Softly shrunk and partially shrunk rank-reduced estimation of the regression coefficients

In this paper we introduce strategies how the ordinary least square estimator of the coefficient vector of the multiple regression could be shrunk. One of the strategies shrinks all components while the other shrinks only some components. We show that the proposed shrunken estimators are admissibile. We also provide theoretical results on risk comparisons.     

Alternative beta estimation for the market model using partially adaptive techniques

The leptokurtosls of many security market return distributions can contaminate ordinary least squares estimates of the β coefficient of the market model. Partially adaptive estimation techniques accommodate the possibility of fat tailed distributions. this methodology limits the influence of extremely large residuals and yields estimates which are both statistically and practically different from ordinary least squares.     

Efficient estimation in a nonlinear counting-process regression model

Suppose we observe i.i.d. copies of X, C, Y, where X is a counting process, C is a censoring process talcing only values 0 and 1, and Y is a covariate process. Assume that the intensity process of X is of the form C(s)a(s, Y(s)) with a unknown, but that the distribution of X, C, Y is unspecified otherwise. McKeague and Utikal proposed an estimator for the doubly cumulative hazard f f a(s, y) ds dy and determined its asymptotic distribution. We show that the estimator is regular and efficient in the sense of a Hájek-Inagaki convolution theorem for partially specified models.     

Outlier identification and robust parameter estimation in a zero-inflated Poisson model

The Zero-inflated Poisson distribution has been used in the modeling of count data in different contexts. This model tends to be influenced by outliers because of the excessive occurrence of zeroes, thus outlier identification and robust parameter estimation are important for such distribution. Some outlier identification methods are studied in this paper, and their applications and results are also presented with an example. To eliminate the effect of outliers, two robust parameter estimates are proposed based on the trimmed mean and the Winsorized mean. Simulation results show the robustness of our proposed parameter estimates.     

Sequential estimation of the sum of sinusoidal model parameters

Estimating the parameters of the sum of a sinusoidal model in presence of additive noise is a classical problem. It is well known to be a difficult problem when the two adjacent frequencies are not well separated or when the number of components is very large. In this paper we propose a simple sequential procedure to estimate the unknown frequencies and amplitudes of the sinusoidal signals. It is observed that if there are p components in the signal then at the k  th (k?p)$(k?p)$ stage our procedure produces strongly consistent estimators of the k   dominant sinusoids. For k>p$k>p$, the amplitude estimators converge to zero almost surely. Asymptotic distribution of the proposed estimators is also established and it is observed that it coincides with the asymptotic distribution of the least squares estimators. Numerical simulations are performed to observe the performance of the proposed estimators for different sample sizes and for different models. One ECG data and one synthesized data are analyzed for illustrative purpose.     

WLAD-LASSO method for robust estimation and variable selection in partially linear models

This paper focuses on robust estimation and variable selection for partially linear models. We combine the weighted least absolute deviation (WLAD) regression with the adaptive least absolute shrinkage and selection operator (LASSO) to achieve simultaneous robust estimation and variable selection for partially linear models. Compared with the LAD-LASSO method, the WLAD-LASSO method will resist to the heavy-tailed errors and outliers in the parametric components. In addition, we estimate the unknown smooth function by a robust local linear regression. Under some regular conditions, the theoretical properties of the proposed estimators are established. We further examine finite-sample performance of the proposed procedure by simulation studies and a real data example.     

Improved pretest nonparametric estimation in a multivariate regression model

Shrinkage pretest nonparametric estimation of the location parameter vector in a multivariate regression model is considered when nonsample information (NSI) about the regression parameters is available. By using the quadratic risk criterion, the dominance of the pretest estimators over the usual estimators has been investigated. We demonstrate analytically and computationally that the proposed improved pretest estimator establishes a wider dominance range for the parameter under consideration than that of the usual pretest estimator in which it is superior over the unrestricted estimator.     

Robust estimation methods for exponential data: a monte-carlo comparison

We compare the performance of seven robust estimators for the parameter of an exponential distribution. These include the debiased median and two optimally-weighted one-sided trimmed means. We also introduce four new estimators: the Transform, Bayes, Scaled and Bicube estimators. We make the Monte Carlo comparisons for three sample sizes and six situations. We evaluate the comparisons in terms of a new performance measure, Mean Absolute Differential Error (MADE), and a premium/protection interpretation of MADE. We organize the comparisons to enhance statistical power by making maximal use of common random deviates. The Transform estimator provides the best performance as judged by MADE. The singly-trimmed mean and Transform method define the efficient frontier of premium/protection.     

Rank estimation for the functional linear model

This article discusses the estimation of the parameter function for a functional linear regression model under heavy-tailed errors' distributions and in the presence of outliers. Standard approaches of reducing the high dimensionality, which is inherent in functional data, are considered. After reducing the functional model to a standard multiple linear regression model, a weighted rank-based procedure is carried out to estimate the regression parameters. A Monte Carlo simulation and a real-world example are used to show the performance of the proposed estimator and a comparison made with the least-squares and least absolute deviation estimators.     

Robust estimation and model identification for longitudinal data varying-coefficient model

It is well known that M-estimation is a widely used method for robust statistical inference and the varying coefficient models have been widely applied in many scientific areas. In this paper, we consider M-estimation and model identification of bivariate varying coefficient models for longitudinal data. We make use of bivariate tensor-product B-splines as an approximation of the function and consider M-type regression splines by minimizing the objective convex function. Mean and median regressions are included in this class. Moreover, with a double smoothly clipped absolute deviation (SCAD) penalization, we study the problem of simultaneous structure identification and estimation. Under approximate conditions, we show that the proposed procedure possesses the oracle property in the sense that it is as efficient as the estimator when the true model is known prior to statistical analysis. Simulation studies are carried out to demonstrate the methodological power of the proposed methods with finite samples. The proposed methodology is illustrated with an analysis of a real data example.     

Improved estimation of the scale parameter, the hazard rate parameter and the ratio of the scale parameters in exponential distributions: An integrated approach

We give new classes of Strawderman-type improved estimators for the scale parameter σ₂ and the hazard rate parameter 1/σ₁ of the exponential distributions E(μ₂,σ₂) and E(μ₁,σ₁) under the entropy loss. We then use these estimators to construct improved estimators for the ratio ρ=σ₂/σ₁. The sampling framework we consider integrates important life-testing schemes separately studied in the literature so far, namely, (i) i.i.d. sampling, (ii) Type-II censoring, (iii) progressive Type-II censoring and adaptive progressive Type-II censoring and (iv) record values data. Furthermore, we establish simple identities connecting the risk functions of the estimators of σ₂ and 1/σ₁ and those of ρ that have a direct impact on studying the risk behavior of the latter estimators. Finally, we indicate that no matter which of the above life-testing schemes is employed for the estimation of σ₂, 1/σ₁ or ρ, the corresponding improved estimator, which may be of Stein-type or Brewster and Zidek-type or Strawderman-type, will offer the same improvement over the usual estimator as long as the number of observed complete failure times is the same for each scheme. Our results unify and extend existing results on the estimation of exponential scale parameters in one or two populations.     

Linear estimation of location and scale parameters in the generalized gamma distribution

The expressions for moments of order statistics from the generalized gamma distribution are derived. Coefficients to get the BLUEs of location and scale parameters in the generalized gamma distribution are computed. Some simple alternative linear unbiased estimates of location and scale parameters are also proposed and their relative efficiencies compared to the BLUEs are studied.     

Interval estimation of the mean in a two-stage nested model

The problem of constructing confidence intervals to estimate the mean in a two-stage nested model is considered. Several approximate intervals, which are based on both linear and nonlinear estimators of the mean are investigated. In particular, the method of bootstrap is used to correct the bias in the ‘usual’ variance of the nonlinear estimators. It is found that the intervals based on the nonlinear estimators did not achieve the nominal confidence coefficient for designs involving a small number of groups. Further, it turns out that the intervals are generally conservative, especially at small values of the intraclass correlation coefficient, and that the intervals based on the nonlinear estimators are more conservative than those based on the linear estimators. Compared with the others, the intervals based on the unweighted mean of the group means performed well in terms of coverage and length. For small values of the intraclass correlation coefficient, the ANOVA estimators of the variance components are recommended, otherwise the unweighted means estimator of the between groups variance component should be used. If one is fortunate enough to have control over the design, he is advised to increase the number of groups, as opposed to increasing group sizes, while avoiding groups of size one or two.     

Robust estimation in the multivariate normal model with variance components

Fisher consistent and Fréchet differentiable statistical functionals have been already used by Bednarski and Zontek [Robust estimation of parameters in a mixed unbalanced model. Ann Statist. 1996;24(4):1493–1510] to get a robust estimator of parameters in a two-way crossed classification mixed model. This way of robust estimation appears also in the variance components model with a commutative covariance matrix [Zmy?lony, Zontek. Robust M-estimator of parameters in variance components model. Discuss Math Probab Stat. 2002;22:61–71]. In this paper it is shown that a modification of this method does not involve any assumptions about commutation of covariance matrix. The theoretical results have been completed with computer simulation studies. Robustness of considered estimator and possibility of approximation of the estimator's distribution with some multivariate normal distribution for both model and contaminated data have been confirmed there.     

Shrinkage estimation in lognormal regression model for censored data

We introduce in this paper, the shrinkage estimation method in the lognormal regression model for censored data involving many predictors, some of which may not have any influence on the response of interest. We develop the asymptotic properties of the shrinkage estimators (SEs) using the notion of asymptotic distributional biases and risks. We show that if the shrinkage dimension exceeds two, the asymptotic risk of the SEs is strictly less than the corresponding classical estimators. Furthermore, we study the penalty (LASSO and adaptive LASSO) estimation methods and compare their relative performance with the SEs. A simulation study for various combinations of the inactive predictors and censoring percentages shows that the SEs perform better than the penalty estimators in certain parts of the parameter space, especially when there are many inactive predictors in the model. It also shows that the shrinkage and penalty estimators outperform the classical estimators. A real-life data example using Worcester heart attack study is used to illustrate the performance of the suggested estimators.     

Exponentiated Chen distribution: Properties and estimation

This article addresses various properties and estimation methods for the Exponentiated Chen distribution. Although, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures, namely, the method of maximum likelihood estimation, percentile estimation, least square and weighted least-square estimation, maximum product of spacings estimation, Cramér-von-Mises estimation, Anderson–Darling, and right-tail Anderson–Darling estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of three real datasets.     

Small-sample results for maximum-likelihood estimation in branching processes

In this article, small sample properties of the maximum-likelihood estimator (m.l.e.) for the offspring distribution (pk) and its mean m are considered in the context of the simple branching process. A representation theorem is given for the m.l.e. of (Pk) from which the m.l.e. of m is obtained. The case where p0 + p1 + p2 = 1 is studied in detail: numerical results are given for the exact bias of these estimators as a function of the age of the process; a curve fitting analysis expresses the bias of m? as a function of the mean and the variance of the offspring distribution and finally an “approximate m.l.e.” for (pk) is given.     

Allowance for skewness in maximum-likelihood estimation with application to the location-scale model

The use of maximum-likelihood estimation as discussed by Sprott and Viveros (1984) is extended to include the log F distribution to accommodate skewness. The role played by linear pivotals in relation to likelihood and efficiency is discussed. Normal, t, and log F likelihoods are defined and used to generate possible normal, t, and log F linear pivotal quantities. The results are applied to the location-scale family, where exact results are available to assess the numerical accuracy of the proposed procedure. Refinements using saddlepoint approximations are obtained.     

When there are outliers in the carriers:the univariate case

Robust regression estimators studied to date are robust against non-normal distributions of the errors only If the carriers ‘Independent variables’ do not also contain outliers. Several alternative estimators that are robust even 1f there are outliers in the carriers are studied. Two estimators seem to be preferable, but even these can be very Inefficient ‘relative to least squares’ If the errors are normally distributed.