The Sensitivity of Detrended Long-Memory Processes

Long-memory tests are often complicated by the presence of deterministic trends. Hence, an additional step of detrending the data is necessary. The typical way to detrend a suspected long-memory series is to use OLS or BSP residuals. Applying the method of sensitivity analysis we address the of question of how robust these residuals are in presence of potential long memory components. Unlike short-memory ARMA process long-memory I(d) processes causes sensitivity to OLS/BSP residuals. Therefore, we develop a finite sample measure of the sensitivity of a detrended series based on the residuals. Based on our sensitivity measure we propose a “rule of thumb” for practitioners to choose between the two methods of detrending, has been provided in this article.     

A note on the generalisation of cochran’s theorem

Khatri (1968) has extended Cochran’s theorem (1934) to matrices which are not necessarily symmetric. An alternative proof of the theorem is furnished here with some generalization with respect to one of Khatri’s conditions.     

A Simple Univariate Outlier Identification Procedure Designed for Large Samples

A simple univariate outlier identification procedure is presented for the detection of multiple outliers in large and moderate sized data sets. This procedure is a modification of the well-known boxplot outlier-labeling rule. Critical values are easy to obtain for the large sample case for a variety of useful distributions, including the normal, t, gamma, and Weibull. Simple adjustment formulas and graphs are provided for handling smaller samples. Basic probability properties are obtained mathematically and through simulation. Two data sets illustrate the procedure's application as a simple and effective screening tool for both moderate and large-sized univariate samples.     

Bayesian analysis of generalized odds-rate hazards models for survival data

In the analysis of censored survival data Cox proportional hazards model (1972) is extremely popular among the practitioners. However, in many real-life situations the proportionality of the hazard ratios does not seem to be an appropriate assumption. To overcome such a problem, we consider a class of nonproportional hazards models known as generalized odds-rate class of regression models. The class is general enough to include several commonly used models, such as proportional hazards model, proportional odds model, and accelerated life time model. The theoretical and computational properties of these models have been re-examined. The propriety of the posterior has been established under some mild conditions. A simulation study is conducted and a detailed analysis of the data from a prostate cancer study is presented to further illustrate the proposed methodology.     

The population characteristics of the East African red legged diplopodMetiche tanganyciense Kraus (Diplopoda: Spirobolidae)

Summary A marked variation exists in the numbers and distribution of East African red legged millipedeMetiche tanganyciense Kraus on the surface and in the lower layer (15 cm) of the soils. Stadia 5 cm and lesser in length are found in the lower layer and those 5 cm and above on the surface soil. Adults are common in varying numbers in both the habitats. It is suggested that after becoming surface active during March–August, and mating, adults migrate to lower layer during September to oviposit. Eggs and early developmental stages are passed here, and when they are 5 cm in length, the stadia move to the surfface soil to complete their development. In keeping with this behaviour, spatial distribution of the adults may change from non-aggregation on surface soil to aggregation in the lower layer. The simulataneous presence of adults and developing stadia in the two habitats suggests and overlapping of generations. This investigation was done while I was in the Department of Entomology, University of Nairobi.     

A JOINT ECONOMIC-LOT-SIZE MODEL FOR PURCHASER AND VENDOR

In a typical purchasing situation, the issues of price, lot sizing, etc., usually are settled through negotiations between the purchaser and the vendor. Depending on the existing balance of power, the end result of such a bargaining process may be a near-optimal or optimal ordering policy for one of the parties (placing the other in a position of significant disadvantage) or, sometimes, inoptimal policies for both parties. This paper develops a joint economic-lot-size model for a special case where a vendor produces to order for a purchaser on a lot-for-lot basis under deterministic conditions. The focus of this model is the joint total relevant cost. It is shown that a jointly optimal ordering policy, together with an appropriate price adjustment, can be beneficial economically for both parties or, at the least, does not place either at a disadvantage.     

Analysis of cure rate survival data under proportional odds model

Due to significant progress in cancer treatments and management in survival studies involving time to relapse (or death), we often need survival models with cured fraction to account for the subjects enjoying prolonged survival. Our article presents a new proportional odds survival models with a cured fraction using a special hierarchical structure of the latent factors activating cure. This new model has same important differences with classical proportional odds survival models and existing cure-rate survival models. We demonstrate the implementation of Bayesian data analysis using our model with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute. Particularly aimed at survival data with cured fraction, we present a novel Bayes method for model comparisons and assessments, and demonstrate our new tool’s superior performance and advantages over competing tools.