A goodness of fit test for the multilevel proportional odds model

It is essential to test the goodness of fit of the model before making inferences based on it. Multilevel modeling of ordinal categorical responses is not as developed as for continuous responses. Assessing model adequacy in terms of the goodness of fit with ordinal categorical responses is still being developed and no satisfactory tests are available so far. As a consequence of that, this study concentrates on developing such a goodness of fit test for Multilevel Proportional Odds models and to study the properties of the test.     

Infill asymptotics for adaptive kernel estimators of spatial intensity

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.     

Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard-adjusted likelihood ratio statistics, which follow a chi-squared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behaviour as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Project on cardiovascular disease.     

Comparing diagnostic tests: test of hypothesis for likelihood ratios

Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.     

Estimation of weibull location

A simulation study was carried out to compare the performances of two different simple estimators of the location parameter for a three-parameter Weibull distribution Both Estimators have been suggested by recent paper in the literature. Bras and mean square error are examined for many different sample-size and shape-parameter-value combinations. Strong evidence of the domination of one estimator over the other is found.     

Testing equality of variances for several normal populations

In this study, we develop a test based on computational approach for the equality of variances of several normal populations. The proposed method is numerically compared with the existing methods. The numeric results demonstrate that the proposed method performs very well in terms of type I error rate and power of test. Furthermore we study the robustness of the tests by using simulation study when the underlying data are from t, exponential and uniform distributions. Finally we analyze a real dataset that motivated our study using the proposed test.     

Tail Behavior and Limit Distribution of Maximum of Logarithmic General Error Distribution

Logarithmic general error distribution, an extension of the log-normal distribution, is proposed. Some interesting properties of the log GED are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and log-normal distributions, and to derive the asymptotic distribution of the partial maximum of an independent and identically distributed sequence obeying the log GED.     

A new estimator of proportion with a linear function using data from two-decks randomized response model

A new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced by solving a linear equation. The proposed estimator has been compared with the estimator proposed by Odumade and Singh (2009) with equal protection to all of the respondents. The asymptotic properties of the proposed estimator are investigated through exact numerical illustrations for different choices of parameters. A non randomized response approach has been suggested. A scope for further research has also been pointed out.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.     

Conditional covariance penalties for mixed models

The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods, cross-validation, and a direct approach called Steinian. The behavior of the different estimation techniques is assessed in a simulation study for the binomial-, the t-, and the gamma distribution and for different kinds of prediction error. Furthermore, the impact of the estimation techniques on the prediction error is discussed based on an application to undernutrition in Zambia.