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On the adaptive partition approach to the detection of multiple change-points.

Lai Y - PLoS ONE (2011)

Bottom Line: However, the widely used recursive combination or partition procedures do not guarantee a global optimization.Our method can provide consistent estimation results.In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics and Biostatistics Center, The George Washington University, Washington, DC, United States of America. ylai@gwu.edu

ABSTRACT
With an adaptive partition procedure, we can partition a "time course" into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age.

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Related in: MedlinePlus

Simulation based comparison of time-point-wise MSE, bias and                            variance.The y-axes represent the time-point-wise MSE (upper row), bias (middle                            row) or variance (lower row). The x-axes represent the time point. The                            plots are generated from the analysis results based on the simulation                            scenario 4. The plots in each column (1–3) are generated from the                            analysis results based on different  (1, 10 and                            100).
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pone-0019754-g009: Simulation based comparison of time-point-wise MSE, bias and variance.The y-axes represent the time-point-wise MSE (upper row), bias (middle row) or variance (lower row). The x-axes represent the time point. The plots are generated from the analysis results based on the simulation scenario 4. The plots in each column (1–3) are generated from the analysis results based on different (1, 10 and 100).

Mentions: In addition to the overall performance based on the overall MSE and the selected , it is also statistically interesting to understand the estimation mean squared error, bias and variance at each time point. The time-point-wise mean squared error (MSE), bias and variance (for the -th time point, ) are shown in Figures 6, 7, 8, 9 for three different methods. For the time-point-wise MSE, even when the sample size is relatively small (one observation at each time point), our proposed method (DP) still shows an overall comparable performance when it is compared to the two approximation methods (RC or RP). As the sample size is increased, its time-point-wise MSEs become overall comparably lower and lower. For the time-point-wise bias, when sample size is relatively small (one at each time point), DP shows an overall worse performance in the simulation scenarios 1 and 3 but it still shows an overall comparable performance in the simulation scenarios 2 and 4. As the sample size is increased, its biases become overall comparably lower and lower (i.e. closer to the zero y-axis value). For the time-point-wise variance, DP always shows an overall comparable performance. (When the sample size is as small as one at each time point, the estimated time-point-wise means are almost all constants from all three different methods in the simulation scenarios 2; then the corresponding time-point-wise variance patterns are relatively flat. For the same sample size, the estimated time-point-wise means are actually all constants from all three different methods in the simulation scenarios 4; then the corresponding time-point-wise variances are actually constant across the whole time period. This also explains the relatively regular patterns of the corresponding time-point-wise MSE and bias.)


On the adaptive partition approach to the detection of multiple change-points.

Lai Y - PLoS ONE (2011)

Simulation based comparison of time-point-wise MSE, bias and                            variance.The y-axes represent the time-point-wise MSE (upper row), bias (middle                            row) or variance (lower row). The x-axes represent the time point. The                            plots are generated from the analysis results based on the simulation                            scenario 4. The plots in each column (1–3) are generated from the                            analysis results based on different  (1, 10 and                            100).
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3101215&req=5

pone-0019754-g009: Simulation based comparison of time-point-wise MSE, bias and variance.The y-axes represent the time-point-wise MSE (upper row), bias (middle row) or variance (lower row). The x-axes represent the time point. The plots are generated from the analysis results based on the simulation scenario 4. The plots in each column (1–3) are generated from the analysis results based on different (1, 10 and 100).
Mentions: In addition to the overall performance based on the overall MSE and the selected , it is also statistically interesting to understand the estimation mean squared error, bias and variance at each time point. The time-point-wise mean squared error (MSE), bias and variance (for the -th time point, ) are shown in Figures 6, 7, 8, 9 for three different methods. For the time-point-wise MSE, even when the sample size is relatively small (one observation at each time point), our proposed method (DP) still shows an overall comparable performance when it is compared to the two approximation methods (RC or RP). As the sample size is increased, its time-point-wise MSEs become overall comparably lower and lower. For the time-point-wise bias, when sample size is relatively small (one at each time point), DP shows an overall worse performance in the simulation scenarios 1 and 3 but it still shows an overall comparable performance in the simulation scenarios 2 and 4. As the sample size is increased, its biases become overall comparably lower and lower (i.e. closer to the zero y-axis value). For the time-point-wise variance, DP always shows an overall comparable performance. (When the sample size is as small as one at each time point, the estimated time-point-wise means are almost all constants from all three different methods in the simulation scenarios 2; then the corresponding time-point-wise variance patterns are relatively flat. For the same sample size, the estimated time-point-wise means are actually all constants from all three different methods in the simulation scenarios 4; then the corresponding time-point-wise variances are actually constant across the whole time period. This also explains the relatively regular patterns of the corresponding time-point-wise MSE and bias.)

Bottom Line: However, the widely used recursive combination or partition procedures do not guarantee a global optimization.Our method can provide consistent estimation results.In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics and Biostatistics Center, The George Washington University, Washington, DC, United States of America. ylai@gwu.edu

ABSTRACT
With an adaptive partition procedure, we can partition a "time course" into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age.

Show MeSH
Related in: MedlinePlus