Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.
0
votes
0answers
37 views
What is the most effective way to estimate the number of strands of string in a wireframe basket?
Objective
Estimate the number of strands of string in a very large, wireframe basket from a distance.
Preconditions
The investigator is fixed to a particular position and cannot change their ...
1
vote
1answer
214 views
Maximum likelihood estimation and the n-th order statistic
Let $X_1, ..., X_n$ be a sample of independent,
identically distributed random variables, with density
$$ f_{\theta}(x)=e^{ (\theta -x)}$$.
$x \ge \theta$, otherwise $f_\theta = 0$
The question ...
5
votes
0answers
63 views
Identification of parameters problem
I always struggle to get the true essence of identification in econometrics. I know that we state that a parameter (say $\hat{\theta}$) can be identified if by simply looking at its (joint) ...
2
votes
2answers
462 views
Why doesn't the Cramer-Rao lower bound apply?
Let $X_1, X_2, \dots, X_n$ be a sample of i.i.d. random variables, with density $$f_\theta=\frac{2}{3\theta}\left(1-\frac{x}{3\theta}\right) $$ for $0 < x < 3\theta$. And
$f_\theta=0$ if $ x ...
2
votes
1answer
222 views
method of moments with variance=$\sigma^2$
I am trying to estimate the value of a parameter by equating variance from a distribution to the sample variance... i.e. using method of moments estimation. Would it better to use the variance formula ...
3
votes
1answer
76 views
Correcting biased polling
Let's say I'm polling for a binary election in different states with known biases. Furthermore, let's say I only manage to poll only a small sample of people in each of these states. How would you ...
0
votes
0answers
37 views
Is there an extension of the James-Stein estimator for cases of nondiagonal covariance matrix?
Is there an extension of the James-Stein estimator for cases of nondiagonal covariance matrix?
James-Stein estimator holds for every multivariate distribution but are there any improved versions ...
1
vote
3answers
264 views
Iterative proportional fitting and independent variables
I'm trying to understand the "classic" iterative proportional fitting (IPF) algorithm.
Does it always assume that the variables being analyzed are independent? If the variables are independent, then ...
11
votes
3answers
467 views
How to do estimation, when only summary statistics are available?
This is in part motivated by the following question and the discussion following it.
Suppose the iid sample is observed, $X_i\sim F(x,\theta)$. The goal is to estimate $\theta$. But original sample ...
0
votes
0answers
48 views
Change Frequency of an AR(1) estimation
Say, I have an AR(1) stochastic volatility model estimated with quarterly data,
That is I have an AR(1) process for the data itself and also an AR(1) process for its volatility.
Now I need to get ...
0
votes
1answer
160 views
Parameter estimation for linear system with correlated noise
Let's say that I have a linear system (e.g. an electrical circuit) and I am trying to estimate the values of parameters in the system (e.g. the resistance, inductances, and capacitances). I do this by ...
3
votes
0answers
208 views
Definition and Convergence of Iteratively Reweighted Least Squares
I've been using iteratively reweighted least squares (IRLS) to minimize functions of the following form,
$J(m) = \sum_{i=1}^{N} \rho \left(\left| x_i - m \right|\right)$
where $N$ is the number of ...
9
votes
1answer
191 views
How to estimate an upperbound for logistic regression by only 5 to 7 data points?
I have data that is of the form $y = \frac{\beta_1}{1 + \exp(\beta_2 + \beta_3 * x)}$. For the estimation of $\beta_1$ to $\beta_3$ I use the formulas of this paper: John Fox - Nonlinear Regression ...
1
vote
1answer
301 views
Composition of probability density
I know probability distribution for parameter $\phi$. I have the empirical distribution/statistical distribution of $X$ that is dependent on parameter $\phi$ for $\phi \in [0,1]$. I assimilate this ...
4
votes
3answers
81 views
How to determine a user's favorite content producer from individual ratings?
Consider the following scenario:
Alice subscribes to a video rental service that allows her to watch movies. Every time A watches a movie, she rates it either thumbs up (1) or thumbs down (0), and ...
4
votes
1answer
139 views
What is the estimation bias of the top estimate in a list sorted by value?
Let's make the problem as simple as possible. Assume two related random variables, $X_1$ and $X_2$. On the basis of some data we estimate their true means $\mu_{X_1}$ and $\mu_{X_2}$ by sample means ...
2
votes
1answer
103 views
Density estimation with scaled sinc-like kernels
Given data points $x_i$ in $\mathbb{R}^d$ with function values $f_i$,
one can estimate the function at a given $x$ by
$\ \ \ \ \text{f}_{est}( x ) = \frac {\sum { w_i f_i }} {\sum { w_i }}$
with $w_i ...
3
votes
0answers
112 views
Calculating the Fisher Information of bivariate normal
I'm lost. If I estimated the a Gaussian mixture model, with a shared diagonal covariance, will the Fisher information of the means be $\Sigma^{-1}$ ?
2
votes
0answers
120 views
Estimating customer waiting time and server idle time on a finite horizon, stochastic, single-server queue
I am working on a problem of scheduling appointments for a stochastic, single-server queue. There are $n$ customers who each have independent, randomly distributed service durations $Z_i$. The ...
3
votes
1answer
78 views
Choosing a robust estimator to account for measurement error in dependent variable
I have cross-sectional regression model $\hat{Y}_i = a + bX_i + e_i$ estimated over 200 cross-sectional observations. The $\hat{Y}_i$'s were generated in 200 time series regressions, and so has ...
7
votes
1answer
151 views
Laplacian-Beltrami approximation based on an empirical sample
Given a probability measure $\nu$ on a subset $M \subseteq \mathbb{R}^N$ we construct the corresponding operator
$$L^tf(x)=f(x)\int_{M} ...
3
votes
2answers
89 views
Rank-ordered cumulative distribution estimation: where does this function come from?
I am reading over some process analysis data for some failure analysis tests, and I have come across the following definition of an "estimated cumulative probability":
$$F(t) = \frac{i-3/8}{N+1/4},$$
...
1
vote
0answers
135 views
Truncated Pareto estimation
Given min and max values, how can I estimate shape parameter (tail index) of data generated by truncated pareto distribution ? I see a package tpareto but find no information on how to estimate tail ...
3
votes
1answer
72 views
Estimating parameters using a different method?
I have a probability distribution which has two parameters $a$ and $b$
I have re-parametrized the distribution such that the new distribution has two parameters $c$ and $d$ where:
$c=a$
but
$d = ...
1
vote
0answers
66 views
Estimating parameter using curve-fitting and model comprised of uncorrelated product of two functions
Suppose that I have a time-series dataset represented by the function $f[t,\omega,q]$, where $t$ is the time as an independent variable, $\omega$ is the frequency as an independent variable and $q_k$ ...
0
votes
2answers
106 views
Estimating bounds on false positives rate
I would like to estimate bounds on the false positive rates of a binary classifier. In my sample data I have 50% positive data points, and 50% negative data points. However, in the real data, which I ...
9
votes
1answer
398 views
Is the theory of minimum variance unbiased estimation overemphasized in graduate school?
Recently I was very embarrassed when I gave an off the cuff answer about minimum variance unbiased estimates for parameters of a uniform distribution that was completely wrong. Fortunately I was ...
9
votes
2answers
223 views
Computationally efficient estimation of multivariate mode
Short version: What's the most computationally efficient method of estimating the mode of a multidimensional data set, sampled from a continuous distribution?
Long version: I've got a data set that I ...
1
vote
1answer
55 views
Alternatives to MAP estimator
Given some data $y$, dependent on parameter $\theta$, I have some density $p(\theta | y)$. I now want to infer what value of $\theta$ is most `likely' to have originated $y$. One possibility of doing ...
0
votes
1answer
401 views
Similarities and differences between regression and estimation
What's the similarities and differences between parametric regression analysis and estimation theory?
I notice that they are both about parameter estimation, and both require some models for ...
2
votes
0answers
104 views
How to compare the results of two benchmarks?
I am writing a program and would be interested in knowing how much faster does a version run compared to another.
For that, I wrote a benchmark script that times the run time of my program, repeats ...
0
votes
0answers
58 views
When are two trend estimates identical within errors?
Given two linear trend estimates $m_1$, $m_2$, with their respective errors $e_1$, $e_2$, how can I determine if the two trend estimates are the same within errors?
EDIT: Both estimates are derived ...
4
votes
2answers
463 views
Advantage of kernel density estimation over parametric estimation
Is there any particular reason you will choose the kernel density estimation over the parametric estimation? I was learning to fit distribution to my data. This question came to me.
My data size is ...
2
votes
0answers
112 views
How to estimate the covariance matrix for repeated measures data given summary statistics?
I've been working on a power analysis for an RCT study for a psychological intervention. And I've been wondering how one would estimate the covariance matrix (or rho) for repeated measures data? This ...
2
votes
0answers
100 views
Estimating HMM parameters from a sequence with missing observations
The BW algorithm to estimate HMM parameters works on a consecutive sequence of observations. But what should be done if only a partial sequence is available? From another point of view, the observable ...
1
vote
0answers
302 views
Estimating the parameters of a beta distribution with zeroes and ones in the sample
I have a list of values in [0,1] that I want to fit to a Beta distribution in order to get the corresponding alpha parameter.
I can't use a beta fitting function because my values might be 0's and ...
3
votes
1answer
274 views
Posterior distribution for multinomial parameter
(topic moved from maths.stackexchange.com)
I'm currently developing an application integrating a probabilistic inference engine for Bayesian Networks. The Bayesian Network integrates some form of ...
2
votes
1answer
93 views
Dealing with project uncertainties: is the sum of the most-likely estimates equal to the sum of the expected times?
I found this document on the internet: Dealing with Project
Uncertainties
In this article I read:
In order for uncertainties to be included in the project estimates it
is necessary to take ...
3
votes
0answers
79 views
Estimation After Selection on Non-central F Random Variables
Suppose that you observe $F_1,F_2,\ldots,F_k$ each independently. drawn from non-central F distributions with common, known, d.f. $\nu_1, \nu_2$, and with (unknown) non-centrality parameters ...
3
votes
3answers
251 views
Optimal estimation of a mean from non-independent data
I have the following model:
$Y_1=\beta+\varepsilon_1+\varepsilon_2$
$Y_2=\beta+\varepsilon_3+\varepsilon_4$
$Y_3=\beta+\varepsilon_1+\varepsilon_4+\varepsilon_5$
...
5
votes
3answers
288 views
Can I use a variable which has a non-linear relationship to the dependent variable in logistic regression?
Let's say I am building a logistic regression model where the dependent variable is binary and can take the values $0$ or $1$. Let the independent variables be $x_1, x_2, ..., x_m$ - there are $m$ ...
4
votes
1answer
180 views
Two unbiased estimators for the same quantity
In several situations, I have two unbiased estimators, and I know one of them is better (lower variance) than the other. However, I would like to get as much information as possible, and I would like ...
1
vote
0answers
83 views
Estimation accuracy of precision matrix
I have a couple of questions related to estimation of high-dimensional precision matrix (inverse of the covariance matrix) in the case where p is close to 100 and n < p. As a measure of estimation ...
2
votes
0answers
58 views
Inferring from a combination of uncertain and certain data
I am trying to estimate the surface (isochrone), zi(x) for which T(x,z)=0 from noisy measurements of T(x,z) everywhere and 3 almost noise free control points:
Instead of using the T(x,z) data ...
0
votes
0answers
71 views
ARIMA function not working as I would expect
My work has stuck me on a forecasting project because of what I learned in school, even though my applied work is zero. So I'm having trouble.
I am applying an ARMAX model to a stationary variable ...
-1
votes
1answer
404 views
Question regarding sampling, estimation and accuracy [closed]
Let's say there are N chunks of metal, each are 4 inches thick. They are to be hammered and reduced to following best possible sizes: 1, 2, 3 or 4 inches. If we were to use sampling to get an estimate ...
0
votes
0answers
23 views
Sample size determination for polling with multiple choice type questions [duplicate]
Possible Duplicate:
Question regarding sampling, estimation and accuray
Let's say there are N sets of diamonds, containing 5 in each set. There can be anywhere between 1 to 5 defective ...
2
votes
1answer
274 views
Parameters’ uncertainty for small sample size
Suppose we have a small set of numbers (5 to 10 observations), and we’re trying to fit a distribution to this set. Also, we know that all numbers are positive. I tried to fit lognormal, but I’m not ...
0
votes
2answers
175 views
How to estimate storage needs using the PERT distribution for filesizes? How to aggregate them without falling into the flaw of extremes?
Lets say I know that I am going to store the information of 10,000 people each year for 4 years, that is 40,000 files. Now If I estimate that on the best case scenario the information from each ...
4
votes
2answers
834 views
Maximum likelihood estimation in a Poisson model for football (soccer) scores
I've got a set of football results and I want to make a probabilty model of football scores as described in Dixon, Coles (1997, http://www.math.ku.dk/~rolf/teaching/thesis/DixonColes.pdf). They ...
