Questions tagged [risk]

Risk has several meanings in different contexts within statistics

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Identify predictors for a symptom in a time series

I have a dataset of time series. The analogy for each series is a medical history (2-3 years) of a patient visiting a clinic. It consists of dates and symptoms per visit: There are few thousands of ...
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Statistical Measurement to Compare Risk Tables of Survival Curves

Disclaimer: not a statistician ;-) Background I have time-to-event data and a computational model that generates time-to-event data. The idea is that the modeled data mimics the actual data. I can ...
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Calculating individual predicted probability from logistic model and 95% confidence interval for shiny app

I have developed a logistic model to predict the risk of an outcome (TRS) based on some predictors. This was developed on a number of imputed datasets generated by mice (imp2) as follows: ...
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Var and Expected Shortfall

I am struggling to find an example which has 2 random variables (say L1 and L2) with same VaR but different Expected Shortfall.
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Minimizing the toal risk under squared-error loss for normal distributions

Suppose that $X_i \sim N(\theta_i,1)$ are independent for $i=1,\dots,n$. Let: $$\hat{\theta_i}(\boldsymbol{x^{n}})= \left(1 - \frac{b}{\sum_{i=1}^{n}x_i^2} \right)x_i $$ Where $b$ is a constant. If we ...
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efficient frontiers are equal

I created 3 different efficient frontiers with 3 different risk factors(sharpe ratio, ulcer performance index and serenity ratio) and I wanted to find both MSR and GMV(and their equivalent for the ...
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Is the expectation in the expression for Risk taken with repect to $\hat{\theta}$?

In Chapter 13 of Larry Wasserman's All of Statistics A Concise Course in Statistical Inference is given: Definition 13.1 The risk of an estimator $\widehat{\theta}$ is $$ R(\theta, \widehat{\theta})=\...
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Difference between ECE (expected calibration error) and ECI (estimated calibration index)

What is the difference between ECE (expected calibration error) and ECI (estimated calibration index) ? ECI: https://www.sciencedirect.com/science/article/pii/S0895435621000482
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Logistic regression for risk adjustment

I'm not sure to understant how you can use logistic regression to calculate risk-adjusted rate. For example, I want to calculate an adjusted rate for acquiring C. difficile in a hospital. I have the ...
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How to compute the combined probability of loss for 2 time series (consisting of historical stock prices)?

May I please ask the community's support with the following problem? I have 2 time series, with approximately 1000 observations each (same number of observations for both). They represent the daily ...
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Why FZ0 loss function will leave log(-e) term when forecasts have no error? Can FZ0 loss function formula be interpreted simply?

I'm working on my thesis about using FZ0 loss function for estimating the model parameter. And I have trouble with interpreting why FZ0 loss function have this form. Fissler and Ziegel(2016) had ...
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Hazard X population density ?`

Not quite able to calculate risk ... I know the hazard across a given geographic region (probability an intensity threshold will be exceeded in a given window of time) and I know the population ...
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Predict risk from pre-trained Cox PH model

I came accross this article about AMD (age-related macular degeneration, a kind of eye diseases) recently. The article fitted a Cox PH model to predict risk of disease advancing to advanced stage. The ...
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Why do we need the concept of Risk in Bayesian Decision theory?

I'm studying Bayesian decision theory as introduction to machine learning and I see the concept of Risk in a lot of places. In the course I read, they define risk as: Risk is the expected error ...
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What is the difference between the risk function used in Bayesian inference and the one used in supervised learning?

In the context of Bayesian inference, given the random parameter $\Theta$, the observed data $\mathcal{D} = \{x_1,x_2,\dots,x_N\}$, the posterior $p(\theta\mid \mathcal{D})$, the estimator $\hat\...
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Combined relative risk in meta study

I am looking at a meta study, and I've never done one (or looked at it much) before. From what I've learned about it so far, the way you calculate the compounded effect is by first calculating this $\...
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Jump diffusion -advantages

What would people say is the advantage of using a Merton jump-diffusion model, in terms of what it models and it's key characteristics/ features?
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Convergence of Empirical Risk Minimizer and True Risk Minimizer

Let $D:= \{ (x_1, y_1), \dots, (x_n, y_n) | x_i \in \mathbb{R}^d, y\in\mathbb{R}\}$ be our dataset. Let $F$ be some function class and $f\in F$. Furthermore, $l$ is some loss function. E.g. the ...
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Risk function equation

How to show risk function = (3-theta)^2? I tried using the mean squared error formula to no avail.
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How does the risk calculation of the EMA / Paul-Ehrlich-Institut regarding AstraZeneca vaccine side effects look like?

When the german government announced that they would stop administering AstraZeneca because of potentially deadly side effects, I was wondering what kind of risk calculation would be happening in the ...
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MSE of randomized decision in Normal distribution

Suppose a sample $\bf{X}$$=(X_1,...,X_n)$ is from $X\sim N(\theta,1)$. The sample mean $T(\bf{X}$$)=\bar{X}$ is sufficient to the population mean $\theta$. For $\delta(\bf{X}$$)=X_1$, the decision $\...
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Credit risk book reference

Credit risk is a beautiful field that relies on basic notions of statistics and stochastic processes. I have been studying it, and now I am trying to understand the market models such as KMV, ...
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Is Bayes risk under MSE (i.e. conditional variance) strictly monotonic?

Formal question: Let $Y,X,X'$ be r.v.s . Let $E_{X}[Var(Y|X)]$ denote the expected conditional variance (i.e. Bayes risk when predicting $Y$ using $X$ under squared error) and $f$ be a bijective ...
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Distribution for ${1^TX}/\sqrt{X^TQX}$, when $X$~$N(\mu, \Sigma)$?

I have been looking for an illustrative way to quantify the risk of an investor not being able stay above the minimum capital requirement. I would like to find a neat solution for the probability that ...
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Single Choice Test

I will have a big exam next week that involves 64 Single-choice questions. There will be two statements of which only one will be correct. I will need to mark only the correct answer. For the correct ...
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How to calculate 95% CI of vaccine with 90% efficacy?

A vaccine is reported in the news to have 90% efficacy. I'd like to know how much confidence there is in that efficacy measure. The protocol for this reports that a vaccine or placebo was administered ...
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How about evaluating an estimator using the VARIANCE of loss (instead of the expectation of loss)?

The risk of an estimator $\delta$ is defined as $$E_\theta[L(\theta,\delta(X))],$$ where, say, $L(\theta,\delta(X)) = (\theta-\delta(X))^2$, and $E_\theta(X)$ is defined as $\int XdP_\theta$, namely ...
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Cause-specific survival function in survival analysis

In survival analysis, when there are competing risks, it is well-known that although the cause-specific hazard function, $\lambda_j^\#(t)$, is interpretable, $S_j^\#(t) = e^{-\Lambda_j^\#(t)}$ may not ...
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Calculating the (colloquial) likelihood of a result

A project that I am working on wants to use two factors to determine risk. First is an assessment by a subject matter expert (SME) on how much damage a calculated result would cause. Second is a ...
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What is the entropy of a riskless random variable?

Variance and standard deviation are often used as proxies for risk and volatility. I make the analogy to information theory as follows, correct if it's wrong: a random variable $x\in \mathbb{R}$ that ...
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Relation between test and train error with gradient descent iterates

My question is about establishing an inequality between population error and expected training error (i.e, expected training error < population error) for a model trained with gradient descent on a ...
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Estimating CVaR for non-Gaussian distributions

Calculating CVaR needs Gaussian distribution, however, what if the distribution is not Gaussian? Or the distribution is unknown? Can I use many Dirac Delta functions to estimate a distribution and ...
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Logistic regression risk prediction model - poor calibration but good discrimination

I am trying to create risk prediction model in R. I am new to logistic regression risk prediction analysis. I obtained reliability curve using ...
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3 votes
1 answer
162 views

How does probability of default evolve over time?

Say I have a probability of default of 0.02 (which is annual so over next year) for a certain client. Then say this client takes out a 180 day loan, how can I adjust my probability of default for this ...
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annualized probability of default for loan including time component

i am struggling with this. say i am given an annual probabilty of default for a company going insolvent as 0.02. so 2%. say this client then takes out a 100k , 150 day loan on jan 1st 2018, what is ...
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Cross entropy vs KL divergence: What's minimized directly in practice?

My understanding is that in ML one can establish a connection between these quantities using the following line of reasoning: Assuming we plan to use ML to make decisions, we choose to minimize our ...
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Is the risk a probability?

The Ktest function in the dbmss package returns: the risk to reject CSR erroneously, based on the distribution of the K ...
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Calculating Conditional Value at Risk given any distribution

Many CVaR methods calculations are based on VaR, which is based on the assumption on the normal distribution. How can I calculate CVaR given any distributions?
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When do expected KL-divergence and expected MSE coincide?

The AIC is an approximately unbiased estimator of the (relative) risk of the Kullback-Leibler loss. I read that If you use AIC to choose among a family of models, AIC (approximately) yields the model ...
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Value-at-Risk formula with GARCH-model

I'm totally aware of that if we look at some loss process $L_t$, then $\text{VaR}(\alpha)$ is a quantile of the loss distribution. If we assume that $L_t=-X_t$ is the negative returns and they follow ...
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Likelihood of Global Catastrophe - Surely it cant be 80%?

I'm not a mathematician, but I'm trying to wrap my head around this statistical problem ... An Oxford 2008 study guessed the likelihood of global extinction at 0.2%pa, which by my calculation is ...
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Player based betting odds VS analysis based odds

there are two kinds of betting sites Player based odds sites (thunderpick.com , csgopositive.com , ...) analysis based odds sited (1xbet , bwin , and almost all of the huge betting sites) when you ...
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We know that The empirical risk is an unbiased estimate of the risk. Then why Is the training error biased ? (How does to proof for the former break)

Setting: Let $S$ be a set of $m$ samples from a set $Z$ and $w^{*}$ be an arbitrary vector. (Samples Are I.I.D and we are operating in a binary classification setting) Then $\mathbb{E}_{S \sim D^{m}}...
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VaR backtesting: counting the number of rejections

Let's say you calculate the number of VaR rejections for every $r_{1,t}$, $r_{2,t}$, should you have the same number of rejections in a model, irrespectively of the weights being different? $[w,\ 1-w]...
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solvency capital requirement using copulas in R

I want to prove that using copulas the SCR for solvency 2 can be lower than using the standard formula. In the following code I simulate three different distributions, I calculate the scr and then I ...
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Expected Shortfall for ARMA-GARCH two day forecast

I need to find the 99% confidence expected shortfall (CVaR) for a long position of 100 dollars at time $t$ for an asset with returns modeled by an ARMA(1,1)-GARCH(1,1) model with $r_t = θr_{t−1} + u_t ...
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5 votes
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Inconsistent Empirical Risk Minimization procedure, but why?

Given a random variable $Y$ and the typical squared loss function: $$L(Y,\hat{Y}) = (Y-\hat{Y})^2$$ the minimizer for expected loss $E[L(Y,\hat{Y})]$ is know to be the mean, $\hat{Y} = E[Y] = \mu$. ...
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Calculating risk score

I'm trying to construct a medical risk score. I was given some advice by a statistician and they said that one of the stages after the variable selection stage is to take the regression coefficients ...
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Compute the Risk function

Suppose we are given $(X_1,...,X_n)$ random variables which are iid. from $\mathcal{N}(\mu,\theta)$ and finite variance. Let $Y=\frac{1}{n}\sum_{i=1}^n(X_i-\overline X)^2$ and define a loss function $...
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Definitions of VaR (Value at Risk)

Here is the definition of VaR (Value at Risk) taken from McNeil, Alexander J., Rüdiger Frey and Paul Embrechts (2015), Quantitative risk management: Concepts, techniques and tools: $$ \textrm{VaR}_{\...
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