Open Access
Nonparametric changepoint analysis for bernoulli random variables based on neural networks
Anthony Waititu Gichuhi
- 01 Jan 2008
TL;DR: In this paper, a neural network based likelihood ratio test statistic is used to detect a change point in a given set of data and derive the limit distribution of the estimator using the results in Gombay and Horvath (1994,1996) under the assumption that the model is properly specified.
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Abstract: In many medical, financial, industrial, e.t.c. applications of statistics, the model parameters may undergo changes at unknown moment of time. In this thesis, we consider change point analysis in a regression setting for dichotomous responses, i.e. they can be modeled as Bernoulli or 0-1 variables. Applications are widespread including credit scoring in financial statistics and dose-response relations in biometry. The model parameters are estimated using neural network method. We show that the parameter estimates are identifiable up to a given family of transformations and derive the consistency and asymptotic normality of the network parameter estimates using the results in Franke and Neumann Franke Neumann (2000). We use a neural network based likelihood ratio test statistic to detect a change point in a given set of data and derive the limit distribution of the estimator using the results in Gombay and Horvath (1994,1996) under the assumption that the model is properly specified. For the misspecified case, we develop a scaled test statistic for the case of one-dimensional parameter. Through simulation, we show that the sample size, change point location and the size of change influence change point detection. In this work, the maximum likelihood estimation method is used to estimate a change point when it has been detected. Through simulation, we show that change point estimation is influenced by the sample size, change point location and the size of change. We present two methods for determining the change point confidence intervals: Profile log-likelihood ratio and Percentile bootstrap methods. Through simulation, the Percentile bootstrap method is shown to be superior to profile log-likelihood ratio method.
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Citations
The Power of the Pruned Exact Linear Time(PELT) Test in Multiple Changepoint Detection
TL;DR: The PELT algorithm is implemented which uses a common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints and it was observed that the power of the test, for a given size of change, is almost the same at all changepoints location.
Neural Networks in Finance: Gaining Predictive Edge in the Markets (a review)
TL;DR: This excellent handbook addresses the criticisms of neural networks, shows how the technique can be resurrected to solve forecasting problems, and may facilitate the resurgence of NN modeling.
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Statistical explorations of gene structure and Its correlation with gene expression and function
Jinda Kongcharoen
- 01 Jan 2012
TL;DR: This thesis proposes the mixture model to investigate statistical modeling of the length distribution of coding and non-coding regions and introduces a new heuristic method, the “multi procedure” (MP), for identifying the change points in gene sequences in the form of a generalized Bernoulli process.
•Journal Article
The power of likelihood ratio test for a change ‐point in binomial distribution
TL;DR: In this article, the power of the likelihood ratio tests for a change point in binomial observations whose mean is dependent on explanatory variables is investigated, and the artificial neural network technique is used to estimate the conditional mean of the change point.
3
The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution
Mundia Simon Maina,Waititu Anthony Gichuhi,Kihoro John Mwaniniki +2 more
- 27 Jun 2013
TL;DR: In this paper, the power of the likelihood ratio tests for a change point in binomial observations whose mean is dependent on explanatory variables is investigated, and the artificial neural network technique is used to estimate the conditional mean of the change point.
2
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