Smoothed detrended fluctuation analysis

ABSTRACT

The method of detrended fluctuation analysis (DFA) is useful in revealing the extent of long-range dependence, it has successfully been applied to different fields of interest. In this paper we proposed a smoothed detrended fluctuation analysis method based on the principle of wavelet shrinkage. The procedure is illustrated and compared with the DFA method by Monte Carlo simulations on fractional Gaussian noise models.     

Estimation in linear models using gradient descent with early stopping

A new shrinkage estimator of the coefficients of a linear model is derived. The estimator is motivated by the gradient-descent algorithm used to minimize the sum of squared errors and results from early stopping of the algorithm. The statistical properties of the estimator are examined and compared with other well-established methods such as least squares and ridge regression, both analytically and through a simulation study. An important result is that the new estimator is shown to be comparable to other shrinkage estimators in terms of mean squared error of parameters and of predictions, and superior under certain circumstances.Supported by the Greek State Scholarships Foundation     

Estimating risk reduction in stein estimation

It is shown that the unbiased estimator of the risk reduction in Stein estimation is unsatisfactory from a mean-squared-error point of view. A truncated form of the unbiased estimator and various empirical Bayes estimators of the risk reduction are shown to perform much better than the unbiased estimator. A simple practical estimator is proposed whose performance is a compromise between that of the truncated and empirical Bayes estimators.     

Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures

This paper presents a Bayesian analysis of partially linear additive models for quantile regression. We develop a semiparametric Bayesian approach to quantile regression models using a spectral representation of the nonparametric regression functions and the Dirichlet process (DP) mixture for error distribution. We also consider Bayesian variable selection procedures for both parametric and nonparametric components in a partially linear additive model structure based on the Bayesian shrinkage priors via a stochastic search algorithm. Based on the proposed Bayesian semiparametric additive quantile regression model referred to as BSAQ, the Bayesian inference is considered for estimation and model selection. For the posterior computation, we design a simple and efficient Gibbs sampler based on a location-scale mixture of exponential and normal distributions for an asymmetric Laplace distribution, which facilitates the commonly used collapsed Gibbs sampling algorithms for the DP mixture models. Additionally, we discuss the asymptotic property of the sempiparametric quantile regression model in terms of consistency of posterior distribution. Simulation studies and real data application examples illustrate the proposed method and compare it with Bayesian quantile regression methods in the literature.     

Efficient estimation for the conditional autoregressive model

Recently, spatial regression models have been attracting a great deal of attention in areas ranging from effect of traffic congestion on accident rates to the analysis of trends in gastric cancer mortality. In this paper, we propose efficient estimators for the regression coefficients of the spatial conditional autoregressive model, when uncertain auxiliary information is available about these coefficients. We provide efficiency comparisons of the proposed estimators based on asymptotic risk analysis and Monte Carlo simulations. We apply the proposed methods to real data on Boston housing prices and illustrate how a bootstrapping approach can be employed to compute prediction errors of the estimators.     

On huntseerger type shrinkage estimator

This paper is concerned with Hintsberger type weighted shrinkage estimator of a parameter when a target value of the same is available. Expressions for the bias and the mean squared error of the estimator are derived. Some results concerning the bias, existence of uniformly minimum mean squared error estimator etc. are proved. For certain c to ices of the weight function, numerical results are presented for the pretest type weighted shrinkage estimator of the mean of normal as well as exponential distributions.     

On shrinkage r-estimation in a multiple regression model

For a multiple regression model, bearing the plausibility of a subset of the regression parameters being close to a pivot, for the complementary subset, based on the usual James-Stein rule, a general formulation of shrinkage R-estimation is considered. In the light of asymptotic distributional risks of estimators, performance characteristics ( under local alternatives) of the classical R-est-imator and its preliminary test and shrinkage versions (all based on the common score function ) are studied. These shed light on the relative dominance picture in a meaningful asymptotic setup.     

Whither jackknifing in stein-rule estimation

In multi-parameter ( multivariate ) estimation, the Stein rule provides minimax and admissible estimators , compromising generally on their unbiasedness. On the other hand, the primary aim of jack-knifing is to reduce the bias of an estimator ( without necessarily compromising on its efficacy ), and, at the same time, jackknifing provides an estimator of the sampling variance of the estimator as well. In shrinkage estimation ( where minimization of a suitably defined risk function is the basic goal ), one may wonder how far the bias-reduction objective of jackknifing incorporates the dual objective of minimaxity ( or admissibility ) and estimating the risk of the estimator ? A critical appraisal of this basic role of jackknifing in shrinkage estimation is made here. Restricted, semi-restricted and the usual versions of jackknifed shrinkage estimates are considered and their performance characteristics are studied . It is shown that for Pitman-type ( local ) alternatives, usually, jackkntfing fails to provide a consistent estimator of the ( asymptotic ) risk of the shrinkage estimator, and a degenerate asymptotic situation arises for the usual fixed alternative case.     

Shrinkage estimation in replicated median ranked set sampling

In this article, we consider the median ranked set sampling estimation and test of hypothesis for the mean for symmetric distributions. We suggest some alternative estimation strategies for parameters based on shrinkage and pretest principles. It is advantageous to use the non-sample information in the estimation process to construct alternative estimations for the parameter of interest. In this article, large sample properties of the suggested estimators will be assessed numerically using computer simulation. The relative performance of the suggested estimators for moderate and large samples will also be simulated. For illustration purposes, the proposed methodology is applied using data collocated from the Pepsi Cola production company in Al-Khobar, Saudi Arabia.