An m-estimation-based model selection criterion with a data-oriented penalty

In Wu and Zen (1999), a linear model selection procedure based on M-estimation is proposed, which includes many classical model selection criteria as its special cases, and it is shown that the selection procedure is strongly consistent for a variety of penalty functions. In this paper, we will investigate its small sample performances for some choices of fixed penalty functions. It can be seen that the performance varies with the choice of the penalty. Hence, a randomized penalty based on observed data is proposed, which preserves the consistency property and provides improved performance over a fixed choice of penalty functions.     

The generalized odd half-Cauchy family of distributions: Properties and applications

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.     

BUSDM – an algorithm for the bottom-up search of departures from a model

Searching for regions of the input space where a statistical model is inappropriate is useful in many applications. The study proposes an algorithm for finding local departures from a regression-type prediction model. The algorithm returns low-dimensional hypercubes where the average prediction error clearly departs from zero. The study describes the developed algorithm, and shows successful applications on the simulated and real data from the steel plate production. The algorithms that have been originally developed for searching regions of the high-response value from the input space are reviewed and considered as alternative methods for locating model departures. The proposed algorithm succeeds in locating the model departure regions better than the compared alternatives. The algorithm can be utilized in sequential follow-up of a model as time goes along and new data are observed.     

Interval-valued data regression using partial linear model

Semi-parametric modelling of interval-valued data is of great practical importance, as exampled by applications in economic and financial data analysis. We propose a flexible semi-parametric modelling of interval-valued data by integrating the partial linear regression model based on the Center & Range method, and investigate its estimation procedure. Furthermore, we introduce a test statistic that allows one to decide between a parametric linear model and a semi-parametric model, and approximate its null asymptotic distribution based on wild Bootstrap method to obtain the critical values. Extensive simulation studies are carried out to evaluate the performance of the proposed methodology and the new test. Moreover, several empirical data sets are analysed to document its practical applications.     

Stationary bootstrapping for realized covariations of high frequency financial data

This paper studies the stationary bootstrap applicability for realized covariations of high frequency asynchronous financial data. The stationary bootstrap method, which is characterized by a block-bootstrap with random block length, is applied to estimate the integrated covariations. The bootstrap realized covariance, bootstrap realized regression coefficient and bootstrap realized correlation coefficient are proposed, and the validity of the stationary bootstrapping for them is established both for large sample and for finite sample. Consistencies of bootstrap distributions are established, which provide us valid stationary bootstrap confidence intervals. The bootstrap confidence intervals do not require a consistent estimator of a nuisance parameter arising from nonsynchronous unequally spaced sampling while those based on a normal asymptotic theory require a consistent estimator. A Monte-Carlo comparison reveals that the proposed stationary bootstrap confidence intervals have better coverage probabilities than those based on normal approximation.     

Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits

We propose a semiparametric estimator for single‐index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non‐parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy‐tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set.     

On Modeling Wood Formation Using Parametric and Semiparametric Regressions for Count Data

Understanding how wood develops has become an important problematic of plant sciences. However, studying wood formation requires the acquisition of count data difficult to interpret. Here, the annual wood formation dynamics of a conifer tree species were modeled using generalized linear and additive models (GLM and GAM); GAM for location, scale, and shape (GAMLSS); a discrete semiparametric kernel regression for count data. The performance of models is evaluated using bootstrap methods. GLM was useful to describe the wood formation general pattern but had a lack of fitting, while GAM, GAMLSS, and kernel regression had a higher sensibility to short-term variations.     

Quantile Regression for Location‐Scale Time Series Models with Conditional Heteroscedasticity

This paper considers quantile regression for a wide class of time series models including autoregressive and moving average (ARMA) models with asymmetric generalized autoregressive conditional heteroscedasticity errors. The classical mean‐variance models are reinterpreted as conditional location‐scale models so that the quantile regression method can be naturally geared into the considered models. The consistency and asymptotic normality of the quantile regression estimator is established in location‐scale time series models under mild conditions. In the application of this result to ARMA‐generalized autoregressive conditional heteroscedasticity models, more primitive conditions are deduced to obtain the asymptotic properties. For illustration, a simulation study and a real data analysis are provided.     

Non parametric mixture of strictly monotone regression models

In this article, we propose the non parametric mixture of strictly monotone regression models. For implementation, a two-step procedure is derived. We further establish the asymptotic normality of the resultant estimator and demonstrate its good performance through numerical examples.     

Comparison of computer programs for simple linear L 1 regression

A number of efficient computer codes are available for the simple linear L ₁ regression problem. However, a number of these codes can be made more efficient by utilizing the least squares solution. In fact, a couple of available computer programs already do so.

We report the results of a computational study comparing several openly available computer programs for solving the simple linear L ₁ regression problem with and without computing and utilizing a least squares solution.