# 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 ...
1 vote
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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: ...
1 vote
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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.
1 vote
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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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1 vote
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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, ...
1 vote
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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 ...
1 vote
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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 ...
1k views

### 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 ...
82 views

### 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 ...
1 vote
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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 ...
98 views

### 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 ...
1 vote
49 views

### 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 ...
26 views

### 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 ...
228 views

### 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 ...
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 ...
1 vote
374 views

### 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 ...
2k views

### 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 ...
1 vote
391 views

### 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 ...
177 views

### 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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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 $r_t = θr_{t−1} + u_t ... 5 votes 1 answer 214 views ### Inconsistent Empirical Risk Minimization procedure, but why? Given a random variable$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,$\hat{Y} = E[Y] = \mu$. ... 2 votes 0 answers 136 views ### 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 ... 0 votes 0 answers 467 views ### 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$...
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}_{\...