Local Polynomial Method Research Articles

More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors

We propose a modification of local polynomial time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that must be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. We show that the proposed estimation procedure is more efficient than the conventional local polynomial method. We also provide simulation evidence to suggest that gains can be achieved in moderate-sized samples.

Hepatitis B in St Petersburg, Russia (1994-1999): incidence, prevalence and force of infection.

Hepatitis B (HB) is thought to be an expanding health problem in Russia. The incidence of infection was estimated from mandatorily reported HB cases in St Petersburg. The two-sided t-test for independent samples and the LOESS (locally-weighted regression) smoother were used to compare the age at infection for symptomatic, asymptomatic and chronic infections, by gender. The force of infection was estimated from seroprevalence data (907 sera taken in 1999) using a newly developed nonparametric method based on local polynomials, as well as an earlier method based on isotonic regression and kernel smoothers. With the local polynomial method, pointwise confidence intervals (95%) were constructed by bootstrapping. On average, men contracted HB infection at a significantly younger age than women (in 1999, 21.8 vs 22.7 years, respectively). The overall male to female ratio was 1.92. In 1999 the overall incidence almost doubled compared with the preceding years and tripled among the age groups with highest incidence (15-29-year olds: 85% of cases in 1999). The incidence increase was associated with a lower average age at infection (24.1 years in 1994 vs 22.1 years in 1999). The age and gender-specific force of infection estimates generally confirmed the incidence estimates and emphasized the usefulness of local polynomials to do this. Hence HB transmission in St Petersburg occurs mainly in young adults. The dramatic increase of infections in 1999 was probably due to injecting drug use. Without intervention, HB virus is expected to continue to spread rapidly with a greater proportion of female infections caused by sexual transmission. These trends may also provide an indication for HIV transmission.