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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7 views

Implicit estimator, it's variance and expectaion

Denote with $V_j$ the firm's value of $j$-th firm. We will speak of default, if the firm's value falls below predefined barrier $c \in \mathbb{R}$. The random variable $L_j$ will indicate, if $j$-th ...
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14 views

Estimating the Parameters of Multivariate Gaussian from Conditioned Distributions

My goal is estimating the distribution parameters of a multivariate Gaussian $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^n$ from observations that were generated from different conditioned variants of ...
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0answers
11 views

Estimation of stochastic parameters in bivariate Poisson model

I need to estimate parameters in bivariate Poisson model. Formulas for parameters: $\lambda_1= exp (\alpha_i-\beta_i+\delta)$ $\lambda_2= exp (\alpha_j-\beta_j)$ where delta is some constant, alpha ...
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0answers
19 views

Non-parametric estimation of error distribution in regression

Consider the following model: $y = 1$ if $g(X\beta) + u > 0$ and $y=0$ otherwise where $u$ is $iid$ according to some distribution function $F$. I want to recover the distribution $F$ without ...
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7 views

Comparing relative error measures

So I have a list of actual values and two models to predict these values. Evaluating the predictions gives me a relative (absolute) error of 50% percent for the first and 25% for the seconds. I'm ...
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26 views

Understanding the derivation of the unbiased expectation estimate

For context, I am reading David Barber's Bayesian Reasoning and Machine Learning book, section 27.1. He presents the following derivation that shows why monte carlo estimates of expectations are ...
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8 views

Structural Equation Models (SEM) what is the number of unknowns?

Lets consider the following vector-matrix equations from the LISREL model (indices indicate the format of the vector/matrix): $$\eta_{n \times 1}=B_{m \times m}\eta_{m \times 1}+\Gamma_{m \times n}\...
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1answer
20 views

Estimate parameters for skew normal distribution

I know there is already at least one question answer with this, but I think the solution does not apply in my case. I have a population for which I know the mean, variance and skewness. I saw how to ...
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20 views

Calculate arm angels between robot arms from tilt sensor data

I need a time series of the angle between two robot arms and I have got measurements of tilt sensors on the arms. (Lets call them A and B). In an ideal world one tilt sensor minus the other one should ...
3
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33 views

Baum-Welch algorithm variation for Hidden Markov model with reward

Following my previous question on the subject I would like to get your feedback on the following alternative solution. (The original solution to this question is the usage of the POMDP model proposed ...
2
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1answer
11 views

Is OLS Unbiased on Count Data in the Positive, Real Domain?

On the domain of positive real number is OLS on count data a consistent estimator of coefficients? I am trying to understand if the estimator is inefficient or produces biased SEs but is nevertheless ...
1
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1answer
26 views

Quantify compatibility between posterior estimates

I performed two distinct, independent experiment $E_1$ and $E_2$ to ideally measure the same quantity $X \in \mathbb{R}$ of interest. For each experiment, I computed the posterior pdf of $X$ via MCMC, ...
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7 views

how to sample “partitioning arrangement” and “parameter” in Dirichlet process?

This is rather a simple question. I know how to sample the partitioning arrangement (i.e. in Chinese restaurant process metaphor the seating arrangements), and parameter of Dirichlet Proces, but I don'...
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7 views

How exactly does one derive the efficient influence curve?

I've been studying targeted maximum likelihood and I come from a CS background. I am pretty lost. Can someone explain, with an example if possible, how exactly one derives the efficient influence ...
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0answers
5 views

How to formulate moving average model in the problem of estimation

The source input $\mathbf{x}$ is in the form of the feature vector having $d$ components of length $d$ is transmitted via a channel whose impulse response is modeled as moving average (finite response,...
3
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1answer
29 views

Estimating a rate of failure/survival using only right censored data?

I am trying to estimate the probability $q$ that a household with certain known covariates will move to a new home in the following year, by estimating an event rate $\lambda$ dependending on some ...
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24 views

How are probabilities calibrated for Boosting Trees?

I am not sure how probabilities are calibrated in the boosting of decision trees. I understand that boosting does a poor job in estimating cross entropy. So does anyone have suggestions as to methods ...
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0answers
20 views

Probability of Drawing Correlated Samples From Known Distribution

Suppose that I have some number n of samples drawn from a normal distribution, and a full covariance matrix for those samples. Is there a way to compute (or at least place bounds on) the probability ...
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13 views

PyMC sampling is slow

I'm using pymc2 to estimate the parameters of a normal distribution. My data has shape 50000 x 6. Basically, I have 50K independent distributions and I want to obtain the parameters for each of them, ...
0
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1answer
16 views

How can I find the standard error of the coefficients from an S-estimator?

I am using a simple model with a response and predictor variable but I am unable to find a package/function that provides the standard error of the coefficients for the S-estimator. So, how do I ...
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0answers
8 views

Particle filtering for multiple parameters

There are several ABC algorithms out there relying on the use of importance sampling/particle filtering in which a value of a parameter is chosen based on its weight. I was wondering what happens if ...
3
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2answers
113 views

RMSE - where this evaluation metric came from?

Does anyone know where this metric came from ? Can someone bring article references or something like this? Im actually wondering if there's any mathematical concept or any way to demonstrate ...
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0answers
3 views

Design experiment to measure dependence of probability on a parameter

I have a physical system that can be modelled as following: there is a function $f:[0,1] \to [0,1]$ so that, given a parameter $\theta$, the physical system computes $p=f(\theta)$, samples $y$ from a ...
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2answers
53 views

Parameter Estimation for intractable Likelihoods / Alternatives to approximate Bayesian computation

Suppose that I have a stochastic model with some parameters that I want to fit to some observed data. Let's assume the Likelihood intractable, i.e. for some reason I cannot work with the analytical ...
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2answers
219 views

Best way to evaluate PDF estimation methods

I wish to test some of my ideas that I think are better than anything that I have seen. I could be wrong but I'd like to test my ideas and vanquish my doubts by more certain observations. What I have ...
12
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1answer
343 views

Why is the arithmetic mean smaller than the distribution mean in a log-normal distribution?

So, I have a random process generating log-normally distributed random variables $X$. Here is the corresponding probability density function: I wanted to estimate the distribution of a few moments ...
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15 views

ARMA coefficients

How to determine the ARMA coefficients for ARMA(p,q)? I explored a lot of technical literature and I understand there are standard rules like Yule-Walker for a pure AR process. Do they apply for ...
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1answer
57 views

Estimating the mean of a random variable from greater than/less than answers

Let $X_1,\dots,X_n$ be $n$ i.i.d. samples from a certain probability distribution (e.g, a normal distribution). Your goal is to estimate the mean of the distribution. However, you are not allowed to ...
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34 views

Some logical questions about parameter estimation in the situations when the model is misspecified

When we have a parametric model, we can use many procedure to estimate the parameters in the model, i.e., obtain many different estimators. We usually focus on the set of consistent estimators. For ...
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1answer
18 views

Should the underlying logic of the model evaluation criterion match with the estimation procedure?

Assume we have a parametric model with parameter $\beta$. We want to use this model to make predictions, e.g., credit card firm using some attributes $X$ of the customer to predict the default rate $Y$...
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6 views

Estimation of parameters from a complicated expression (double integration) with optime [migrated]

I am trying to estimate paramters of a function with optime This is the code: ...
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0answers
42 views

Prove consistency of estimator

Let $X$ be a random variable with density $f(x;\theta)=\frac{1}{2\theta}I_{(-\theta,\theta)}(x), \ \theta>0$. Is $\hat \theta = \dfrac{1}{n}\sum_{i=1}^nX_i$ a consistent estimator for $\theta$...
3
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1answer
32 views

Uncertainty in parameter estimates when fitting distributions

I used the fitdist function from the "fitdistrplus" package in R to estimate the parameters of my data. Once I get the parameters, I must get the confidence ...
2
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1answer
26 views

estimating variance using only data at the tails without resorting to Gibbs sampling

Suppose we know that the population size is $n=1,000$ but for whatever reason, we only have the bottom $n_1=100$ observations and the top $n_2 = 200$ observations. Furthermore, suppose we know the ...
5
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1answer
73 views

Variance computed using Taylor series does not agree with numerical experiment

I would like to estimate an angle $\theta\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ given the noisy observations of its sine and cosine (this is related to my earlier question). My estimator is ...
0
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0answers
32 views

Equivalent of standard error for variance?

I would like to know if there is an equivalent formula of standard error for variance or standard deviation, that is, I would like to know how far the variance of my sample is from the real variance ...
3
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1answer
81 views

What is the proper way to measure error for an estimation algorithm?

Our algorithm is about estimating the true statistic values from a data set. The data set is a table in relational database, we are going to estimate the statistic value for filtered records, like <...
3
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1answer
24 views

methods to estimate 2 sinusoids in noise

Are there some strategies to estimate a function which has the form $y=A\sin(f_1x+O_1)+B\sin(f_2x+O_2)+\epsilon$ (where $\epsilon$ is small-variance Gaussian noise) I have initial estimates of of ...
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2answers
105 views

Estimate of parameter of exponential distribution with binned data

I have the following data, which can be modeled by exponential distribution ...
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0answers
54 views

Variance of Maximum Entropy solution [closed]

Background: Assume we are interested in solving the Maximum Entropy solution for a six sided dice with expected value of 4. $$H= - \sum_{i=1}^6 p_i \log(p_i) $$ $$\sum_{i=1}^6 p_i = 1$$ $$\sum_{i=...
0
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1answer
36 views

Likelihood between two functions

I have a function $f(x)$ describing a physical process, and a function $g(x)$ that tries to approximate it. I can clearly see by eye when the two functions are close enough, but I would like a ...
0
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0answers
30 views

Maximum likelihood estimation for non-stationary time series

I want to estimate how the taxes influence the retail price of alcoholic beverages. The price function is tricky because in EU countries there is excise duty and also VAT. The non-linearity (which is ...
0
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0answers
15 views

simulation and model comparison

I created a simulation to compare a number of regression type models/estimators, lets call them M1, ...,Mn. for each iteration of the simulation run: I generate randomly data set X I generare ...
0
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0answers
13 views

How to make a covariance matrix from multiple observations of different objects?

I have $N$ objects. From each object, I sample $M$ values $(x,y)$ like so: ...
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0answers
22 views

How can I decompose the error after an ARIMA estimation, and how do I store the estimated values?

EDIT (in response to Stephan's comments): I was able to read a paper by Bessembinder & Seguin (1992) on futures trading and stock price volatility, wherein they used the ARIMA model to decompose ...
1
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1answer
42 views

How to show the least square estimator of $b$ has the minimum variance in the class $\sum a_iy_i$

Consider the regression model: $$ y_i=bx_i+e_i,1\leq i\leq n.$$ where $x_i$'s are fixed non-zero real numbers and $e_i$'s are independent random variables with mean zero and equal variance. $(a)$...
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0answers
6 views

Theoretical/intuitive question about time-varying Generalized Pareto Distribution

I fitted the GPD to the right tail of nine log return series (I multiplied log returns by -1, so modeling the right tail equals modeling the losses) with a threshold equal to the 95% quantile. Some of ...
2
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0answers
19 views

Why are standard errors downward biased when considering weak instruments

I was wondering why standard errors are (severely) downward biased when you are using the (general) instrumental variable - estimator or the generalized method of moments (gmm) estimator.
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12 views

Sparsity estimators

I've recently started to read about sparsity estimation. Let's recall that the sparsity function is defined as $s(\tau)=f(Q(\tau))$, where $f$ is the population density and $Q$ is its quantile ...
1
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1answer
38 views

Comparison of Stahel-Donoho and Minimum Covariance Determinant estimation

I am interested in detecting multivariate outliers in a low dimensional data set ($n<p$). Various high-breakdown robust methods for multivariate settings such as Stahel-Donoho and Minimum ...