On Constructing Optimum Strata and Determining Optimum Allocation

The problem of constructing optimum stratum boundaries (OSB) and the problem of determining sample allocation to different strata are well known in the sampling literature. To increase the efficiency in the estimates of population parameters these problems must be addressed by the sampler while using stratified sampling. There were several methods available to determine the OSB when the frequency distribution of the study (or its related) variable is known. Whereas, the problem of determining optimum allocation was addressed in the literature mostly as a separate problem assuming that the strata are already formed and the stratum variances are known. However, many of these attempts have been made with an unrealistic assumption that the frequency distribution and the stratum variances of the target variable are known prior to conducting the survey. Moreover, as both the problems are not addressed simultaneously, the OSB and the sample allocation so obtained may not be feasible or may be far from optimum. In this paper, the problems of finding the OSB and the optimum allocation are discussed simultaneously when the population mean of the study variable y is of interest and its frequency distribution f(y) or the frequency distribution f(x) of its auxiliary variable x is available. The problem is formulated as a Nonlinear Programming Problem (NLPP) that seeks minimization of the variance of the estimated population parameter of the target variable, which is subjected to a fixed total sample size. The formulated NLPP is then solved by executing a program coded in a user’s friendly software, LINGO. Two numerical examples, when the study variable or its auxiliary variable has respectively a uniform and a right-triangular distribution in the population, are presented to demonstrate the practical application of the proposed method and its computational details. The proposed technique can easily be applied to other frequency distributions

Optimal Stratification of Univariate Populations via stratify R Package

Stratification reduces the variance of sample estimates for population parameters by creating homogeneous strata. Often, surveyors stratify the population using the most convenient variables such as age, sex, region, etc. Such convenient methods often do not produce internally homogeneous strata, hence, the precision of the estimates of the variables of interest could be further improved. This paper introduces an R-package called ’stratifyR’ whereby it proposes a method for optimal stratification of survey populations for a univariate study variable that follows a particular distribution estimated from a data set that is available to the surveyor. The stratification problem is formulated as a mathematical programming problem and solved by using a dynamic programming technique. Methods for several distributions such as uniform, weibull, gamma, normal, lognormal, exponential, right-triangular, cauchy and pareto are presented. The package is able to construct optimal stratification boundaries (OSB) and calculate optimal sample sizes (OSS) under Neyman allocation. Several examples, using simulated data, are presented to illustrate the stratified designs that can be constructed with the proposed methodology. Results reveal that the proposed method computes OSB that are precise and comparable to the established methods. All the calculations presented in this paper were carried out using the stratifyR package that will be made available on CRAN

Distribution of coconut stick insect, Graeffea crouanii and its parasitoids in selected islands of Fiji

The Coconut stick insect, Graeffea crouanii (Le Guillou)(Orthoptera: Phasmidae), known as “mimimata” in Fiji, is a widespread economic pest of coconut palms in Fiji and in many Pacific Island countries. The nymphs and adults stages of pest are polyphagous, but prefer coconut palms.This paper reveals findings from the surveys conducted between 2009 and 2012 during the field work in selected islands of Fiji, and discusses needed research to enhance natural-mortality control mechanisms. Preliminary studies of G. crouanii in selected islands of Fiji (Viti Levu, Vanua Levu and Taveuni) showed that the pest was localised and abundant in areas with low temperature, which was also statistically proven.The pest was found to be feeding on leaves with damage starting from tip and ends up leaving only the midribs. The older fronds had more damage than new frond due to longest pest exposure. The two elasmid egg parasitoids in Fiji, Paranastatus verticalis and Paranastatus nigriscutellatus of order Hymenoptera have potential as a biological control agent. This study on the G. crouanii in Fiji provides significant recommendations for further management of G. crouanii in coconut farms

Distribution of surface sediments off Indus delta on the continental shelf of Pakistan

Surface sediments from the continental shelf area off Indus delta were analysed for their textural characteristics and carbonate content. The sediments are largely silt, silty clay and clayey silty sand. Sandy fraction is dominant in the outer region with relatively high carbonate content. The study shows that distribution of carbonate in sediments off Indus delta continental shelf is controlled by the dilution of terrigenous material and its distance from source area

Assessment of sugarcane varieties for their stability and yield potential in Fiji

The Sugar Research Institute of Fiji breeds and produces new varieties of sugarcane for the Fiji sugar industry for commercial production. The development of sugar cane varieties that show superior performance in different environments is a major challenge for breeders due to the response of genotypes across environments. This study was to evaluate the relative performance the genotypes during breeding program and identify promising ones that could be released for cultivation. Thus, an investigation was carried out to determine the magnitude of Genotype Environment interactions and the stability analysis of the genotypes cultivated in Fiji. Seventeen genotypes including three commercial varieties were evaluated in five locations using a randomized block design with three replications. The pooled analysis of variance carried out for the effect of environments, genotypes, and their interactions. The stability analysis was also performed using the Eberhart & Russell’s (1966) model. Further, a cluster analysis was proposed for identifying the similar and stable genotypes. The results showed that there were highly significant (p < 0.001) variations among the genotypes (G), environments (E) and GE interactions. Two genotypes LF82-2122 and LF60-3917 had higher yield and stability statistics for the two most important traits: cane and sugar yields. Thus, the genotypes can be recommended for adoption and cultivation on all soil types in Fiji

Are students studying in the online mode faring as well as students studying in the face - to - face mode? Has equivalence in learning been achieved?

With the shift in pedagogy from learning in the traditional classroom setting (face-to face mode) to online learning, it is important to find out how students are faring in the online mode and if equivalence in learning is achieved in the two modes. To answer these questions, the course results of students studying a first year undergraduate mathematics course in the two different modes at The University of the South Pacific were compared. The study revealed that there was no statistical significant difference in the pass rates of the students studying in the two modes but the students studying in the online mode had a significantly higher attrition rate. From the results, it was also discovered that students studying via the online mode achieved higher coursework marks but lower exam marks compared to students studying via the face to-face mode. Yet the students’ total marks in the two modes were similar, which led to the conclusion that students studying in the online mode are faring just as well as students studying in the face-to-face mode. It was evident that equivalent learning was occurring in the two modes albeit in different ways. The coursework assessments methods in the two modes were also compared

On optimum stratification

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique

The relationship between South Asian stock returns and macroeconomic variables

This article investigates whether economic variables have explanatory power for share returns in South Asian stock markets. In particular, using data for four South Asian emerging stock markets over the period 1998 – 2012, the article examines the influence of a selection of local, regional and global economic variables in explaining equity returns; most previous studies that have examined this issue have tended to focus on only local and/or global factors. Important factors are identified by distilling the macroeconomic variables into principal components. Economic activities, real interest rates, real exchange rates and the trade balance represent local factors. Regional factors are represented by inter-regional trade and regional economic activity while global factors are represented by world financial asset returns and world economic activity. The Vector Autoregression results suggest that the South Asian markets examined are not efficient. Both local and regional factors can directly and indirectly explain Bangladeshi, Pakistani and Sri Lankan stock returns while the lagged returns of the Pakistani stock market and world economic activity can explain Indian stock returns

A Goal Programming Approach: Multi-objective Optimization

The purpose of this paper is to accentuate the development of multi-objective non-linear programming (MONLP) technique and its advantages of applying to numerical problems. In particular, non-linear programming model is the process of solving an optimization problem defined by a system of inequalities along with an objective function of several variables that exist in various fields. In certain instances, there are situations in these fields where multiple objectives are required to be achieved simultaneously, owing to limited timeframe and convenience of budget. The Multi-objective programming under non-linear conditions and the solution procedure on the goal programming approach is embedded with algorithm and the relevant technique is developed. Numerical examples, specifically, multi-objective quadratic programming problem and examples of other multi-objective non-linear programming problem are presented to illustrate practical use and the computational details of the proposed procedure. The proposed goal programming technique is then solved using a user-friendly optimization software LINGO

Latent Embedding Feedback and Discriminative Features for Zero-Shot Classification

© 2020, Springer Nature Switzerland AG. Zero-shot learning strives to classify unseen categories for which no data is available during training. In the generalized variant, the test samples can further belong to seen or unseen categories. The state-of-the-art relies on Generative Adversarial Networks that synthesize unseen class features by leveraging class-specific semantic embeddings. During training, they generate semantically consistent features, but discard this constraint during feature synthesis and classification. We propose to enforce semantic consistency at all stages of (generalized) zero-shot learning: training, feature synthesis and classification. We first introduce a feedback loop, from a semantic embedding decoder, that iteratively refines the generated features during both the training and feature synthesis stages. The synthesized features together with their corresponding latent embeddings from the decoder are then transformed into discriminative features and utilized during classification to reduce ambiguities among categories. Experiments on (generalized) zero-shot object and action classification reveal the benefit of semantic consistency and iterative feedback, outperforming existing methods on six zero-shot learning benchmarks. Source code at https://github.com/akshitac8/tfvaegan