## How is Martingale residual calculated?

Martingale residuals rMi can be defined as rMi=δi−rCi where δi is a switch taking the value 0 if observation i is censored and 1 if observation i is uncensored. Martingale residuals take a value between [1,−∞] for uncensored observations and [0,−∞] for censored observations.

## What assumption needs to be checked for the Cox proportional hazards?

The Cox proportional hazards model makes two assumptions: (1) survival curves for different strata must have hazard functions that are proportional over the time t and (2) the relationship between the log hazard and each covariate is linear, which can be verified with residual plots.

What are residuals in linear regression?

The difference between an observed value of the response variable and the value of the response variable predicted from the regression line.

What is Schoenfeld test?

The Schoenfeld Residuals Test is used to test the independence between residuals and time and hence is used to test the proportional Hazard assumption in Cox Model. One of key assumptions in the Cox Proportional Hazard model is that of proportional hazards.

### How do you test a martingale?

The useful property of martingales is that we can verify the martingale property locally, by proving either that E[Xt+1|ℱt] = Xt or equivalently that E[Xt+1 – Xt|ℱt] = E[Xt+1|ℱt] – Xt = 0. But this local property has strong consequences that apply across long intervals of time, as we will see below.

### What is martingale test?

The martingale test com- monly applied in a risk neutral ESG, referred to as the standard martingale test hereinafter, consists in testing that the mean of discounted asset prices is equal to the time zero asset price (simply put, the mean of the discounted asset prices is constant over time).

What are Cox Snell residuals?

Cox-Snell residuals are a type of standardized residuals used in reliability analysis. A residual is the difference between an observed data point and a predicted or fitted value. A Cox-Snell residual considers the distribution and estimated parameters from the lifetime regression model.

How do you interpret Cox proportional hazards?

If the hazard ratio is less than 1, then the predictor is protective (i.e., associated with improved survival) and if the hazard ratio is greater than 1, then the predictor is associated with increased risk (or decreased survival).

#### What does the residual tell you?

A residual is a measure of how far away a point is vertically from the regression line. Simply, it is the error between a predicted value and the observed actual value. Figure 1 is an example of how to visualize residuals against the line of best fit. The vertical lines are the residuals.

#### How do you find the residual in a linear regression?

Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low. The aim of a regression line is to minimise the sum of residuals.

What is Schoenfeld residuals used for?

Schoenfeld residuals are used to test the assumption of proportional hazards. Schoenfeld residuals “can essentially be thought of as the observed minus the expected values of the covariates at each failure time” (Steffensmeier & Jones, 2004: 121). There is a Schoenfeld residual for each subject for each covariate.

What is a Schoenfeld residual?

Schoenfeld residuals. The Schoenfeld residual is defined as the covariate value for the individual that failed minus its expected value. (Yields residuals for each individual who failed, for each covariate).