The modified maximum likelihood estimators for the parameters of the regression model under bivariate median ranked set sampling

This paper describes the modified maximum likelihood estimator (MMLE) of location and scale parameters based on selected ranked set sampling (SRSS) for normal, uniform and two-parameter exponential distributions. For these distributions, the MMLE of location and scale parameters for SRSS data were compared with the estimators of location and scale parameters for simple random sample (SRS) and ranked set sample (RSS). The MMLE based on SRSS data were found to be advantageous as compared to SRS and RSS estimators for the same number of measurements. The SRSS method with errors in ranking was also described. The minimum correlation between the actual and erroneous ranking was required for MMLE of SRSS to achieve better precision than usual SRS and RSS estimators. When the wrong assumption about the underlying distribution was present, the MMLE of the population mean based on SRSS was better than the RSS estimator ofthe population mean for all the cases considered.

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Modified maximum likelihood estimator under the Jones and Faddy's skew t-error distribution for censored regression model

Journal of Applied Statistics ◽

10.1080/02664763.2020.1786673 ◽

2020 ◽

pp. 1-16

Author(s):

Sukru Acitas ◽

Ismail Yenilmez ◽

Birdal Senoglu ◽

Yeliz Mert Kantar

Keyword(s):

Maximum Likelihood ◽

Regression Model ◽

Maximum Likelihood Estimator ◽

Error Distribution ◽

Censored Regression ◽

Likelihood Estimator ◽

Modified Maximum Likelihood ◽

Censored Regression Model ◽

Modified Maximum Likelihood Estimator

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Maximum likelihood estimation in location-scale families using varied L ranked set sampling

RAIRO - Operations Research ◽

10.1051/ro/2020124 ◽

2020 ◽

Author(s):

Amer Al-Omari

Keyword(s):

Maximum Likelihood ◽

Random Sampling ◽

Maximum Likelihood Estimators ◽

Likelihood Estimation ◽

Simple Random Sampling ◽

Ranked Set Sampling ◽

Sampling Schemes ◽

Scale Parameters ◽

Insight Into ◽

Family Of Distributions

Recently, a generalized ranked set sampling (RSS) scheme has been introduced which encompasses several existing RSS schemes, namely varied L RSS (VLRSS), and it provides more precise estimators of the population mean than the estimators with the traditional simple random sampling (SRS) and RSS schemes. In this paper, we extend the work and consider the maximum likelihood estimators (MLEs) of the location and scale parameters when sampling from a location-scale family of distributions. In order to give more insight into the performance of VLRSS with respect to SRS and RSS schemes, the asymptotic relative precisions of the MLEs using VLRSS relative to that using SRS and RSS are compared for some usual location-scale distributions. It turns out that the MLEs with VLRSS are more precise than those with the existing sampling schemes.

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Inference in Multiple Linear Regression Model with Generalized Secant Hyperbolic Distribution Errors

Ingeniería y Ciencia ◽

10.17230/10.17230/ingciencia.17.33.3 ◽

2021 ◽

Vol 17 (33) ◽

pp. 45-70

Author(s):

Álvaro Alexander Burbano Moreno ◽

Oscar Orlando Melo-Martinez ◽

M Qamarul Islam

Keyword(s):

Maximum Likelihood ◽

Linear Regression ◽

Regression Model ◽

Multiple Linear Regression ◽

Linear Regression Model ◽

Multiple Linear Regression Model ◽

Least Square ◽

Model Parameters ◽

Modified Maximum Likelihood ◽

Test Of Hypothesis

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. We derive the estimators of model parameters by using modified maximum likelihood methodology and explore the properties of the modified maximum likelihood estimators so obtained. We show that the proposed estimators are more efficient and robust than the commonly used least square estimators. We also develop the relevant test of hypothesis procedures and compared the performance of such tests vis-a-vis the classical tests that are based upon the least square approach.

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