Robust model-based sampling designs

We investigate methods for the design of sample surveys, and address the traditional resistance of survey samplers to the use of model-based methods by incorporating model robustness at the design stage. The designs are intended to be sufficiently flexible and robust that resulting estimates, based on the designer’s best guess at an appropriate model, remain reasonably accurate in a neighbourhood of this central model. Thus, consider a finite population of N units in which a survey variable Y is related to a q dimensional auxiliary variable x. We assume that the values of x are known for all N population units, and that we will select a sample of n≤N population units and then observe the n corresponding values of Y. The objective is to predict the population total $T=\sum_{i=1}^{N}Y_{i}$ . The design problem which we consider is to specify a selection rule, using only the values of the auxiliary variable, to select the n units for the sample so that the predictor has optimal robustness properties. We suppose that T will be predicted by methods based on a linear relationship between Y—possibly transformed—and given functions of x. We maximise the mean squared error of the prediction of T over realistic neighbourhoods of the fitted linear relationship, and of the assumed variance and correlation structures. This maximised mean squared error is then minimised over the class of possible samples, yielding an optimally robust (‘minimax’) design. To carry out the minimisation step we introduce a genetic algorithm and discuss its tuning for maximal efficiency.     

A comparison of several analysis of variance programs with unequal cell size

Various programs in statistical packages for analysis of variance with unequal cell size give different results to the same data because of nonorthogonality of the main effects and interactions. This paper explains how these programs treat the problem of analysis of variance of unbalanced data.     

Multinomial Selection Problem: A Study of BEM and AVC Algorithms

The two well-known and widely used multinomial selection procedures Bechhofor, Elmaghraby, and Morse (BEM) and all vector comparison (AVC) are critically compared in applications related to simulation optimization problems.

Two configurations of population probability distributions in which the best system has the greatest probability p _i of yielding the largest value of the performance measure and has or does not have the largest expected performance measure were studied.

The numbers achieved by our simulations clearly show that none of the studied procedures outperform the other in all situations. The user must take into consideration the complexity of the simulations and the performance measure probability distribution properties when deciding which procedure to employ.

An important discovery was that the AVC does not work in populations in which the best system has the greatest probability p _i of yielding the largest value of the performance measure but does not have the largest expected performance measure.     

Selecting a Good Stochastic System for the Large Number of Alternatives

In this article, we present the problem of selecting a good stochastic system with high probability and minimum total simulation cost when the number of alternatives is very large. We propose a sequential approach that starts with the Ordinal Optimization procedure to select a subset that overlaps with the set of the actual best m% systems with high probability. Then we use Optimal Computing Budget Allocation to allocate the available computing budget in a way that maximizes the Probability of Correct Selection. This is followed by a Subset Selection procedure to get a smaller subset that contains the best system among the subset that is selected before. Finally, the Indifference-Zone procedure is used to select the best system among the survivors in the previous stage. The numerical test involved with all these procedures shows the results for selecting a good stochastic system with high probability and a minimum number of simulation samples, when the number of alternatives is large. The results also show that the proposed approach is able to identify a good system in a very short simulation time.     

Sequential Pattern Analysis: A Statistical Investigation of Sequence Length and Support

In sequential pattern analysis, the frequency of patterns is evaluated by the support. While computed efficiently from large databases, we show that the support cannot be compared between different databases, since it is influenced by the actual sequence length distribution. Models for this sequence length distribution are surveyed. One of these models, the Good distribution, appears to be sufficiently flexible for practice. It is used to exemplify an approach for adjusting the relative support such that the resulting adjusted support values are better comparable between different databases. We illustrate our findings with texts from the bilingual FinDe corpus.     

Clustering of seasonal events: A simulation study using circular methods

ABSTRACT

In a changing climate, changes in timing of seasonal events such as floods and flowering should be assessed using circular methods. Six different methods for clustering on a circle and one linear method are compared across different locations, spreads, and sample sizes. Best results are obtained when clusters are well separated and the number of observations in each cluster is approximately equal. Simulations of flood-like distributions are used to assess and explore clustering methods. Generally, k-means provides results that are close to the expected results, some other methods perform well under specific conditions, but no single method is exemplary.     

The modified permutation entropy-based independence test of time series

Abstract

In time series, it is essential to check the independence of data by means of a proper method or an appropriate statistical test before any further analysis. Therefore, among different independence tests, a powerful and productive test has been introduced by Matilla-García and Marín via m-dimensional vectorial process, in which the value of the process at time t includes m-histories of the primary process. However, this method causes a dependency for the vectors even when the independence assumption of random variables is considered. Considering this dependency, a modified test is obtained in this article through presenting a new asymptotic distribution based on weighted chi-square random variables. Also, some other alterations to the test have been made via bootstrap method and by controlling the overlap. Compared with the primary test, it is obtained that not only the modified test is more accurate but also, it possesses higher power.     

Parameter estimation by minimizing a probability generating function-based power divergence

Abstract

Generating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases.