Maximum Likelihood Estimation of Linear Models for Longitudinal Data with Inequality Constraints

2008 ◽  
Vol 37 (6) ◽  
pp. 931-946 ◽  
Author(s):  
Jing Xu ◽  
Jinde Wang
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Longitudinal Data ◽  
Linear Models ◽  
Inequality Constraints ◽  
Likelihood Estimation

Maximum likelihood estimation for longitudinal data with truncated observations

2000 ◽  
Vol 19 (21) ◽  
pp. 2975-2988 ◽  
Author(s):  
Kishan G. Mehrotra ◽  
Pandurang M. Kulkarni ◽  
Ram C. Tripathi ◽  
Joel E. Michalek
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Longitudinal Data ◽  
Likelihood Estimation

Negative incremental claims: chain ladder and linear models

1993 ◽  
Vol 120 (1) ◽  
pp. 171-183 ◽  
Author(s):  
R. J. Verrall ◽  
Z. Li
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Lognormal Distribution ◽  
Linear Models ◽  
Likelihood Estimation ◽  
Loglinear Models ◽  
Run Off ◽  
Chain Ladder ◽  
Actuarial Method

AbstractThis paper considers the application of loglinear models to claims run-off triangles which contain negative incremental claims. Maximum likelihood estimation is applied using the three parameter lognormal distribution. The method can be used in conjunction with any model which can be expressed in lognormal form. In particular the chain ladder technique is considered. An example is given and the results compared with the basic actuarial method.

Extracting paraphrase patterns from bilingual parallel corpora

2009 ◽  
Vol 15 (4) ◽  
pp. 503-526 ◽  
Author(s):  
SHIQI ZHAO ◽  
HAIFENG WANG ◽  
TING LIU ◽  
SHENG LI
Keyword(s):  
Natural Language Processing ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Language Processing ◽  
Linear Models ◽  
Likelihood Estimation ◽  
Word Alignment ◽  
Inference Rules ◽  
Parallel Corpora ◽  
Log Linear

AbstractParaphrase patterns are semantically equivalent patterns, which are useful in both paraphrase recognition and generation. This paper presents a pivot approach for extracting paraphrase patterns from bilingual parallel corpora, whereby the paraphrase patterns in English are extracted using the patterns in another language as pivots. We make use of log-linear models for computing the paraphrase likelihood between pattern pairs and exploit feature functions based on maximum likelihood estimation (MLE), lexical weighting (LW), and monolingual word alignment (MWA). Using the presented method, we extract more than 1 million pairs of paraphrase patterns from about 2 million pairs of bilingual parallel sentences. The precision of the extracted paraphrase patterns is above 78%. Experimental results show that the presented method significantly outperforms a well-known method called discovery of inference rules from text (DIRT). Additionally, the log-linear model with the proposed feature functions are effective. The extracted paraphrase patterns are fully analyzed. Especially, we found that the extracted paraphrase patterns can be classified into five types, which are useful in multiple natural language processing (NLP) applications.

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