The estimation-theory tag has no wiki summary.

**0**

votes

**0**answers

13 views

### How to generalize uncertainty coefficient to set-valued classes?

This question is the reason I asked How to estimate the entropy of a distribution on a power set?
Proficiency (AKA uncertainty coefficient) is an information-theoretic measure of predictor quality, ...

**1**

vote

**3**answers

89 views

### How to estimate the entropy of a distribution on a power set?

Given a probability distribution $(X,p)$, its entropy is defined as $H=-\sum_{x\in X} p(x)\log p(x)$.
Given a sample of observations $x_n,n=1..N$, one can estimate $p(x)=\frac{\#\{i:x_i=x\}}{N}$ and ...

**2**

votes

**2**answers

63 views

### estimating variance of dependent normal distributed data

Let $X_{ij}$ with $1\leq i<j\leq n$ (that are $X_{12},\dots, X_{1n},\dots,X_{(n-1)n}$) be ${n \choose 2}$ identically normal distributed $N(0,\sigma^2)$ such that
$
\text{corr}(X_{ij},X_{rs})=\rho
...

**2**

votes

**2**answers

63 views

### Markov-type functions

I'd like to have some informations about Markov-type functions (or Cauchy-type):
\[ f(z)=\int_{\Gamma} \frac{\mathrm{d}\gamma(\xi)}{\xi-z}.\]
$\gamma$ is a positive measure with compact support ...

**1**

vote

**0**answers

51 views

### Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function"
$Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset
$s \subset U$. One can see $Sig(t)$ as a stochastic process.
...

**3**

votes

**1**answer

129 views

### Equivalent method for maximum likelihood estimation of covariance parameters

My goal is to estimate the parameters of a covariance matrix $\Omega$, by maximizing the following log-likelihood function:
$$\log L(\vec\tau, \rho, \sigma \mid W, X) = -m\ln(\left | \Omega \right |) ...

**0**

votes

**1**answer

60 views

### About the suboptimality of linear estimators

Let $X$ be a random variable and $N$ a Gaussian noise independent from $X$. We observe $Y=X+N$ and want to estimate $X$ based on $Y$ to minimize the mean square error $mmse(X|Y):=E(\hat X(Y)-X)^2$.
...

**1**

vote

**0**answers

50 views

### Moments of Matrix Gamma distribution

Matrix gamma distribution (defined for example in http://en.wikipedia.org/wiki/Matrix_gamma_distribution) is one way to generalize Wishart distribution. In our course work that distribution was used ...

**1**

vote

**0**answers

94 views

### Shrinkage (or Stein's phenomenon) in low dimensions, discrete contexts

I am trying to understand shrinkage, or the Stein phenomenon. As someone without a statistics background, the focus in most introductory presentations on normal distributions and squared error loss ...

**4**

votes

**0**answers

155 views

### Pair of two-variable polynomial equations of high order

I have the following pair of equations to be solved for two variables $\rho$ and $D$ resulting from a certain Maximum Likelihood Estimation for a time series $X_n > 0$, $n=0, \ldots, N+1$ with $N ...

**0**

votes

**1**answer

103 views

### Signal model classification between two possbile candidates

How to decide the most possible signal model between two model candidates besed on the received signal vector?
Assume the received signal vector is $y$, the possible signal model candidates could be:
...

**3**

votes

**0**answers

134 views

### Worst-case error and Cramer-Rao Lower Bound - is there any mathematical relation between them?

I would like to understand the relation (if any) between the Cramer-Rao Lower Bound of estimation theory and the following simple definition of "reconstruction accuracy" which doesn't use any ...

**1**

vote

**0**answers

341 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 ...

**0**

votes

**0**answers

126 views

### Better estimate than Sample mean?

Today I came a cross an old math thing I did some years ago. I remembered that I didn't find a similar result from anywhere at that time but forgot the thing altogether. So now I would like to ask if ...

**0**

votes

**0**answers

95 views

### What are Effective Regression Techniques for Linguistic Analysis of Linked Data?

I am in the early stages of a problem that involves parsing a large number ($\approx 5 \times 10^9$) of documents (web pages) and estimating values from them. In particular I need to identify pages ...

**0**

votes

**1**answer

168 views

### Estimation of Temporal Correlation of Signal

I have a signal and i'd like to estimate its temporal correlation.
My limited understanding is i should compute the PSD by estimation using a parametric model such as AR.
However, i'm not quite ...

**1**

vote

**1**answer

182 views

### Is an unbiased estimator with arbitrarily small variance necessarily consistent?

Given an unbiased estimator $\hat \theta_n$ of a parameter $\theta$, if the estimator has small variance (approaching $0$ as $n\to\infty$), it seems reasonable to expect that the estimator is ...

**0**

votes

**2**answers

434 views

### Estimating a sum

Sorry for the vague title but I couldn't find a better one.
I want to compute the sum $S = \frac{1}{N}\sum_{i=1}^N c_i x_i$ where $c_i$s are known positive constants. The problem is that computing ...

**0**

votes

**0**answers

73 views

### Estimation of X in Gaussian noise

Given
$\textbf{x}=[x_1 x_2 ... x_n]^T$ where $\textbf{x} \in \{ 0, a_1, a_2, a_3\}^n, a_i \in \mathbb{C}$ and $\textbf{z} = \{z_1 z_2,...,z_n \}$ where $z_i \textbf{~} N(0,\sigma^2)$ is a Complex ...

**0**

votes

**0**answers

118 views

### Why does the OLS estimator simplify as follows for the single regressor case?

I was reading in "A Guide to Econometrics" that given $Y = X \beta + \epsilon$, the variance covariance matrix of $\beta^\text{OLS}$ is given by $\sigma^2 (X' X)^{-1}$ where $\sigma^2$ is the variance ...

**1**

vote

**2**answers

2k views

### Maximum likelihood estimator for Power-law with Exponential cutoff

Hi,
for fitting empirical data to power-law I am aware of the work by Clauset et al. (http://arxiv.org/abs/0706.1062) and how to use maximum likelihood estimation. There exists also a simple maximum ...

**3**

votes

**0**answers

606 views

### Interpolating Wavelet Coefficients

Hi! I was instructed via reddit that this place would be the best place to post this question. Fingers cross you can help...
Ive been writing some code to get rid of noise "spikes" in a signal. I'm ...

**2**

votes

**1**answer

339 views

### Why doesn't Stein effect happen for multinomial distributions?

(Medeen, et all, 1998)" show that Maximum Likelihood estimate is admissible for multinomial distribution under squared error. On other hand, James and Stein showed that arithmetic average is not an ...

**4**

votes

**0**answers

1k views

### Using Fisher Information to bound KL divergence

Is it possible to use Fisher Information at p to get a useful upper bound on KL(q,p)?
KL(q,p) is known as Kullback-Liebler divergence and is defined for discrete distributions over k outcomes as ...

**1**

vote

**1**answer

258 views

### Is there a text on estimation theory online?

Where can I find graduate level, thorough, parameter estimation/ estimation theory material on the web?