In computerized adaptive testing, updating parameter estimates using adaptive testing data is often called online calibration. In this paper, how to evaluate whether the adaptive testing model used for online calibration fits the item response model used sufficiently is studied. Three approaches are investigated, based on a Lagrange multiplier (LM) statistic (J. Aitchison and S. Silvey, 1958), ...

A measure of closeness among three or more means from normal populations was proposed by Ng (2000). The F-statistic was proposed to test the null hypothesis that this measure of closeness is greater than or equal to some prespecified δ (>0), against the alternative hypothesis that this measure of closeness is smaller than δ. The null distribution of the F-statistic at the boundary has a non-cen...

Kulldorff’s spatial scan statistic and the software implementation (SaTScan) are widely used for the detection and evaluation of geographic clusters, particularly within the health care community. Unfortunately, the computational time of the scan statistic depends on a wide variety of variables, and, depending on the chosen parameter settings and operations, the computational time can be on the...

A. Distribution of the test statistic In the sequential test, we first compute the test statistic from a mini-batch of size m. If a decision cannot be made with this statistic, we keep increasing the mini-batch size by m datapoints until we reach a decision. This procedure is guaranteed to terminate as explained in Section 4. The parameter ✏ controls the probability of making an error in a sing...

The main purpose of statistical inference is 1. to estimate the parameters(the quantities that represent a particular characteristic of a population) on the basis of sample observations through a statistic ( a function of sample values which does not involve any parameter). (Theory of Estimation). 2. to compare these parameters among themselves on the basis of observations and their estimates (...

In this study, the residuals in time series analysis, which were classified in four different classes as ”conditional residuals”, ”unconditional residuals”, ”innovation” and ”normalized residuals”, are calculated by a simulation study for the ARMA model under certain parameter values for different numbers of observation and their conditions in diagnostic checking are examined using the test sta...

Solutions to the Thirring model are constructed in the framework of algebraic quantum field theory. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is λ = √ 2(2n+ 1)π, n ∈ N. These fermions are inequivalent and only for n = 1 they are canonical fields. In the general case solutions are anyons. Different anyons (which are uncountably man...

A dynamical system model for tumor-immune system interaction together with a method to mimic radiation therapy are proposed. A large population of virtual patients is simulated following an ideal radiation treatment. The dependency of the results on system parameter values is studied. Conclusions for treatment optimization and patient classification are drawn from the statistic treatment of the...

flood frequency analysis is faced with the problem of data and information limitation in arid and semi-arid regions. particularly in these regions, the length of records is usually too short to ensure reliable quantile estimates. more than 75% of iran is located in arid and semi-arid regions and despite the low annual precipitation, often large floods occur. one way to provide more information ...