Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.

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4 views

what's the difference between MMSE estimation and MAP estimation

can anyone answer the question regarding difference between minimize estimation error and minimize wrong estimation? Thank you
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1answer
23 views

Use of infinity norm instead of SSE for machine learning accuracy?

Are there any examples or arguments in favor of using an infinity norm (or equivalent) over sum of squared errors or root mean squared error for evaluating machine learning algorithms?
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1answer
18 views

Dirichlet Process Hyperparameter Estimation with Sampling

I have a dirichlet process for which I need to learn the concentration (strength) hyperparameter (with gamma prior on it). One way of doing is via maximizing the Likelihood. Another way of doing this ...
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15 views

Online moving median [duplicate]

So I can use "EWMA" (1) to update an estimate of the mean as each new measurement is received. If I know the window size of the smooth($\eta$), the previous estimate($ \bar{x}_t$), and the new ...
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0answers
3 views

Noise Contrastive Estimation gradients

I'm trying to derive gradients of the Noise Contrastive Estimation cost which is referenced at equation 9 in Mnih et. al from equation 8. Can you give me some hint? What I derive seems to be totally ...
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1answer
36 views

Finding the unbiased variance estimator in high dimensional spaces

The problem comes from linear regression. Assume the regression function is linear, i.e. $$ f(X) = \beta_0+\sum_{j=1}^pX_j\beta_j $$ .Given a set of training data $(x_1, y_1),\ldots,(x_N,y_N)$,we try ...
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29 views

R Bayesian prediction of a Gaussian process

I have a Gaussian model with mean zero, variance is arbitrary constant, and correlation function $e^{-\theta(x-x')^2}$ where $\theta$ is again an arbitrary constant. I've plotted some realizations of ...
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6 views

Question on the estimation of a complex matrix

I would like to find a complex matrix C from (huge) set of the data { y }, where every complex-scalar y can be described by a following model which includes the matrix C (whose size is say M x M), y ...
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37 views

Estimating number of balls by successively selecting a ball and marking it

Lets say I have N balls in a bag. On my first draw, I mark the ball and replace it in the bag. On my second draw, if I pick up a marked ball I return it to the bag. If, however I pick up a ...
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1answer
195 views

Why don't we use the unbiased sample variance to calculate the standard error?

The standard error is an approximation of the standard deviation of the sampling distribution of the sample means. The real standard deviation of the sampling distribution, $\sigma _{\bar x}$ is: ...
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17 views

multidimensional time series nonlinear parameter estimation

I am trying to fit time series data for performing parameter estimation of a nonlinear multidimensional dynamical model (grey-box). At the moment I'm successfully using MATLAB's ...
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0answers
18 views

Determine a distribution of a gaussian stochastic with different time

I would like to determine the autocorrelation function of a Gaussian stochastic. Let see my problem So my solution is The distribution of $y=x(t_1)-x(t_2)$ is also a Gaussian stochastic with ...
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16 views

Marginal pseudo-likelihood and consistency?

For a given set of random variables, $X_1,...,X_n$ we know that in many cases finding the maximum of the pseudo likelihood: $$PL(x_1,\ldots,x_n) = \prod_{i=1}^n p(x_i | ...
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33 views

Estimate the covariance matrix of a normal distribution if the mean vectors is given by a linear rule

Let $X=(x_1,\ldots,x_n)^\top\in\Bbb{R}^n$ be a random vector that follows a multivariate Gaussian distribution with known mean vector $\mu=(\mu_1,\ldots,\mu_n)^\top\in\Bbb{R}^n$. The covariance matrix ...
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0answers
26 views

demostrate Jensen's inequality (i think) [duplicate]

Please any help is very good. I was trying to start with the definition of expected value but I don't know how to finish.
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0answers
17 views

Error of bounded mean estimation with quantization

I have a distribution whose mean $\theta \in [0,1]$. Given $n$ observations, I compute the sample mean (say $\hat{\theta}$) and quantize it to accuracy $\frac{1}{n}$ (basically I can use only ...
2
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1answer
33 views

Sufficient and complete statistic

Let $ X_1, ... , X_n $ be i.i.d random variables with pdf given by $$f(x;\theta) = \exp(-(x-\theta))I_{(\theta, \infty)}(x)$$ It is asked to find a sufficient statistics for $ \theta $ and to verify ...
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1answer
75 views

Unbiased estimator based on geometric mean for random sample on an exponential distribution

Let $X_1, \ldots, X_n$ be a random sample on an exponential distribution with mean $\theta$. Obtain an unbiased estimator for $\theta$ based on $G$, where $G$ is the geometric mean of the ...
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2answers
70 views

Show that the value is, indeed, the MLE

Let $ X_1, ... X_n$ i.i.d with pdf $$f(x;\theta)=\frac{x+1}{\theta(\theta+1)}\exp(-x/\theta), x>0, \theta >0$$ It is asked to find the MLE estimator for $\theta.$ The likelihood function is ...
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0answers
28 views

Distribution of sample variance for non-normal random variable [duplicate]

For a sample of size $n$ of non-normal random variables $x_1,...,x_n$. Is it possible to know which distribution the sample variance estimator follows? Details: The distribution of $x_i$'s is not ...
2
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1answer
22 views

Estimation probability in related binomial distribution

I have two binomial experiments with an unknown probability - But i do know that the ratio between the probability in the first experiment and the probability in the second experiment - For example I ...
2
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1answer
52 views

What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$. The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
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21 views

Follow-on to “Training with the full dataset after cross-validation” - sequential parameter estimation

Background: Here is the background for the question, both the question itself and the answer given by Dikran Marsupial. Training with the full dataset after cross-validation? It asks about after ...
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0answers
29 views

Question about Lagrangian Multiplier (Gradient) Statistic of constrained GMM

I am trying to derive the Lagrangian multiplier statistic (GMM version) under a restriction. The question is given below The quadratic form is given by $Q_n(\theta,\alpha)=[m(\theta)', ...
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1answer
32 views

Missing data analysis software

Does any standard statistical software like R, SAS or SPSS have procedures or codes to analyze log-linear models for missing data in contingency tables using maximum likelihood estimation (or EM ...
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12 views

Plotting of density estimates in matlab [migrated]

Given the biometric match scores, I am required to plot the graphs of estimated densities of matching genuine and impostor scores. Following are the graphs I got for genuine and impostor scores ...
2
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1answer
42 views

How is lasso an M-Estimator?

The definition of an M-estimator is an estimator (from Casella and Berger) of the form $$\hat{\theta}=\min \sum_{i=1}^n \rho(X_i-\theta),$$ where $X_1,X_2, \cdots, X_n$ is the data for some function ...
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0answers
7 views

What is the meaning of “finite sample error control”?

I encountered this phrase while reading a paper which goes like this -- "These methods lack finite sample error control due to instability". Although it might not be important, the paper deals with a ...
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2answers
60 views

How does one interpret the distribution over parameters in bayesian estimation?

I am new to Bayesian estimation. The assumption that the parameters are random variables seems a little unsettling to me. For example when considering a model for data, what physical interpretation ...
3
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0answers
61 views

Unbiased estimator with minimum variance for $1/\theta$

Let$ X_1, ...,X_n$ be a random sample feom a distribution $Geometric(\theta)$ for $0<\theta<1$. I.e, $$p_{\theta}(x)=\theta(1-\theta)^{x-1} I_{\{1,2,...\}}(x)$$ Find the unbiased estimator ...
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24 views

Predicting stock returns - in a panel data specification or by using portfolio formation strategies?

I'm working on an empirical analysis where I try to predict stock returns using weekly data. Ideally, I would like to use a panel data model like the following: $$ ...
3
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1answer
68 views

Unable to understand derivation of Expectation Maximizaton

In Paper, System Identification using Symbolic Chaotic Sequence, Authored by A. Kurian and H. Leung download link under section II B, can somebody please explain ...
3
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2answers
133 views

How to estimate model with both linear and exponential parameters?

I have a theoretical growth function that can be perturbed by events, and I'd like to estimate the growth parameters as well as the perturbation, and the rate of falloff after that perturbation. I'm ...
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13 views

Estimating a vector from a rank-one symmetric matrix plus scaled identity

I have a problem regarding estimating a $M\times 1$ vector from a given $M\times M$ symmetric matrix. The known matrix is a scaled identity matrix with a rank-one update. I have some idea how to ...
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0answers
23 views

How many models I need?

I am doing an estimation using a bunch of sparse data. Suppose that I have a 100x100 grid and 20 data is available on this 2D grid. One solution is to use a determiastic method and estimate the other ...
3
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1answer
23 views

Estimate a proportion using priority sampling (I just made that up)

I have this idea in my head that is either bunk or has a name I don't know. (I'm not naive enough to think I'm breaking new ground here!) Here's my scenario: I would like to know the proportion of a ...
3
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0answers
83 views

Kalman Filter to correct model simulation bias

I am working with a large scale deterministic model, which attempts to simulate CO2 emissions in different regions. When compared to historic data, the model output suffers from systematic biases. ...
3
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1answer
121 views

Doubts in linear regression

If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1) $, then what does this constant term imply? Will it hamper the estimates if ...
5
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1answer
101 views

Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population

A brief motivation: $n$ critters live in an aquarium, where sadly they often hide in, under or behind things. When the aquarium is observed, each critter is only seen with probability $p$ ...
2
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1answer
51 views

Unbiased estimator for $P(X_1=1)$

If $ X_1, ... ,X_n$ are IID binomial with parameters $ n$ and $p, $ find an unbiased estimator for $$G(p)=P(X_1=1)=np(1-p)^{n-1}\, .$$ I need to find this estimator so I can apply Lehmann-Scheffé ...
3
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1answer
111 views

What location parameter is modelled by robust regression?

There is quite some number of ways how to robustly fit a linear regression model, e.g. using M-estimation based on Tukey's biweight loss or on Huber's loss, see e.g. Wikipedia. I got two questions ...
2
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1answer
31 views

Run Many Small or a Few Big Simulations to Estimate the Mean?

I was just running some simulations on tossing a coin given certain conditions, to test out some ideas I had. I was trying to find the ratio $\frac{\mathtt{successful\ tosses}}{\mathtt{total\ ...
2
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0answers
48 views

Difference between blind and semi-blind estimation

Parameter estimation of nonlinear systems unscented kalman filter ( paper and many others are categorized under semi-blind identification technique because the Authors say that the dynamics of the ...
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0answers
21 views

How do I determine the innovation term in an ARIMA equation?

I am not a statistics specialist : I had to take over the internship subject of another student to include it in mine. He was working with $SARIMAX$ models and I would like to import them in an ...
6
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2answers
184 views

Why is the geometric median called the $L_1$ estimator?

My question is simply, why is the geometric median called the $L_1$ estimator? This always reminds of $L_p$ spaces but the distance being minimized in the geometric median's definition isn't $L_1$ but ...
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0answers
16 views

Untransforming unbiased estimates

Suppose I have some measured experimental data and I want to fit it to a power law of the form $y=ax^b$. Suppose I transform the data to log-log space and then I fit a straight line of the form ...
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33 views

General theoretical properties of empirical Bayes estimates

I was wondering if someone could provide reference (if such exists) for the theoretical properties of empirical Bayes(EB) point estimates, in the sense of what can we say about their risk under ...
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44 views

Numerical estimation of MLE in Python — normal distribution and gradient is close to zero away from the mean

I am exploring how to model a data set using normal distributions with both mean and variance defined as linear functions of independent variables. Something like $\mathcal{N} \sim \left (f(x), ...
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1answer
47 views

Gaussian Mixture Model parameters from density

How do I estimate parameters of subpopulations in a 1D gaussian mixture model when I already have density (measured on a grid) of the mixture? All the algorithms I can find (like the well-known EM ...
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0answers
19 views

Can you combined two sources with difference variance to reduce error? [duplicate]

I have two samples of data each estimates of a position x, y with Gaussian noise. One source has a larger variance than the other. Is this source in any way useful ...