Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.
2
votes
2answers
97 views
Unbiased estimator of variance of binomial variable
$Y_{1...n}\sim \operatorname{Bin}(1,p)$, iid, and I need to find an unbiased estimator for $\theta=\operatorname{var}(y_i)$.
I did some calculations and I think that the answer is ...
2
votes
1answer
31 views
How to estimate the parameter of this time series?
The time series is governed by the equation $S(T)=S(0)e^{(\mu-\frac{\delta^2}{2})T+\delta(w(T)-w(0))}$, in which $w(t)$ is a standard Brownian motion. Now given the data $\{S(t)\}_{t=0}^{t=T}$， how to ...
-1
votes
0answers
44 views
Likelihood Function [closed]
$n$ random variables or a random sample of size $n$ $\quad X_1,X_2,...,X_n$ assume a particular value $\quad x_1,x_2,...,x_n$ .
$\bullet$ What does it mean? The set $\quad x_1,x_2,...,x_n$ ...
1
vote
2answers
52 views
Statistical workload estimation
I am a software developer and am frequently asked by prospects to provide a workload estimate for a potential project. I would like to implement a statistical approach to estimation that works as ...
0
votes
0answers
43 views
Convergence of expression involving $\frac{\phi(t)}{1-\Phi(t)}$ [closed]
The expression is given by
$G(t) = \frac{1}{\frac{\phi(t)}{1-\Phi(t)} - t}\left(\frac{1}{\frac{\phi(t)}{1-\Phi(t)} - t} -t\right)$
$\phi(.)$ is the pdf of standard normal and $\Phi(.)$ the ...
0
votes
0answers
11 views
System Identification regarding to L1-norm (absolute operator)
I am doing some control and system identification work right now, and I really need some help with respect to the system identification part.
Basically, I have a discrete state-space model, such as
...
0
votes
1answer
67 views
How can I compute the following situation in R? [closed]
Suppose that an urn contains a number of black and a number of white balls, and suppose that it is known that the ratio of the numbers is $\,3\mathbin{:}1\,$ but that it is not known whether the black ...
0
votes
0answers
35 views
MLE and MoM for parameters of truncated normal
I observe a r.v. $Y$ which is bounded from the right by $a = \frac{c - \mu}{\sigma}$. Hence I observe the moments:
$(1) E(Y) = \mu -\sigma \frac{\phi(a)}{\Phi(a)}$
and
$(2) Var(Y) = \sigma^2[1 - ...
0
votes
1answer
16 views
Choice Modeling and MaxDiff
I am new to the market research industry and have been exposed to a procedure called MaxDiff. I have seen this also called Best-Worst scaling. I am looking for good literature overview for this method ...
2
votes
1answer
54 views
What is the correct process of finding the point estimators for the following situation?
Let $X_1,X_2,...,X_n$ be a random sample from a uniform distribution on $(\mu-\sqrt 3\sigma,\mu+\sqrt3\sigma)$.
Here the unknown parameters are two, namely $\mu$ and $\sigma$, which are the ...
1
vote
1answer
43 views
Point estimator
When the point estimator under consideration has a pdf, then
$P[T=\tau(\theta)]=0 $
where $\tau(.)$ is some function of parameter $\theta$
$T$ is an estimator of $\tau(\theta)$
But I did many ...
4
votes
0answers
76 views
Is it possible to have an estimator that is unbiased and bounded?
I have a parameter $\theta$ which lies between $[0,1]$. Let us say that I can run an experiment and obtain
$\hat{\theta} = \theta + w$, where $w$ is a standard Gaussian. What I need is an
estimate of ...
2
votes
1answer
57 views
Estimating the population variance [duplicate]
I'm trying to understand the emphasized phrase in the following passage:
The usual method of determining the probability that the mean of the population lies within a given distance of the mean of ...
2
votes
1answer
55 views
Estimation of simultaneous equations model
My model is as follows:
$$
\begin{aligned}
y&=a_0 + a_1x_1 + a_2x_2 \\
x_2 &= b_0 + b_1x_1 + b_2z
\end{aligned}
$$
I'm only interested in the effect of $x_2$ on $y$. More precisely, I want ...
5
votes
1answer
70 views
Estimating a distribution from above/below observations
Let $P$ be an unknown distribution on $(-\infty,\infty)$. Let $X_1,\ldots,X_n$ be an iid sample from $P$. Let $c_1,\ldots,c_n\in(-\infty,\infty)$ be a known set of constants. We observe ...
1
vote
0answers
43 views
Estimating number of data points in specific range from percentile data
If I have a dataset broken down into percentiles, such that I know there are n values, and 10% of these values fall below x1, 20% are below x2 and so on, how can I estimate an answer to the following ...
1
vote
1answer
40 views
AR(1) parameter estimation
Given a time series, I'd like to estimate the parameters of an AR(1) model for it. As explained on wikipedia, there are different ways for doing that. What may be called a naive method is to compute ...
0
votes
0answers
32 views
Multivariate EWMA covariance estimation?
I want to calculate the VaR of my portfolio consisting of 4 assets with the following formula:
$VaR_t=\sqrt{w^T\Sigma_tw}z_\alpha$
So for each time point I need to calculate the covariance matrix. ...
0
votes
0answers
29 views
Strength of prior in Maximum Aposteriori estimation
Lets say I estimate the parameters of a logistic regression model with some data (say 10 data points). Now, I later get some fresh data which might not be enough in sample size. So, I want to use my ...
1
vote
1answer
42 views
Mode estimation in high dimensions
Suppose we have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$-dimensional unimodal density $f(\boldsymbol{x})$. I would like to estimate the mode of $f(\boldsymbol{x})$.
The ...
1
vote
0answers
27 views
MLE: Two parameter or three parameter Weibull?
I would like to calculate the MLE estimates of the mean and variance of a Weibull distributional assumption, from a given sample. Now, there are two parameter and three parameter weibull ...
1
vote
0answers
31 views
The meaning of translation completeness w.r.t a random variable
I stumbled upon this term in McFadden - Analysis of qualitative choice behavior (page 111).
It is said that
"A random Variable $X$ is translation complete if for a function h
of bounded ...
1
vote
1answer
51 views
Best way to estimate mean of RV from independent samples
Suppose we have N independently drawn samples from an unknown random variable $X$. What is the best way to estimate the expectation of $X$?
For simplicity, we can assume that $X$ only returns values ...
1
vote
0answers
24 views
Trying to understand an example where unbiased estimators don't exist
I am new to statistics especially in the topic of estimators and sufficient statistic.
I am reading a note which says "unbiasedness is a desirable (but not necessary) property of a good estimator". ...
2
votes
1answer
41 views
Uncertainty from Box–Cox estimation
Consider the model
$$
Y_i^{(\lambda)} = \alpha+\beta x_i + \varepsilon_i,\qquad \varepsilon_i,\ (i=1,\ldots,n) \sim \mathrm{i.i.d.}\ N(0,\sigma^2)
$$
where
$$
\begin{align}
y_i^{(\lambda)} & =
...
-1
votes
1answer
38 views
Fitting GARCH Model
I'am getting more and more familiar with this kind of model (and others models too).
I'm now used to fit this model with my data (rmgarch package in R).
How is it done ? What is the theory behind ...
1
vote
0answers
45 views
Parameters estimation of ODE system
I have all the data and an ODE system of three equations which has 9 unknown coefficients (a1, a2,..., a9).
...
2
votes
2answers
73 views
Estimating values of a sequence from observed differences
I have a sequence of random variables $S_1, S_2 \dots S_N$ that is guaranteed to satisfy
$$S_1 + S_2 + \cdots + S_N = 0$$
I can't observe any of these random variables directly, however I can ...
1
vote
0answers
59 views
Idea of the Nyblom-Hansen test?
The Nyblom-Hansen test gives information 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
vote
0answers
24 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
70 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
32 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
36 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
51 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
137 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 ...
0
votes
0answers
28 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
votes
0answers
27 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
2answers
31 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
35 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?
0
votes
0answers
53 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?
1
vote
1answer
48 views
Error in estimation with continuous data
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 ...
3
votes
1answer
72 views
how to estimate CTR (ctr-click-through-rate)?
How many times should a banner be shown to estimate its click-through-rate (CTR)? For example, if a banner was shown $x$ times, and was clicked $y$ times.
$$\text{CTR} = \frac{y}{x}$$
How could I ...
2
votes
1answer
59 views
Cauchy M estimator of regression in R
Was wondering if anyone knows of an R package to estimate the Cauchy-M estimator of regression (see for example the end of this section, but with simultaneous estimation of the scale parameter as in ...
0
votes
0answers
22 views
Length of time series and likelihood estimation
In ARMA (with normal errors) model estimation, are there any empirical studies or tests to judge the minimum number of observations (length) of the time series that are required such that OLS is an ...
1
vote
1answer
32 views
Relation between minimum contrast estimate and minimum distance estimate?
What relation are between minimum contrast estimate and minimum distance estimate?
If I understand correctly, these two are different methods? or are they equivalent?
Thanks and regards!
Minimum ...
2
votes
1answer
74 views
Under what conditions do Bayesian and frequentist point estimators coincide?
With a flat prior, the ML (frequentist -- maximum likelihood) and the MAP (Bayesian -- maximum a posteriori) estimators coincide.
More generally, however, I'm talking about point estimators derived ...
0
votes
0answers
25 views
What if the MVUE depends on the parameter?
The minimum variance, unbiased estimator $\hat \theta$ of $\theta$ is defined by
$$\hat \theta = \text{argmin}_{\hat \theta} \; \mathbb{E} \left( (\hat \theta - \theta)^2 \, | \, \theta\right), \quad ...
3
votes
1answer
50 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
44 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
$\begin{align*}
\hat{\mu}(x) &= \bar{x} + \left(1-\frac{k}{||x-\bar{x}||_2^2}\right)(x - \bar{x})
\end{align*}$
...
