REVSTAT-Statistical Journal

Bootstrap Resampling Method for Estimation of Fuzzy Regression Parameters and a Sample Application

Derviş Topuz — 2024-11-08

In fuzzy regression modeling, the fuzzy least squares technique is based on minimizing the squares of the total difference between observed and predicted outcomes. When the sample size is small, bootstrap resampling method is appropriate and useful for improving model estimation. The bootstrap resampling technique relies on resampling observations and resampling errors for bootstrap regression. The aim of this study is to investigate the use of Bootstrap in fuzzy regression modeling to estimate mean prediction with smaller errors at a particular α-segment, and apply it on a clinical data set. The behavior and properties of the least-squares estimators are affected when deviations or fuzziness arise in the sample and/or by slight changes in the data set. Bootstrap technique, on the other hand, provide robust estimators of the parameters which avoid such adverse effects.

Estimation and Diagnostic for a Partially Linear Regression based on an Extension of the Rice Distribution

J. C. S. Vasconcelos — 2024-11-08

We introduce an extension of the Rice distribution and estimate its parameters by maximum likelihood. We define two regressions based on this extended distribution to model volumetric shrinkage of the wood and milk production. The performance of the parameter estimators is investigated infinite samples using Monte Carlo simulations. Also, we propose the quantile residuals for the regression models whose empirical distribution is close to normality. The usefulness of the new regressions is proved empirically through two applications to agricultural data.

Applications of Composite Lognormal Distributions

Jiahang Lyu — 2024-11-08

The use of a power law distribution to model upper tails is common in many areas, most notably in physics. In this paper, we consider two data sets published in the physics literature. We show that composite lognormal distributions can provide better fits than the power law distribution even when the former are applied to the full data (as described in the data section) and the latter is applied just to the upper tail of the data.

Estimations of Confidence Sets for the Parameters of Unit Generalized Rayleigh Model under Records Data

Xuanjia Zuo — 2024-11-08

This paper discusses the confidence sets estimation for the unit generalized Rayleigh distribution parameters when the record value is available. By constructing series of pivotal quantities, equal-tailed confidence intervals and region are constructed for unknown parameters. Further, optimal confidence sets with minimum-size are also pursued by using the non-linear optimization technique, whereas various numerical algorithms are also established to obtain the estimates in consequence. For comparison and complementary, traditional likelihood-based asymptotic confidence sets of the parameters are also constructed. Extensive simulation studies are carried out to evaluate the performance of different methods and two real-life examples are used to present their applicability. Additionally, some alternative extension works are also presented for pursuing high-accuracy confidence sets under proposed criteria and the effectiveness of the extended results is also investigated correspondingly.

A Simple Mean-Parameterized Maxwell Regression Model for Positive Response Variables

Arthur J. Lemonte — 2024-11-08

We study a quite simple parametric regression model that may be very useful to model positive response variables in practice. The frequentist approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive a closed-form expression for the second-order bias of the maximum likelihood estimator, which is easily computed as an ordinary linear regression and is then used to define bias-corrected maximum likelihood estimates. We consider the normalized quantile residuals for the new parametric regression model to assess departures from model assumptions, and global and local influence methods are also discussed. Applications to real data are considered to illustrate the new regression model in practice, and comparisons with two of the most popular existing regression models are made.

Kernel Estimation of The Dynamic Cumulative Past Inaccuracy Measure for Right Censored Dependent Data

Viswakala K. V. — 2024-11-08

This paper proposes a nonparametric estimator for the lifetime distribution’s dynamic cumulative past inaccuracy measure based on censored dependent data. The asymptotic properties of the estimator are discussed under suitable regularity conditions. We use Monte-Carlo simulations to compare the estimator’s performance to that of an empirical estimator using mean squared errors to test the estimator’s properties numerically. The methods are demonstrated using two different real data sets.

Bootstrapping Order Statistics with Variable Rank

Mohamed Ebrahim Sobh — 2024-11-08

This work investigates the strong consistency of bootstrapping central and intermediate order statistics for an appropriate choice of re-sample size for known and unknown normalizing constants. We show that when the normalizing constants are estimated from the data, the bootstrap distribution for central and intermediate order statistics may be weakly or strongly consistent. A simulation study is conducted to show numerically how to choose the bootstrap sample size to give the best approximation of the bootstrapping distribution for the central and intermediate quantiles.