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Econometrics Procedures
 

The SEVSELECT Procedure

Overview: SEVSELECT Procedure

The SEVSELECT procedure estimates parameters of any arbitrary continuous probability distribution that is used to model the magnitude (severity) of a continuous-valued event of interest. Examples of such events include loss amounts paid by an insurance company and demand of a product as depicted by its sales. PROC SEVSELECT is especially useful when the severity of an event does not follow typical distributions (such as the normal distribution) that are often assumed by standard statistical methods.

PROC SEVSELECT provides a default set of probability distribution models that includes the Burr, exponential, gamma, generalized Pareto, inverse Gaussian (Wald), lognormal, Pareto, Tweedie, and Weibull distributions. In the simplest form, you can estimate the parameters of any of these distributions by using a list of severity values that are recorded in a data table. You can optionally group the values by a set of BY variables. PROC SEVSELECT computes the estimates of the model parameters, their standard errors, and their covariance structure by using the maximum likelihood method for each of the BY groups.

PROC SEVSELECT can fit multiple distributions at the same time and choose the best distribution according to a selection criterion that you specify. You can use seven different statistics of fit as selection criteria. They are log likelihood, Akaike’s information criterion (AIC), corrected Akaike’s information criterion (AICC), Schwarz Bayesian information criterion (SBC), Kolmogorov-Smirnov statistic (KS), Anderson-Darling statistic (AD), and Cramér–von Mises statistic (CvM).

You can request that the procedure output different types of diagnostic and inferential results, including the summary statistics of analysis variables, progress and status of the nonlinear estimation process, parameter estimates and their standard errors, estimated covariance structure of the parameters, and statistics of fit.

The following key features make PROC SEVSELECT unique among SAS procedures that can estimate continuous probability distributions:

  • It enables you to fit a distribution model when the severity values are truncated, censored, or both. You can specify any combination of the following types of censoring and truncation effects: left-censoring, right-censoring, left-truncation, or right-truncation. This is especially useful in applications with an insurance-type model, where a severity (loss) is reported and recorded only if it is greater than the deductible amount (left-truncation) and where a severity value greater than or equal to the policy limit is recorded at the limit (right-censoring). Another useful application is that of interval-censored data, where you know both the lower limit (right-censoring) and upper limit (left-censoring) on the severity, but you do not know the exact value.

    PROC SEVSELECT also enables you to specify a probability of observability for the left-truncated data, which is a probability of observing values greater than the left-truncation threshold. This additional information can be useful in certain applications to more correctly model the distribution of the severity of events.

  • It uses an appropriate estimator of the empirical distribution function (EDF). EDF is required to compute the KS, AD, and CvM statistics of fit. The procedure also provides the EDF estimates to your custom parameter initialization method. When you specify truncation or censoring, the EDF is estimated by using either Kaplan-Meier’s product-limit estimator or Turnbull’s estimator. The former is used by default when you specify only one form of censoring effect (right-censoring or left-censoring), and the latter is used by default when you specify both left-censoring and right-censoring effects.

  • It enables you to define any arbitrary continuous parametric distribution model and to estimate its parameters. You just need to define the key components of the distribution, such as its probability density function (PDF) and cumulative distribution function (CDF), as a set of functions and subroutines written with the FCMP procedure, which is part of Base SAS software. As long as the functions and subroutines follow certain rules, the SEVSELECT procedure can fit the distribution model defined by them.

  • It can model the influence of exogenous or regressor variables on a probability distribution, as long as the distribution has a scale parameter. A linear combination of regression effects is assumed to affect the scale parameter via an exponential link function. This type of model is referred to as the scale regression model.

    If a distribution does not have a scale parameter, then either it needs to have another parameter that can be derived from a scale parameter by using a supported transformation or it needs to be reparameterized to have a scale parameter. If neither of these is possible, then regression effects cannot be modeled.

    You can easily specify many types of regression effects by using various operators on a set of classification and continuous variables. You can specify classification variables in the CLASS statement. You can also construct the following special effects by using the EFFECT statement: collection effects, multimember effects, polynomial effects, and spline effects.

    If you specify a large number of regression effects, then you can use the SELECTION statement to tell PROC SEVSELECT to perform scale regression model selection.

  • It enables you to specify your own objective function to be optimized for estimating the parameters of a model. You can write SAS programming statements to specify the contribution of each observation to the objective function. You can use keyword functions such as _PDF_ and _CDF_ to generalize the objective function to any distribution. If you do not specify your own objective function, then PROC SEVSELECT estimates the parameters of a model by maximizing the likelihood function of the data.

  • It enables you to create scoring functions that offer a convenient way to evaluate any distribution function, such as PDF, CDF, QUANTILE, or your custom distribution function, for a fitted model on new observations.

PROC SEVSELECT is the next-generation version of PROC HPSEVERITY. It requires SAS Cloud Analytic Services (CAS) in order to run. Because PROC SEVSELECT is a next-generation high-performance analytical procedure, it also does the following:

  • enables you to run on a cluster of machines that distribute the data and the computations

  • exploits all the available cores and concurrent threads

Last updated: January 27, 2023