Consistency of the recursive nonparametric regression estimation for dependent functional data

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.     

ROC curve estimation based on local smoothing

ROC curve is a graphical representation of the relationship between sensitivity and specificity of a diagnostic test. It is a popular tool for evaluating and comparing different diagnostic tests in medical sciences. In the literature,the ROC curve is often estimated empirically based on an empirical distribution function estimator and an empirical quantile function estimator. In this paper an alternative nonparametric procedure to estimate the ROC Curve is suggested which is based on local smoothing techniques. Several numerical examples are presented to evaluate the performance of this procedure.     

Estimating and testing effect size from an arbitrary population

In this article, we develop inference tools for an effect size parameter in a paired experiment. A class of estimators is defined that includes natural, shrinkage and shrinkage preliminary test estimators. The shrinkage and preliminary test methods incorporate uncertain prior information on the parameter. This information may be available in the form of a realistic guess on the basis of the experimenter’s knowledge and experience, which can be incorporated into the estimation process to increase the efficiency of the estimator. Asymptotic properties of the proposed estimators are investigated both analytically and computationally. A simulation study is also conducted to assess the performance of the estimators for moderate and large samples. For illustration purposes, the method is applied to a data set.     

A method for estimating parameters and quantiles of the three-parameter inverse Gaussian distribution based on statistics invariant to unknown location

The inverse Gaussian (IG) distribution, also known as the Wald distribution, is a long-tailed positively skewed distribution and a well-known lifetime distribution. In this paper, we propose an efficient method of estimation for the parameters and quantiles of the three-parameter IG distribution, which is based on statistics invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared with other prominent methods in terms of bias and variance. Finally, we present two illustrative examples.     

On exact confidence intervals in a competing risks model with generalized hybrid type-I censored exponential data

In a recent paper by Mao, Shi and Sun that appeared in Journal of Statistical Computation and Simulation, the authors discuss, among other approaches, the construction of exact confidence intervals for the underlying parameters by ‘pivoting the cumulative distribution functions’ of the corresponding maximum likelihood estimators (MLEs). The authors assume that this method is applicable without providing the appropriate justification. In this short note the two requirements for the applicability of this method are discussed, namely, the stochastic monotonicity of the MLEs and the existence of solutions to the equations defining the exact confidence interval's endpoints.     

Linear estimation for the extended exponential power distribution

Tiao and Lund [The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. J Amer Statist Assoc. 1970;65(329):370–386] tabulated the coefficients of the best linear unbiased estimators (BLUEs) of location and scale for a particular family of symmetric distributions. This family was a reparameterization of the extended exponential power distribution (EEPD) with the shape parameter restricted to be greater than or equal to one. In this work, we consider the BLU estimation of the location and scale parameters of the EEPD when the shape parameter is one-third and one-half. We obtain closed-form expressions for the single and product moments of the order statistics when the shape parameter is in general in the form of a reciprocal of an integer. These expressions are then used to determine the BLUEs and the corresponding variances for complete samples of size 20 and less. We consider some other linear estimators of the location and scale parameters and then compare them with the BLUEs. Finally, we present a numerical example to illustrate the developed results.     

Notes on odds ratio estimation for a randomized clinical trial with noncompliance and missing outcomes

The odds ratio (OR) has been recommended elsewhere to measure the relative treatment efficacy in a randomized clinical trial (RCT), because it possesses a few desirable statistical properties. In practice, it is not uncommon to come across an RCT in which there are patients who do not comply with their assigned treatments and patients whose outcomes are missing. Under the compound exclusion restriction, latent ignorable and monotonicity assumptions, we derive the maximum likelihood estimator (MLE) of the OR and apply Monte Carlo simulation to compare its performance with those of the other two commonly used estimators for missing completely at random (MCAR) and for the intention-to-treat (ITT) analysis based on patients with known outcomes, respectively. We note that both estimators for MCAR and the ITT analysis may produce a misleading inference of the OR even when the relative treatment effect is equal. We further derive three asymptotic interval estimators for the OR, including the interval estimator using Wald’s statistic, the interval estimator using the logarithmic transformation, and the interval estimator using an ad hoc procedure of combining the above two interval estimators. On the basis of a Monte Carlo simulation, we evaluate the finite-sample performance of these interval estimators in a variety of situations. Finally, we use the data taken from a randomized encouragement design studying the effect of flu shots on the flu-related hospitalization rate to illustrate the use of the MLE and the asymptotic interval estimators for the OR developed here.     

An efficient and fast algorithm for estimating the parameters of two-dimensional sinusoidal signals

In this paper we propose a computationally efficient algorithm to estimate the parameters of a 2-D sinusoidal model in the presence of stationary noise. The estimators obtained by the proposed algorithm are consistent and asymptotically equivalent to the least squares estimators. Monte Carlo simulations are performed for different sample sizes and it is observed that the performances of the proposed method are quite satisfactory and they are equivalent to the least squares estimators. The main advantage of the proposed method is that the estimators can be obtained using only finite number of iterations. In fact it is shown that starting from the average of periodogram estimators, the proposed algorithm converges in three steps only. One synthesized texture data and one original texture data have been analyzed using the proposed algorithm for illustrative purpose.