LSE method using the CHSS model

Testing the reliability at a nominal stress level may lead to extensive test time. Estimations of reliability parameters can be obtained faster thanks to step-stress accelerated life tests (ALT). Usually, a transfer functional defined among a given class of parametric functions is required, but Bagdonavi?ius and Nikulin showed that ALT tests are still possible without any assumption about this functional. When shape and scale parameters of the lifetime distribution change with the stress level, they suggested an ALT method using a model called CHanging Shape and Scale (CHSS). They estimated the lifetime parameters at the nominal stress with maximum likelihood estimation (MLE). However, this method usually requires an initialization of lifetime parameters, which may be difficult when no similar product has been tested before. This paper aims to face this issue by using an iterating least square estimation (LSE) method. It will enable one to initialize the optimization required to carry out the MLE and it will give estimations that can sometimes be better than those given by MLE.     

DASSO: connections between the Dantzig selector and lasso

Summary.  We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to the least angle regression algorithm. Comparison of the two algorithms sheds new light on the question of how the lasso and Dantzig selector are related. In addition, we provide theoretical conditions on the design matrix X under which the lasso and Dantzig selector coefficient estimates will be identical for certain tuning parameters. As a consequence, in many instances, we can extend the powerful non-asymptotic bounds that have been developed for the Dantzig selector to the lasso. Finally, through empirical studies of simulated and real world data sets we show that in practice, when the bounds hold for the Dantzig selector, they almost always also hold for the lasso.     

A comparison of robust estimators based on two types of trimming

The least trimmed squares (LTS) estimator and the trimmed mean (TM) are two well-known trimming-based estimators of the location parameter. Both estimates are used in practice, and they are implemented in standard statistical software (e.g., S-PLUS, R, Matlab, SAS). The breakdown point of each of these estimators increases as the trimming proportion increases, while the efficiency decreases. Here we have shown that for a wide range of distributions with exponential and polynomial tails, TM is asymptotically more efficient than LTS as an estimator of the location parameter, when they have equal breakdown points.     

A Summary of Some Research on PC and Bayesian PC Criterion in China

In the past two decades, Pitman closeness (PC) criterion has been studied intensively in China. But many of research works were written in Chinese, which cannot be accessed by researchers from other countries. In this paper, we briefly summarize part of main results on the PC criterion in linear model in China. First, we present the basic model and some definitions. Then, we introduce the PC superiority for covariance adjustment estimate, and a class of biased estimates such as a kind of linear estimate, James–Stein estimate and the principal components estimate. Third, we introduce Bayesian PC superiorities for several different linear models such as ordinary univariate regression model, multivariate linear model and analysis of variance model. Finally, some results of robustness under Bayesian PC criterion are shown.     

Weighted Median of the Data in Solving Least Absolute Deviations Problems

We consider the weighted median problem for a given set of data and analyze its main properties. As an illustration, an efficient method for searching for a weighted Least Absolute Deviations (LAD)-line is given, which is used as the basis for solving various linear and nonlinear LAD-problems occurring in applications. Our method is illustrated by an example of hourly natural gas consumption forecast.     

A consistency result in general censoring models

In this paper we prove a consistency result for sieved maximum likelihood estimators of the density in general random censoring models with covariates. The proof is based on the method of functional estimation. The estimation error is decomposed in a deterministic approximation error and the stochastic estimation error. The main part of the proof is to establish a uniform law of large numbers for the conditional log-likelihood functional, by using results and techniques from empirical process theory.     

Bootstrapping a time series model: some empirical results

The bootstrap is a methodology for estimating standard errors. The idea is to use a Monte Carlo simulation experiment based on a nonparametric estimate of the error distribution. The main objective of this article is to demonstrate the use of the bootstrap to attach standard errors to coefficient estimates in a second-order autoregressive model fitted by least squares and maximum likelihood estimation. Additionally, a comparison of the bootstrap and the conventional methodology is made. As it turns out, the conventional asymptotic formulae (both the least squares and maximum likelihood estimates) for estimating standard errors appear to overestimate the true standard errors. But there are two problems:i. The first two observations y₁ and y₂ have been fixed, and ii. The residuals have not been inflated. After these two factors are considered in the trial and bootstrap experiment, both the conventional maximum likelihood and bootstrap estimates of the standard errors appear to be performing quite well.     

An easy way to tell what you are esting in analysis of variance

Least squares regression models are often used to analyze unbalanced fixed effect data sets with u unique cells defined by design or by post-hoc stratification. Constraints exist among the regression coefficients if there are more coefficients than cells. Models with fewer linearly independent regression coefficients than cells or with empty cells impose constraints on estimated cell means. An easy method of determining constraints among the estimated cell means and among the estimated regression coefficients for any model is developed and illustrated using a small data set.     

Bayesian Analysis of Least Absolute Relative Error Regression

In an important article by Chen et al. (2010) introduced a new distribution compatible with maximum likelihood estimation in a Least Absolute Relative Error (LARE) setting. In this article, we show first that the posterior of the model is log – concave and thus specialized and highly efficient techniques can be used to perform Bayesian inference without the use of MCMC since they provide independent draws from the posterior. Second, we approximate the distribution using a finite mixture of normals. Surprisingly, the log-LARE distribution can be approximated using a finite scale mixture of normals with few components.     

Efficient design of experiments in the Monod model

Summary. Estimation and experimental design in a non-linear regression model that is used in microbiology are studied. The Monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, water research, pharmacokinetics and plant physiology. It is proved that least squares estimates are asymptotically unbiased and normally distributed. The asymptotic covariance matrix of the estimator is the basis for the construction of efficient designs of experiments. In particular locally D -, E - and c -optimal designs are determined and their properties are studied theoretically and by simulation. If certain intervals for the non-linear parameters can be specified, locally optimal designs can be constructed which are robust with respect to a misspecification of the initial parameters and which allow efficient parameter estimation. Parameter variances can be decreased by a factor of 2 by simply sampling at optimal times during the experiment.