Questions tagged [risk]

Risk has several meanings in different contexts within statistics

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Implementation of CoVaR (a systemic risk measure) in R

I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this ...
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2answers
575 views

Credit Risk and Concentration

I am working with a UK credit-union and we are looking to build a model to assess our credit risk and changes to this over time. We have a number of loans to borrowers who each have a credit rating (...
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1k views

How does the RMS package's nomogram calculate points for continuous variables?

I have been reading a number of papers where researchers have created risk scores based on logistic regression models. Often they refer to "Sullivan's method" but I have no access to this paper and ...
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36 views

Bounds for the expected value of the Kolmogorov-Smirnoff loss function

Let $$ \mathcal{F}=\{F:\mathbb{R}\longrightarrow\mathbb{R}: \text{$F$ is the CDF of some probability measure on $\mathbb{R}$}\}. $$ Consider the loss function, $L:\mathcal F\times\mathcal F\to\mathbb ...
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Copula-based Value-at-risk in R

I'm working on a value-at-risk calculation using copulas on different stock market indices. I know how to fit the copula, but I can't figure out how to apply the VaR approach in the next step. The ...
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1answer
41 views

Conditional correlation, copula, portfolio optimization and diversification

I have a data set which consists of > 500 hedge funds, their historical monthly returns, and their benchmark (index) monthly returns. The number of data points (# of monthly returns) differs from a ...
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423 views

Predict probability of rare event

Let's say I have a dataset about passages of cars on a road. The dataset contains information about time, driver, car, weather, and most importantly whether the car was involved in an accident. Of ...
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505 views

How to find a conditional probability using copula-based Markov process?

I have a monthly time series of a water quality parameter. I used copula-based Markov process of C(Y(t), Y(t-1) and I forecasted the mean behavior of Yt by following equation: Now, I need to find ...
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3k views

How can I convert annual standard deviation to a longer period?

Quicken provides annual standard deviation of returns for a given portfolio using analysis done by the Newport Group. I'd like to convert this to a longer term number--say 10, 20, or 30 years. ...
2
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105 views

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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108 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 ...
2
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32 views

Characterization of risk factors for a very rare condition

I am looking at a cohort of patients including 13000 patients, out of which only 160 have condition A. Out of these patients, only 6 have condition B. I would like to be able to characterize those ...
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185 views

Equity Risk Model using an autoencoder

I am trying to create a statistical equity risk model using an autoencoder in a similar fashion to how one would use PCA to derive the systematic and specific risk components of a stock's returns. I ...
2
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655 views

True risk vs emprical risk

I tried to understand the difference between true and empirical risk by the post in wiki. There it states that the true risk cannot be computed because the distribution P(x,y) is unknown. My first ...
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183 views

Simulation of a random variable given the moment generating function after exponential tilt

The random variable $S$ follows a distribution with moment generating function $$M_S(v)=\frac{\beta\mu v}{1+(1+\beta)\mu v-M_X(v)}$$ I have been looking in some books about this m.g.f and I found ...
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22 views

Probability - Plant Production

I work for an agricultural company. We grow plant varieties that yield fruit. Some varieties do well, others do not. All plants need the key drivers of success: good soil, water, sun, etc. So here ...
2
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1answer
62 views

How to predict the risk of an event?

I'm working on a medical problem, where I want to analyze the effect of taking cholesterol medications on the occurrence of heart attack. Once a medication with a specific dosage is prescribed, it'll ...
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304 views

Why is the risk set convex, when we allow for randomized estimators

A randomized estimator $\delta^*(X)$ such that its loss function $L(\theta,\delta^*(x))=\int_\mathcal{D}L(\theta,a)\delta^*(x,a) \ da$, where $\delta^*(x, \cdot)$ is the estimator's density on the ...
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470 views

Value at risk under Student-$t$, skew Student-$t$ and Generalized error distribution

I'm trying to calculate Value-at-risk (VaR) in the context of GARCH models. VaR is defined as the minimum potential loss that a portofolio may suffer in the $x\%$ worst cases over a given horizon. ...
2
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31 views

pruning : why if T1 and T2 (2 subtrees) with the same risk imply that one must be a subree of the other

I don't understand the following assertion from "An Introduction to Recursive Partitioning" page 13. If T1 and T2 are sub trees of T with Rα(T1) = Rα(T2), then either T1 is a sub tree of T2 or ...
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296 views

How to do Hierarchical (Nested) Elliptical Copula simulation sampling

I am doing a project to aggregate about 30 risks into total loss (15 of them are market risks, and 15 of them are insurance risks). The current approach is to simulate millions of scenario with ...
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133 views

Fitting distributions

I have some data on serving sizes of a particular food (raw oysters), and I am trying to determine what probability distribution I should select to model these data for a risk assessment (RA). The R ...
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233 views

What differentiates a population risk model versus Individual risk model?

I am trying to determine why people ask if a model of a health care risk (for inpatient stay, or acquiring a disease or any outcome) is a population risk model or an individual risk model. This is in ...
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217 views

Defining Empirical Risk Minimization

I am reading Machine Learning - A probabilistic Perspective by Kevin Murphy and in chapter 6.5 the author discusses Empirical Risk Minimization, and provides the following definition: $p_*(\mathbf{x},...
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935 views

Monte Carlo calculation of value at risk

I want to calculate the VaR with Monte Carlo Simulation, I am referring to this page: http://financetrain.com/calculating-var-using-monte-carlo-simulation/ which was created to the JP Morgan ...
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53 views

Estimating risk parameters from observed choices

My background is in labor economics/applied micro but I am currently working with data collected from a field experiment. My experimental/micro skills are rusty to say the least. In my data, I ...
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1answer
111 views

Is risk modeling a hypothesis-driven, scientific endeavor?

One could hypothesize that factors x1, x2, x3 predict y. ...
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23 views

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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36 views

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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22 views

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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62 views

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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1answer
17 views

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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17 views

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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41 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 ...
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22 views

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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247 views

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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56 views

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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134 views

RiskMetrics VAR calculations and conditional distribution of sum of log returns

According to Tsay's book in Chapter 7, for the Risk Metrics model: A nice property of such a special random-walk IGARCH model is that the conditional distribution of a multiperiod return is ...
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52 views

Using Keras NN to predict risk

Question What is the best activation to use for a keras NN predicting risk of a single binary outcome? Is it sigmoid? And are there some approaches I can use to ...
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184 views

Why would results from cmprsk differ from those from riskRegression in competing risk analysis?

I have a dataframe with a number of covariates or different types (binary, numeric, factors) and 2 competing outcomes. The presence of one outcome would preclude the occurrence of the other outcome. ...
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141 views

comparison of two estimators

Assume we have a data set $\mathbf{x}_{n} = (x_{1}, \dots, x_{n})$. Let $\delta_{1}(\mathbf{x}_{n})$ and $\delta_{2}(\mathbf{x}_{n})$ be two consistent estimators of some parameter $\theta \in R^{k}$. ...
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116 views

Monte Carlo approach in a distribution of a loss process

I am trying to estimate the next quantity using Monte Carlo method. I have the next well-known quantity called the Crámer-Lundberg risk process, given by the expression $$Y_t=x+ct-Z_t$$ where $Z_t=\...
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47 views

Value-at-Risk Interpretation

Regarding the VaR formula: VaR = -U-ZX Where U is the average return, X is the standard deviation and Z is the negative number of standard deviations that specifies the probability level associated ...
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223 views

definition of Black swan random variables

What's the precise mathematical definition of a black swan random variable? Taleb describes it approximately here(http://highlands.vmhost.psu.edu/_reading/docs/blackswan.pdf), where he describes ...
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120 views

Which country has better road traffic safety, Japan or USA?

This is more a question about how to weigh several statistical numbers. Or, which statiscal measure does exist to properly compare these two countries on this matter of road traffic safety? ...
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0answers
1k views

Cross-Validation and Generalization Error with SVM

Background: I am having some issues generalizing my data in robustness tests. I have a large data set (a little over 6.5 million images) which I am feeding through a CNN-SVM pipeline. The CNN is ...
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89 views

Risk Premium Formula

I was once served the formula below for calculating the risk premium in insurance. The intent is to model the risk premium in two steps, first "capping" claims larger than a certain limit, and then ...
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0answers
35 views

Intensity of fractional Gaussian noise

I try to understand the 2nd formula stated in the picture. It yields the intensity/volatility of an fGN process. It depends solely on H ?? Why is that? How is this volatility different from simply ...
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240 views

Bayesian logit model in Psychometric or Behavioural Testing for Credit Scoring in Developing Countries

A lot of parameters in one title, I know. So there's credit scoring but not using credit history. Then there's using a Bayesian logit model. Then there's doing so in a developing country such as Haiti ...
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70 views

Risk communication and in epidemiology

I have looked at the risk of hospital admission in the general population and in those with lung disease when exposed to an environmental toxin. The patients with lung disease are also part of the ...