The Convergence Rate of High-Dimensional Sample Quantiles for φ-Mixing Observation Sequences

In this paper, we obtain the convergence rate for the high-dimensional sample quantiles with the φ-mixing dependent sequence. The resulting convergence rate is shown to be faster than that obtained by the Hoeffding-type inequalities. Moreover, the convergence rate of the high-dimensional sample quantiles for the observation sequence taking discrete values is also provided.

Block bootstrap optimality and empirical block selection for sample quantiles with dependent data

Summary We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the sub- sampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample size to block length. The hybrid block bootstrap is shown to give theoretical benefits, and startling improvements in accuracy in distribution estimation in important practical settings. The conclusion that bootstrap samples should be of smaller size than the original sample has significant implications for computational efficiency and scalability of bootstrap methodologies with dependent data. Our main theorem determines the optimal number of blocks and block length to achieve the best possible convergence rate for the block bootstrap distribution estimator for sample quantiles. We propose an intuitive method for empirical selection of the optimal number and length of blocks, and demonstrate its value in a nontrivial example.

Probabilistic Identification and Estimation of Noise: Application to MR Images

For proper modelling of signal and noise in MR data requires proper interpretation and analysis of data, the different approaches with this degradation due to random fluctuations in the MR data, probabilistic modeling is power solution, which needs correctness in the computation of noise is challenging task and various stastical approaches can be utilized. After modelling the noise it can be integrated to denoising pipeline, in this research work, the recognition of noise only pixels and the evaluation of standard deviation of noise using median, mean or other optimal sample quantiles are combined in to single frame work for noise assement and uses fixed point iterative procedure to obtain standard deviation of noise. We tested the effectiveness of the algorithm to the MR clinical and synthetic data base.