estimated by using the maximum likelihood method for the following model:
Are there different methods of estimation? Please explain them.
- 11
3
votes
1
answer
69
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Sample mean or James-Stein estimator?
I have a simple practical question, which I posted in Quant Finance SE (posting here as well, as I am not getting an answer(s) for it).
Suppose we have $n\geq3$ financial time series (correlated or ...
- 557
0
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0
answers
48
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Computing Fisher information for a Poisson distribution with any number of events
The context for the question is this paper. I am trying to understand how to get from Eq. (5) to Eq. (7).
For simplicity I will only consider 1 dimension, whereas the equations in the paper are ...
- 13
1
vote
0
answers
37
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Estimating from two sensors [closed]
We want to measure the distance between two objects. One sensor gives a reading of 120. Other sensor gives a reading of 200. We know that the readings of the first sensor has a Standard Deviation of ...
- 11
3
votes
0
answers
64
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Is this a mistake on Wikipedia on Standard Deviation?
On the Wikipedia page about standard deviation, in the section `Estimation', it says
Unlike in the case of estimating the population mean, for which the sample mean is a simple estimator with many ...
- 181
8
votes
3
answers
613
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How to Interpret Statistically Non-Significant Estimates and Rule Out Large Effects?
I'm working on a regression analysis and have obtained a point estimate that is statistically non-significant. Economically, a non-significant result makes sense in my context, but I want to ensure ...
- 3,209
1
vote
0
answers
59
views
How to speed up the following ELBO evaluation?
I have an estimation problem where I need to maximize the evidence lower bound:
$$ \mathrm{ELBO} = -\frac{1}{2} \Bigg( \mathbb{E}_{q(\theta)} \left[ \mathrm{vec}(\mathbf{Z})^{\mathrm{H}} \mathbf{C}^{-...
- 315
1
vote
1
answer
62
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Estimation of model coefficients of ARIMA model
Let say I have below ARIMA model estimation in R
...
- 405
1
vote
0
answers
19
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Bayesian estimation and biased estimators
I just learned nonBayesian vs Bayesian parameter estimation. My own summary:
nonBayesian: When statistics of a parameter are unavailable, CRLB holds for unbiased estimators, but there is a case in ...
- 111
1
vote
2
answers
59
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How to properly "subtract" a known covariance component from a sample covariance? regression
I have a situation where observed random variables $X_i$ are the sum of two independent (but unobserved) variables, $$X_i = S_i + N_i,$$ (e.g. what you observe is a random signal plus random noise).
I ...
- 111
1
vote
1
answer
33
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Example of Minimum Variance Estimator with Rate worst than $\frac{1}{n}$
Consider $n$ i.i.d. observation from a distribution $p(X| \theta)$. Suppose we are interested in estimating $\theta$ from this data.
I am interested in an example that would show that:
There exists a ...
- 205
1
vote
0
answers
57
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Transformation w/ Rolling Regression (Residual Function)
In a time series with OLS regression curve $\widehat Y$ (rolling linear regression), and with $n=20,$ what can I say about this transformation? This formula is similar to a differential minus its ...
- 11
1
vote
1
answer
42
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'Adding' confidence intervals of multiple estimations
I have estimates of the number of injuries seen by ambulance services on a quarterly basis, together with a confidence interval. I want to add these estimations to retrieve one estimation of the total ...
- 13
2
votes
1
answer
65
views
estimating preference rate
I'm offering an online service and want to determine how often people choose my service compared to my competitors. To estimate this, I have some data that tracks when users are presented with a list ...
- 91
0
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0
answers
30
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Comparing probabilistic estimation functions
Origin
In The Clever Way to Count Tanks - Numberphile,
the Dr James Grime presents how the allies mathematically estimated the number of tanks produced by Germany during WWII.
The video is very ...
- 101
1
vote
1
answer
38
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Breakdown with respect to a non stratification variable
Suppose we want to study the Investment of enterprises in a country. Suppose the enterprises are stratified by number of employees: three strata $s_1$ from $1$ to $9$ employees, $s_2$ from $10$ to $49$...
- 145
2
votes
1
answer
42
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Estimating the success of an approximation of a known matrix
I am trying to approximate a known $N\times N$ matrix $A$ with an 'estimation' matrix $A'$. The question is, how is it possible to quantify the error in this approximation - the difference between $A$...
- 177
0
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0
answers
32
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UMVUE for the Product of Means from Independent Samples
Let $ x_1, \ldots, x_m $ be i.i.d. samples drawn from a distribution $P$, and $ y_1, \ldots, y_n $ be i.i.d. samples drawn from a distribution $Q$. Assume that the samples $x_i$ and $y_j$ are ...
0
votes
0
answers
19
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Measuring the accuracy after transforming function in logistic kernel
I have a non-parametric estimator using gaussian kernel and logistic kernel. Lets say estimation using Gaussian kerel is defined as $E_G$ and logistic kernel is defined as $R_L$. For increasing sample ...
- 171
0
votes
0
answers
10
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How to find the bias gradient for localization problem?
The work is about finding the cramer-rao bound when the estimator is biased. The algorithm based on is from Rethinking Biased Estimation: Improving Maximum Likelihood and the Cram´er–Rao Bound, and it ...
0
votes
1
answer
29
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How to solve the ARCH effect problem in estimating linear bivariate regression model?
I estimated a linear bivariate regression model by OLS method.
I did the ARCH effect test. And there is the presence of ARCH effect in residuals.
How can I deal with the presence of ARCH effect while ...
- 1,152
1
vote
1
answer
143
views
Prove that $T$ is a complete statistic and find a UMVUE for $p$
While preparing for my prelims, I came across this problem:
Let $X_1, X_2,\cdots, X_n$ be a sequence of Bernoulli trials, $n \geq 4.$ It is given that, $X_1,X_2,X_3 \stackrel{\text{i.i.d.}}{\sim} Ber(\...
- 23
0
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0
answers
14
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How to deal with Bias Gradient Matrix for biased CRB(Cramér–Rao bound) calculation if the gradient matrix is m-by-n but $m \neq n$?
I am doing a model for collabrative localization and using the CRB(Cramér–Rao bound) as the localization performance measurement. I want to consider interference caused by NLOS and clutter, therefore ...