{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:24:25Z","timestamp":1760243065462,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T00:00:00Z","timestamp":1433376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper develops a class of density regression models based on proportional hazards family, namely, Gamma transformation proportional hazard (Gt-PH) model . Exact inference for the regression parameters and hazard ratio is derived. These estimators enjoy some good properties such as unbiased estimation, which may not be shared by other inference methods such as maximum likelihood estimate (MLE). Generalised confidence interval and hypothesis testing for regression parameters are also provided. The method itself is easy to implement in practice. The regression method is also extended to Lasso-based variable selection.<\/jats:p>","DOI":"10.3390\/e17063679","type":"journal-article","created":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T11:54:59Z","timestamp":1433418899000},"page":"3679-3691","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Density Regression Based on Proportional Hazards Family"],"prefix":"10.3390","volume":"17","author":[{"given":"Wei","family":"Dang","sequence":"first","affiliation":[{"name":"Business School, Shihezi University, Xinjiang, 831300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keming","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Management, Hefei University of Technology, Hefei, 230009, China"},{"name":"Department of Mathematics, College of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge, UB8 3PH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"370","DOI":"10.2307\/2344614","article-title":"Generalized linear models","volume":"135","author":"Nelder","year":"1972","journal-title":"J. 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