We introduce a class of linear quantile regression estimators for panel data. Our framework contains dynamic autoregressive models, models with general predetermined regressors, and models with multiple individual e?ects as special cases. We follow a correlated random-e?ects approach, and rely on additional layers of quantile regressions as a flexible tool to model conditional distributions. Conditions are given under which the model is nonparametrically identified in static or Markovian dynamic models. We develop a sequential method-of-moment approach for estimation, and compute the estimator using an iterative algorithm that exploits the computational simplicity of ordinary quantile regression in each iteration step. Finally, a Monte-Carlo exercise and an application to measure the e?ect of smoking during pregnancy on children’s birthweights complete the paper. K-means and K-medoids clustering algorithms are widely used for many practical applications. Original k-mean and k-medoids algorithms select initial centroids and medoids randomly that affect the quality of the resulting clusters and sometimes it generates unstable and empty clusters which are meaningless. The original k-means and k-mediods algorithm is computationally expensive and requires time proportional to the product of the number of data items, number of clusters and the number of iterations. The new approach for the k mean algorithm eliminates the deficiency of exiting k mean. It first calculates the initial centroids k as per requirements of users and then gives better, effective and stable cluster. It also takes less execution time because it eliminates unnecessary distance computation by using previous iteration. The new approach for k- medoids selects initial k medoids systematically based on initial centroids. It generates stable clusters to improve accuracy.
Panel data, quantile regression, expectation-Maximization
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