Tagged Questions

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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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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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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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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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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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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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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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 ...
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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 ...
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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 ...
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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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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 ...
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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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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 ...
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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.
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 ...
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 ...