Sample selection procedure in daily trading volume processes

Abstract

In this paper, we propose a procedure of selecting samples from a set of samples coming from Markovian processes of finite order and finite alphabet. Under the assumption of the existence of a law that prevails in at least q% of the samples of the collection, we show that the procedure allows to identify samples governed by the predominant law. The approach is based on a local metric between samples, which tends to zero when we compare samples of identical law and tends to infinity when comparing samples with different laws. The local metric allows to define a criterion which takes arbitrarily large values when the previous assumption about the existence of a predominant law does not hold. By means of this procedure, we map similarities and dissimilarities of some Brazilian stocks' daily trading volume dynamic.

Classification of autochthonous dengue virus type 1 strains circulating in Japan in 2014

“…As we can perceive from the Definition 2.2, low values of V indicate that these samples represent the whole group better, while high values of V indicate little representativeness. The next result (proved in [1]), give us an adequate tool to classify sequences, according to their underlying laws, it allows to consolidate V as a robust and consistent classifier.…”

“…In this paper we use two stochastic and statistically consistent notions to, (i) establish the proximity between genomic sequences (see [2]), (ii) classify the sequences in terms of their representativeness (see [1]). The classification rule gives low values to more representative sequences and it gives high values to less representative sequences.…”

“…Definition 2.1. Consider two Markov chains (X 1,t ) and (X 2,t ), of order o, with finite alphabet A, state space S ¼ A o and independent samples x n 1 1;1 ; x n 2 2;1 respectively.…”

“…This metric also has very convenient statistical characteristics, such as being statistically consistent. The second aspect and perhaps the most relevant one is the construction of a metric-based classification between the sequences (see [1]). A criterion for classifying samples, statistically consistent as is the case, could be used in the future to construct standard representations for genomic structures.…”

Risk of fraud classification

“…; values reported from left to right in increasing order. Using the process (Y i,t ) tsee equation (5). 6) and (7).…”