Dverview and Main Advances in Permutation Tests for Linear Regression Models

When the population, from which the samples are extracted, is not normally distributed, or if the sample size is particularly reduced, become preferable the use of not parametric statistic test. An alternative to the normal model is the permutation or randomization model. The permutation model is nonparametric because no formal assumptions are made about the population parameters of the reference distribution, i.e., the distribution to which an obtained result is compared to determine its probability when the null hypothesis is true. Typically the reference distribution is a sampling distribution for parametric tests and a permutation distribution for many nonparametric tests. Within the regression models, it is possible to use the permutation tests, considering their ownerships of optimality, especially in the multivariate context and the normal distribution of the response variables is not guaranteed. In the literature there are numerous permutation tests applicable to the estimation of the regression models. The purpose of this study is to examine different kinds of permutation tests applied to linear models, focused our attention on the specific test statistic on which they are based. In this paper we focused our attention on permutation test of the independent variables, proposed by Oja, and other methods to effect the inference in non parametric way, in a regression model. Moreover, we show the recent advances in this context and try to compare them.

SADDLEPOINT APPROXIMATIONS TO THETWO-SAMPLE PERMUTATION TESTS

A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.

Single-trial EEG-based emotion recognition using temporally regularized common spatial pattern

This study addresses the problem of classifying emotional words based on recorded electroencephalogram （EEG） signals by the single-trial EEG classification technique. Emotional two-character Chinese words are used as experimental materials. Positive words versus neutral words and negative words versus neutral words are classified, respectively, using the induced EEG signals. The method of temporally regularized common spatial patterns （TRCSP） is chosen to extract features from the EEG trials, and then single-trial EEG classification is achieved by linear discriminant analysis. Classification accuracies are between 55% and 65%. The statistical significance of the classification accuracies is confirmed by permutation tests, which shows the successful identification of emotional words and neutral ones, and also the ability to identify emotional words. In addition, 10 out of 15 subjects obtain significant classification accuracy for negative words versus neutral words while only 4 are significant for positive words versus neutral words, which demonstrate that negative emotions are more easily identified.

Diversity, composition and host-species relationships of epiphytic orchids and ferns in two forests in Nepal

Epiphytic plant species are an important part of biological diversity. It is therefore essential to understand the distribution pattern and the factors influencing such patterns. The present study is aimed at observing the patterns of species richness, abundances and species composition of epiphytic orchids and ferns in two subtropical forests in Nepal. We also studied the relationship of host plants(Schima wallichii and Quercus lanata) and epiphyte species. Data were collected in Naudhara community forest(CF) and the national forest(NF) in Shivapuri Nagarjun National Park. The data were analyzed using univariate and multivariate tests. In total, we recorded 41 species of epiphytes(33 orchid and 8 fern species). Orchid species abundance is significantlyhigher in CF compared to NF. Orchid species richness and abundance increased with increasing southern aspect whereas it decreased with increasing canopy cover, and fern species richness increased with host bark roughness. Orchid abundance was positively correlated with increasing bark p H, stem size, tree age and tree height and negatively correlated with increasing steepness of the area. Likewise, fern abundances were high in places with high canopy cover, trees that were tall and big, but decreased with increasing altitude and southern aspect. The composition of the orchid and fern species was affected by altitude, aspect, canopy cover, DBH, number of forks and forest management types. We showed that the diversity of orchid and fern epiphytes is influenced by host characteristics as well as host types. The most important pre-requisite for a high epiphyte biodiversity is the presence of oldrespectively tall trees, independent of the recent protection status. This means:(i) for protection, e.g.in the frame of the national park declaration, such areas should be used which host such old tall trees;and(ii) also in managed forests and even in intensively used landscapes epiphytes can be protected by letting a certain number of trees be and by giving them space to grow old and tall.

The Future University Choices of Secondary Schools Students： Statistical Evaluations in Messina Side

In the last decades, especially since the 1990s, there was a gradual rising of educational levels, due to a growing schooling. This paper aims to analyze the propensity toward university enrolment in the Messina area, by means of appropriate statistical methods. In particular, we compared the students of different secondary school institutes in Messina, with reference to the choice of the future university career and other information about the scholastic profit and the scholastic context. Our comparative analysis has been performed through a non-parametric approach, using the Non Parametric Combination （NPC） test based on permutation test. This methodology was chosen for optimal characteristics of which it is characterized.

High-dimensional Tests for Mean Vector: Approaches without Estimating the Mean Vector Directly

Several tests for multivariate mean vector have been proposed in the recent literature.Generally,these tests are directly concerned with the mean vector of a high-dimensional distribution.The paper presents two new test procedures for testing mean vector in large dimension and small samples.We do not focus on the mean vector directly,which is a different framework from the existing choices.The first test procedure is based on the asymptotic distribution of the test statistic,where the dimension increases with the sample size.The second test procedure is based on the permutation distribution of the test statistic,where the sample size is fixed and the dimension grows to infinity.Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.