Robust ridge estimation methods for predicting u. s. coal mining fatalities

Abstract

FOR PREDICTING U . S. COAL MINING FATALITIES AThT B e d m i n s t e r , N J 07921 Lawrence C . Marsh U n i v e r s i t y of N o t r e Dame N o t r e Dame, I N 46556 Key Words and Phrases: rnuZticoZZinearity; robust regression; ridge regression; o u t l i e r s ; robust veighting. ABSTRACT T h i s p a p e r compares a l t e r n a t i v e c o m b i n a t i o n s o f r i d g e r e g r e s s i o n and r o b u s t r e g r e s s i o n t e c h n i q u e s i n p r e d i c t i n g f a t a l i t i e s i n t h e U.S. c o a l m i n i n g i n d u s t r y . The combined r o b u s t r i d g e a p p r o a c h is needed b e c a u s e of t h e s i m u l t a n e o u s o c c u r r e n c e of m u l t i c o l l i n e a r i t y and o u t l i e r s i n t h e d a t a . Not s u r p r i s i n g l y , t h e r e l a t i v e e f f e c t i v e n e s s of d i f f e r e n t r i d g e e s t i m a t o r s i n p r e d i c t i n g c o a l m i n i n g f a t a l i t i e s i s found t o b e d e p e n d e n t upon t h e p a r t i c u l a r c h o i c e of t h e r o b u s t w e i g h t i n g scheme employed.

Robust Ridge Regression Based on an M‐estimator

“…In the next section we define a ridge-type M-estimator and investigate its properties. The robust ridge estimators in Ercil (1985), Holland (1973) and Lawrence & Marsh (1984) are somewhat similar to our ridge-type Mestimator. Section 3 reports the results of a simulation study investigating the MSE properties of our estimator.…”

“…This paper introduces a new class of ridge-type estimators which have good MSE properties compared to the ordinary ridge estimators when the errors have long tails. The problem of obtaining ridge-type estimators which are not very sensitive to outliers in the y-variable has been discussed by Askin & Montgomery (1980, Ercil (1985), Holland (1973), Lawrence & Marsh (1984), Askin (1981), andPa.riente &Welsch (1977). The small sample MSE properties of the estimators proposed in these articles are yet to be evaluated, for example, by simulation studies; such studies are very important since hardly any analytical results are available for them.…”

The Analysis of Fatal Accidents in Indian Coal Mines

“…Thus, in Sections 3-6, we consider the effects of four categorical variables, taking one variable at a time. In Section 7 we look for a single regression model that incorporates all these variables, starting with a model similar to that used by Lawrence and Marsh (1984). In this section we look for the partial effects of each factor mentioned above in the presence of the other factors.…”

A Combined Biased-Robust Estimator for Dealing with Influence and Collinearity in Regression

“…Pfaffenberger and Dieiman (1984) used a similar approach but replaced the M-estimate with LAV estimation. Lawrence and Marsh (1984), Askin and Montgomery (1984), and Pfaffenberger and Dielman (1990) The approach suggested by Hogg (1979) and Askin and Montgomery (1980) A natural extension of augmented robust estimators are augmented bounded-influence estimators (Walker, 1987). The estimator in this case is the solution to min p(y, -)X,…”

“…Relative to the amount of research in biased-only and robust-only techniques, the research in biased-robust regression has been sparse. Most of the advances in this area have been made in the last two decades by Holland (1973), Pariente and Welsch (1977), Hogg (1979), Askin and Montgomery (1980) Montgomery and Askin (1981), Pfaffenberger and Dielman (1984), Lawrence and Marsh (1984), Walker andBirch (1985, 1988), Walker (1987). Askin and Montgomery (1984) and Pfaffenberger and Dielman (1990) have followed up the development of their techniques by performing Monte Carlo simulation studies to compare various approaches.…”