Following the approach employed by Casella and Berger (2002) for finding the maximum likelihood estimate of a sample from the nontruncated normal distribution, let us define the following function:

Obtained the maximum likelihood estimates of the ZIP model, we proceeded with the evaluation of the score test, whose statistic defined under [H.sub.0]: p = 0 is given by Equation (8) that asymptotically converges to the chi-square distribution with one degree of freedom.

METHODS: We used a subsampling bootstrap procedure to obtain the maximum likelihood estimates and confidence bounds for common national effects of the criteria pollutants, as measured by the percentage increase in daily mortality associated with a unit increase in daily 24-hr mean pollutant concentration on the previous day, while controlling for weather and temporal trends.

We define the local maximum likelihood estimates for copula models, we argue that they are asymptotically normally distributed, and analytically find their asymptotic variance in the case of Gaussian copulas.

Accuracy Accuracy (%) for (%) Mean Atlantic for GOM accuracy Model Parameters region region (%) Females 2001 Ro, Re, 3, 7, 20 81.7 71.1 76.4 Males 2001 3, 5, 6, 8, 9, 10 69.7 67.6 67.8 Females 2002 P, Ro, 2, 9, 13, 15, 16 67.9 70.8 69.4 Males 2002 P, Re, 2, 8, 11, 13 70.4 61.2 65.8 Table 2 Maximum likelihood estimates (MLE) of the contribution (%) of Atlantic stock king mackerel (Scomberomorus cavalla) to winter landings in each of three south Florida winter sampling zones by sex and year, with 90% bias-corrected confidence intervals (CI) provided.

The maximum likelihood estimate (MLE) per 1,000 mosquitoes tested (bias corrected MLE) was calculated by using software recommended for this purpose by the Centers for Disease Control and Prevention (Atlanta, GA, USA) (26).

Stigler (1977) shows that while Newton did not explicitly use the sampling distribution of the mean or a maximum likelihood estimate, both of these techniques produce intervals almost identical to Newton's, demonstrating that he distinguished between the distribution of the mean and the distribution of the data.

Estimation of one maximum likelihood estimate requires the numerical optimization of a function that sums over all possible configurations of the ancestral sample and typically takes several hours for datasets containing more than 50 individuals.

Bai, Kim and Lee[4] and Miller and Nelson[5] obtained the stress-change time which minimize the asymptotic variance of maximum likelihood estimate of the log scale parameter at the design condition.

That is, if [Mathematical Expression Omitted] is the maximum likelihood estimate (MLE) of x, then the MLE of f(x) is [Mathematical Expression Omitted] (Casella and Berger 1990).

Thus, the maximum likelihood estimate value [??] of the shape parameter [xi] and the maximum likelihood estimate value [??] of the scale parameter [beta] can be obtained from (7).