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The zero-inflated negative binomial regression (ZINBR) model is used for modeling count data that exhibit both overdispersion and zero-inflated counts. However, a persistent challenge in the efficient estimation of parameters within ZINBR models is the issue of multicollinearity, where high correlations between predictor variables can compromise the stability and reliability of the maximum likelihood estimator (MLE). We propose a new two-parameter hybrid estimator, designed for the ZINBR model, to address this problem. This estimator aims to mitigate the effects of multicollinearity by incorporating a combination of existing biased estimators. To test the effectiveness of the proposed estimator, we conduct a comprehensive theoretical comparison with conventional biased estimators, including the Ridge and Liu, the Kibria-Lukman, and the modified Ridge estimators. An extended Monte Carlo simulation study complements the theoretical results, evaluating the estimator’s performance under various multicollinearity conditions. The simulation results, evaluated by metrics such as mean squared error (MSE) and mean absolute error (MAE), show that the proposed hybrid estimator consistently outperforms conventional methods, especially in high multicollinearity. Furthermore, we apply it to two real-world datasets. The experimental application demonstrates the superior performance of the estimator in producing stable and accurate parameter estimates. The simulation study and experimental application results strongly suggest that the new two-parameter hybrid estimator offers significant progress in parameter estimation in ZINBR models, especially in complex scenarios due to multicollinearity.

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a nonasymptotic point of view. In particular, we define estimators with a sub-Gaussian behavior even for certain heavy-tailed distributions. We also prove various impossibility results for mean estimators.

We solve the comparison problem for generalized ψ-estimators introduced by Barczy and Páles (arXiv: 2211.06026, 2022). Namely, we derive several necessary and sufficient conditions under which a generalized ψ-estimator less than or equal to another ψ-estimator for any sample. We also solve the corresponding equality problem for generalized ψ-estimators. We also apply our results for some known statistical estimators such as for empirical expectiles and Mathieu-type estimators and for solutions of likelihood equations in case of normal, a Beta-type, Gamma, Lomax (Pareto type II), lognormal and Laplace distributions.

In this paper, we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in [0, 1] d with d ≥ 2 and N(0, 1) noise, the minimax rate for the ℓ₂ risk is known to be bounded from below by n −1/d when the unknown mean function f is non-decreasing and its range is bounded by a constant, while the least squares estimator (LSE) is known to nearly achieve the minimax rate up to a factor (log n) γ where n is the sample size, γ = 4 in the lattice design and γ = max{9/2, (d² + d + 1)/2} in the random design. Moreover, the LSE is known to achieve the adaptation rate (K/n)−2/d {1 ∨ log(n/K)}2γ when f is piecewise constant on K hyperrectangles in a partition of [0, 1] d . Due to the minimax theorem, the LSE is identical on every design point to both the max-min and min-max estimators over all upper and lower sets containing the design point. This motivates our consideration of estimators which lie in-between the max-min and min-max estimators over possibly smaller classes of upper and lower sets, including a subclass of block estimators. Under a qth moment condition on the noise, we develop ℓ q risk bounds for such general estimators for isotonic regression on graphs. For uniform deterministic and random designs in [0, 1] d with d ≥ 3, our ℓ₂ risk bound for the block estimator matches the minimax rate n −1/d when the range of f is bounded and achieves the near parametric adaptation rate (K/n){1 ∨ log(n/K)}d when f is K-piecewise constant. Furthermore, the block estimator possesses the following oracle property in variable selection: When f depends on only a subset S of variables, the ℓ₂ risk of the block estimator automatically achieves up to a poly-logarithmic factor the minimax rate based on the oracular knowledge of S.

Regression models are essential for understanding the relationship between dependent and independent variables. However, multicollinearity poses a significant challenge, leading to unstable and inefficient parameter estimates and inflated variance. The Poisson-Inverse Gaussian regression model (P-IGRM), a mixture of the Poisson and Inverse Gaussian distributions, is widely used to address overdispersion in count data. Although the maximum likelihood (ML) estimator is commonly used for parameter estimation in P-IGRM, it performs poorly in the presence of multicollinearity. To overcome this issue, several biased estimators, such as ridge, Liu, and Liu-type estimators, have been proposed. In this paper, we introduce a new class of Poisson-Inverse Gaussian Liu-type regression estimators as an alternative to existing methods. We compare the proposed estimator with ML, ridge, Liu, and Liu-type estimators using scalar mean square error (MSE) and matrix mean square error (MMSE) criteria. Monte Carlo simulations are conducted to evaluate the performance of the proposed estimator under different conditions. Additionally, we illustrate the effectiveness of all considered estimators using real data analysis.

Ranked set sampling (RSS) is an efficient method for estimating parameters when exact measurement of observation is difficult and/or expensive. In the current paper, several traditional and ad hoc estimators of the scale and shape parameters θ and α from the Pareto distribution p(θ,α) will be respectively studied in cases when one parameter is known and when both are unknown under simple random sampling, RSS and some of its modifications such as extreme RSS(ERSS) and median RSS(MRSS). It is found for estimating of θ from p(θ,α) in which α is known, the best linear unbiased estimator (BLUE) under ERSS is more efficient than the other estimators under the other sampling techniques. For estimating of α from p(θ,α) in which θ is known, the modified BLUE under MRSS is more efficient than the other estimators under the other sampling techniques. For estimating of θ and α from p(θ,α) in which both are unknown, the ad hoc estimators under ERSS are more efficient than the other estimators under the other sampling techniques. All efficiencies of these estimators are simulated under imperfect ranking. A real data set is used for illustration.

Research Summary Strategy research addresses endogeneity by incorporating econometric techniques, including Heckman's two‐step method. The economics literature theorizes regarding optimal usage of Heckman's method, emphasizing the valid exclusion condition necessary in the first stage. However, our meta‐analysis reveals that only 54 of 165 relevant papers published in the top strategy and organizational theory journals during 1995–2016 claim a valid exclusion restriction. Without this condition being met, our simulation shows that results using the Heckman method are often less reliable than OLS results. Even where Heckman is not possible, we recommend that other rigorous identification approaches be used. We illustrate our recommendation to use a triangulation of identification approaches by revisiting the classic global strategy question of the performance implications of cross‐border market entry through greenfield or acquisition. Managerial Summary Managers make strategic decisions by choosing the best option given the particular circumstances of their firm. However, researchers had previously not taken into consideration these circumstances when evaluating the outcome of that choice. The Heckman method importantly addresses this situation, but requires that the researcher have some variable that effects the best option for the firm, but not the outcome. We show that researchers frequently do not utilize such a variable, and demonstrate that the Heckman method can exacerbate estimation issues in this case. We then provide an approach that researchers can use to address the challenge of determining the outcome of a strategic decision, and illustrate it with an empirical examination of the performance implications of cross‐border market entry through greenfield or acquisition.

The Poisson maximum likelihood (PML) is used to estimate the coefficients of the Poisson regression model (PRM). Since the resulting estimators are sensitive to outliers, different studies have provided robust Poisson regression estimators to alleviate this problem. Additionally, the PML estimator is sensitive to multicollinearity. Therefore, several biased Poisson estimators have been provided to cope with this problem, such as the Poisson ridge estimator, Poisson Liu estimator, Poisson Kibria–Lukman estimator, and Poisson modified Kibria–Lukman estimator. Despite different Poisson biased regression estimators being proposed, there has been no analysis of the robust version of these estimators to deal with the two above-mentioned problems simultaneously, except for the robust Poisson ridge regression estimator, which we have extended by proposing three new robust Poisson one-parameter regression estimators, namely, the robust Poisson Liu (RPL), the robust Poisson Kibria–Lukman (RPKL), and the robust Poisson modified Kibria–Lukman (RPMKL). Theoretical comparisons and Monte Carlo simulations were conducted to show the proposed performance compared with the other estimators. The simulation results indicated that the proposed RPL, RPKL, and RPMKL estimators outperformed the other estimators in different scenarios, in cases where both problems existed. Finally, we analyzed two real datasets to confirm the results.

Data subject to heavy-tailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and least absolute deviation regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in ultrahigh dimensional settings with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss. Such a penalized robust approximate (RA) quadratic loss will be called the RA lasso. In the ultrahigh dimensional setting, where the dimensionality can grow exponentially with the sample size, our results reveal that the RA lasso estimator produces a consistent estimator at the same rate as the optimal rate under the light tail situation. We further study the computational convergence of the RA lasso and show that the composite gradient descent algorithm indeed produces a solution that admits the same optimal rate after sufficient iterations. As a by-product, we also establish the concentration inequality for estimating the population mean when there is only the second moment. We compare the RA lasso with other regularized robust estimators based on quantile regression and least absolute deviation regression. Extensive simulation studies demonstrate the satisfactory finite sample performance of the RA lasso.

In many different fields, social scientists desire to understand temporal variation associated with age, time period, and cohort membership. Among methods proposed to address the identification problem in age-period-cohort analysis, the intrinsic estimator (IE) is reputed to impose few assumptions and to yield good estimates of the independent effects of age, period, and cohort groups. This article assesses the validity and application scope of IE theoretically and illustrates its properties with simulations. It shows that IE implicitly assumes a constraint on the linear age, period, and cohort effects. This constraint not only depends on the number of age, period, and cohort categories but also has nontrivial implications for estimation. Because this assumption is extremely difficult, if not impossible, to verify in empirical research, IE cannot and should not be used to estimate age, period, and cohort effects.