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Classical continuous goodness-of-fit (GOF) testing is employed for examining whether the data come from an assumed parametric model. In many cases, GOF tests assume a uniform null distribution and examine extreme values of the order statistics of the samples. Many of these statistics can be expressed by a function of the order statistics and the p-values amount to a joint probability statement based on the uniform order statistics. In this paper, we utilize Steck's recursion method and propose two high precision computing algorithms to compute the p-values for these GOF statistics. The numerical difficulties in implementing Steck's method are discussed and compared with solutions provided in high precision libraries. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) design as a cost-effective sampling is a powerful tool in situations where measuring the variable of interest is costly and time-consuming; however, ranking information about sampling units can be obtained easily through inexpensive and easy to measure characteristics at little or no cost. In this paper, we study RSS data for analysis of an ordinal population. First, we compare the problem of non-representative extreme samples under RSS and commonly-used simple random sampling. Using RSS data with tie information, we propose non-parametric and maximum likelihood estimators for population parameters. Through extensive numerical studies, we investigate the effect of various factors including ranking ability, tie generating mechanisms, the number of categories and population setting on the performance of the estimators. Finally, we apply the proposed methods to the bone disorder data to estimate the proportions of patients with osteopenia and osteoporosis status. [ABSTRACT FROM AUTHOR]

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques – at least when multicollinearity exist among the regressors. [ABSTRACT FROM AUTHOR]

Before releasing survey data, statistical agencies usually perturb the original data to keep each survey unit's information confidential. One significant concern in releasing survey microdata is identity disclosure, which occurs when an intruder correctly identifies the records of a survey unit by matching the values of some key (or pseudo-identifying) variables. We examine a recently developed post-randomization method for a strict control of identification risks in releasing survey microdata. While that procedure well preserves the observed frequencies and hence statistical estimates in case of simple random sampling, we show that in general surveys, it may induce considerable bias in commonly used survey-weighted estimators. We propose a modified procedure that better preserves weighted estimates. The procedure is illustrated and empirically assessed with an application to a publicly available US Census Bureau data set. [ABSTRACT FROM AUTHOR]

The case of size-biased sampling of known order from a finite population without replacement is considered. The behavior of such a sampling scheme is studied with respect to the sampling fraction. Based on a simulation study, it is concluded that such a sample cannot be treated either as a random sample from the parent distribution or as a random sample from the corresponding r-size weighted distribution and as the sampling fraction increases, the biasness in the sample decreases resulting in a transition from an r-size-biased sample to a random sample. A modified version of a likelihood-free method is adopted for making statistical inference for the unknown population parameters, as well as for the size of the population when it is unknown. A simulation study, which takes under consideration the sampling fraction, demonstrates that the proposed method presents better and more robust behavior compared to the approaches, which treat the r-size-biased sample either as a random sample from the parent distribution or as a random sample from the corresponding r-size weighted distribution. Finally, a numerical example which motivates this study illustrates our results. [ABSTRACT FROM AUTHOR]