Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.
1
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1answer
32 views
Parameters estimation of ODE system
I have all the data and an ODE system of three equations which has 9 unknown coefficients (a1, a2,..., a9).
...
2
votes
1answer
43 views
Estimating values of a sequence from observed differences
I have a sequence of random variables $S_1, S_2 \dots S_N$ that is guaranteed to satisfy
$$S_1 + S_2 + \cdots + S_N = 0$$
I can't observe any of these random variables directly, however I can ...
1
vote
0answers
20 views
Idea of the Nyblom test?
The nyblom-hansen test gives informations about the stability of the estimated parameters in a model. As far as I understand this test, it looks at the score of the ML at evaluates, how near to zero ...
1
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0answers
14 views
How do I best estimate population parameters from multiple sets of summary statistics on one sample?
Suppose that I have an assortment of summary statistics on a sample, and some beliefs about the underlying distribution, but no access to the sample itself. Each of the sets of summary statistics is ...
2
votes
2answers
63 views
Difference between “estimated” and “fitted”?
Currently I am using a r package to fit an ARMA-GARCH process. Afterwards, I want to use the fitted values to calculate the Value at Risk. So these values are not the forecasts, but the ...
1
vote
0answers
25 views
What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?
I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g:
...
0
votes
0answers
31 views
Bias in EM estimation for a mixture of normal distributions
Are the parameter estimates for a mixture of two normal distribution using EM algorithm biased or unbiased?
More specifically, if I use the EM-algorithm to obtain ML estimates of $μ_1$, $μ_2$, ...
2
votes
1answer
48 views
Borrowing strength
What are the principles of Borrowing Strength?
What does it mean in terms of estimating parameters for hierarchical models?
Where can this information can be read from?
3
votes
2answers
130 views
Exponential family in testing and estimation
In the Annals of Statistics paper "Defining the curvature of a statistical problem(with applications to second order efficiency)" by Bradley Efron, he claims the following two statements in the first ...
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0answers
24 views
More suitable cross validation method for estimation method
I have a sparse dataset of graph of size about (7k*7k).I estimate some values for each not existence edge according to the information of graph. I want to validate the method(The accuracy of the ...
0
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0answers
23 views
SV model estimation
I have been trying to estimate the basic stochastic volatility model using OpenBUGS via R and at an stage of the following command. Please can you comment for the command that can give me the ...
0
votes
1answer
21 views
Combined Individual Error
This is from my college project management course. Reading through an example question here it says:
When estimating in parts, the total error will be less than the sum
of the part errors.
...
0
votes
1answer
30 views
Estimating the number of birds in a specific area
I want to count the birds in an area. What's the proper statistical method for it? What are the good references for this topic?
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0answers
34 views
EM algorithms - confidence interval estimation
Does anybody know how to find the confidence intervals for estimated parameters of a mixture of Gaussians by using EM algorithm?
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1answer
36 views
error in estimation with continuous data (New to Statistics)
Is there a way to correlate error in a fit (MSD) to the error of the a calculation performed with the parameters associated with the fit? My specific problem is dealing with spectroscopic data. I ...
2
votes
1answer
52 views
how to estimate CTR (ctr-click-through-rate)?
How many times banner should be shown to estimate CTR? For example, a banner was shown x times, and was clicked y times.
$$\text{CTR} = \frac{y}{x}$$
How to evaluate incaccuracy of this value?
1
vote
1answer
47 views
Cauchy M estimator of regression in R
Was wondering if anyone knows of an R package to estimate the Cauchy-M estimator of regression (see for example the end of this section, but with simultaneous estimation of the scale parameter as in ...
0
votes
0answers
21 views
Length of time series and likelihood estimation
In ARMA (with normal errors) model estimation, are there any empirical studies or tests to judge the minimum number of observations (length) of the time series that are required such that OLS is an ...
1
vote
1answer
27 views
Relation between minimum contrast estimate and minimum distance estimate?
What relation are between minimum contrast estimate and minimum distance estimate?
If I understand correctly, these two are different methods? or are they equivalent?
Thanks and regards!
Minimum ...
2
votes
1answer
63 views
Under what conditions do Bayesian and frequentist point estimators coincide?
With a flat prior, the ML (frequentist -- maximum likelihood) and the MAP (Bayesian -- maximum a posteriori) estimators coincide.
More generally, however, I'm talking about point estimators derived ...
0
votes
0answers
24 views
What if the MVUE depends on the parameter?
The minimum variance, unbiased estimator $\hat \theta$ of $\theta$ is defined by
$$\hat \theta = \text{argmin}_{\hat \theta} \; \mathbb{E} \left( (\hat \theta - \theta)^2 \, | \, \theta\right), \quad ...
3
votes
1answer
49 views
Will two estimators converge to the same answer?
Say I have two estimators for the same quantity and using the same model, $E[f(X)]$. I also know that these two estimators are consistent, meaning, if we have a lot of data, they will be close to the ...
0
votes
1answer
43 views
Transforming the distance value from a center, to a probability value
Let $c_i$ be the center of a micro-cluster (i.e. we have many centers representing some fragments of clusters). Let $c_1$ be the center which is the closest to a new data-point $x$, such that ...
0
votes
0answers
18 views
Shrinkage estimator's risk function
How do you compute the risk function under squared loss of an estimator of the form
$\begin{align*}
\hat{\mu}(x) &= \bar{x} + \left(1-\frac{k}{||x-\bar{x}||_2^2}\right)(x - \bar{x})
\end{align*}$
...
0
votes
0answers
11 views
How to choose grid for SMM and report results?
In estimating a model with two variables by simulated method of moments. How does one generally choose the number of points on the grids? For example, consider one variable as interest rate between 0% ...
1
vote
0answers
20 views
Robust mean estimation with O(1) update efficiency
I am looking for a robust estimation of the mean that has a specific property. I have a set of elements for which I want to calculate this statistic. Then, I add new elements one at a time, and for ...
1
vote
0answers
37 views
Estimating right-censored data
I am VERY new to stats. I have a large amount of life-time data (delay in arrival since start of experiment) from repeat experiments. Some data is missing, but essentially represents a delay longer ...
0
votes
0answers
14 views
Parzen Estimation used in Classification
How would I use a Parzen window estimate to classify an arbitrary test point x using 3 dimensional data from three categories.
0
votes
1answer
51 views
Given MCMC samples, what are the options for estimating posterior of parameters?
Markov chain Monte Carlo (MCMC) is a class of algorithms for sampling from probability distributions. In the end, given a parametric model explaining the data, MCMC could also be used for parameter ...
2
votes
1answer
32 views
Estimating point of phase transition
I have stochastic simulations that depend on a parameter $k$. As I vary $k$ the quantities I track vary gradually and then suddenly transition to very different values and continue to vary gradually ...
3
votes
1answer
89 views
What is an unbiased estimate of population R-square?
I am interested in getting an unbiased estimate of $R^2$ in a multiple linear regression.
On reflection, I can think of two different values that an unbiased estimate of $R^2$ might be trying to ...
2
votes
1answer
105 views
What technical language to describe the degree to which probabilities are likely to be modified by future data?
I'm trying to reason about something I call "estimate stability," and I'm hoping you can tell me whether there’s some relevant technical language, so that I can learn about it and then write a ...
0
votes
1answer
106 views
Standard errors of hyperbFit?
I want to fit a hyperbolid distribution according to my notation:
\begin{align*}
H(l;\alpha,\beta,\mu,\delta)&=\frac{\sqrt{\alpha^2-\beta^2}}{2\alpha \delta K_1 (\delta\sqrt{\alpha^2-\beta^2})} ...
2
votes
0answers
49 views
Estimator bias without a closed form?
Given a regression loss function $l(Z,\beta)=||Y-Z\beta||_2 + \lambda \beta^TD\beta + r(X,Z)$ where $X$ is the predictor matrix, I would like to estimate a $Z$ that minimizes the above loss in a ...
0
votes
1answer
84 views
Jointly estimation of model or single step estimation?
I have financial data (return) and use the following model:
where $R_t$ is the return at time t, $\mu$ is set to zero, $\sigma$ is the volatility and $\epsilon$ is an innovation process.
The ...
0
votes
1answer
27 views
Output of hyperbfit?
I want to fit a hyperbolid distribution to my data, in my notation, I have the density
\begin{align*}
H(l;\alpha,\beta,\mu,\delta)&=\frac{\sqrt{\alpha^2-\beta^2}}{2\alpha \delta K_1 ...
0
votes
0answers
19 views
Is it possible to Reduce/Correct Bias through EM algorithm?
I am dealing with few overdispersed count models and using mixed Poisson distributions to deal with overdispsered data. I've used MLE technique to estimate the paramters, however ML estimates are ...
0
votes
1answer
39 views
Why does KL divergence show up in the proof of Hoeffding's inequality?
In some textbook the KL divergence shows up in the proof of Hoeffding's inequality (e.g., eq. (5) of this material). In contrary, most other textbooks seem not mention this fact. I know that KL ...
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votes
0answers
20 views
Why Hoeffding's inequality has a sharper bound than Markov's inequality?
Basically, I can understand the proofs' details for both inequalities, but still I have no idea why the bound of Hoeffding is sharper than that of Markov? Is there any underlying intuitive that can be ...
0
votes
0answers
23 views
How can you reconstruct “base” (profile/headshot) image of face using several obscured images of the face?
I recently read a paper titled "3D Face Reconstruction from a Single Image using a Single Reference Face Shape" which got me thinking about the fact that it is rare for one to encounter unobscured ...
0
votes
1answer
89 views
Dropping a variable from a multiple linear regression model, causes another to become non-significant [duplicate]
Suppose we have a regression model that measures college Grade Point Averages. The variables that we are using are hsize (the size of the graduating class in ...
1
vote
2answers
46 views
If the empirical distribution of a sample is same as the true distribution, how shall the deviation be estimated?
Suppose we can always generate a sample $\{X_1, \dots, X_n\}$ of size $n$ for a discrete distribution, such that its empirical pmf is the same as the true pmf. One of the reason that we can have such ...
0
votes
1answer
67 views
Gaussian vs non-gaussian distribution
Let we have data of 3D (example angular velocity x, angular velocity y, angular velocity z).Can anyone explain/give example/how to differentiate between gaussian distribution and non-gaussian ...
1
vote
0answers
51 views
Pooling asymmetric confidence intervals for proportions?
I have several measurements of proportions (values in [0, 1]) $\theta_1,...,\theta_n$, each with an (asymmetric) 95% confidence interval. The $\theta$'s are repeated measurements of the same variable ...
1
vote
1answer
21 views
minimax and transformations
for two real random $n$-vector $y$ and $x$
and a random $n$-vector $e$ with distribution
$F$ independent of $x$ we know (1) that the
estimator
$$\text{med}\left( \frac{y_i}{x_i}\right)$$
is ...
1
vote
1answer
86 views
Nelson-Aalen estimator and interval censoring/tied events
I just noticed that the Nelson-Aalen estimate of the cumulative hazard changes depends on the existence of tied events. As a toy example, consider a study with 3 patients. The patients die on day 1, ...
-1
votes
1answer
91 views
t distribution method of moments
This is a further question to my original question, where I did not get an helpful answer (at leas not helpful for me) :Methods of moments for t distribution
I want to fit a t distribution to my data ...
1
vote
1answer
56 views
Creating a CI for the mean from an approximation of x-bar
The "classical" $100(1-\alpha)\%$-confidence interval starts from the Student's t statistic $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}.$$
Then, one obtains the desired result, e.g. $\bar{x}\pm ...
0
votes
0answers
21 views
Ideas and issues related to parameter estimation
MPSV paper describes the method of parameter estimation. I have a set of measurements obtained from hardware. It is a vector of 1000 data samples representing a measurement.I need to formulate a model ...
10
votes
1answer
163 views
Why must an estimator be independent from the parameter?
This is an excerpt from "Modern mathematical statistics with applications" by Devore et al.
What puzzles me is that the estimator cannot help being dependent on $\theta$, since the sample depends on ...
