Bayesian estimation and prediction intervals for a Rayleigh distribution under a conjugate prior

This paper is an effort to obtain Bayes estimators of Rayleigh parameter and its associated risk based on a conjugate prior (square root inverted gamma prior) with respect to both symmetric loss function (squared error loss), and asymmetric loss function (precautionary loss function). We also derive the highest posterior density (HPD) interval for the Rayleigh parameter as well as the HPD prediction intervals for a future observation from this distribution. An illustrative example to test how the Rayleigh distribution fits a real data set is presented. Finally, Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different conditions.     

Comparing two dependent groups via quantiles

This paper considers two general ways dependent groups might be compared based on quantiles. The first compares the quantiles of the marginal distributions. The second focuses on the lower and upper quantiles of the usual difference scores. Methods for comparing quantiles have been derived that typically assume that sampling is from a continuous distribution. There are exceptions, but generally, when sampling from a discrete distribution where tied values are likely, extant methods can perform poorly, even with a large sample size. One reason is that extant methods for estimating the standard error can perform poorly. Another is that quantile estimators based on a single-order statistic, or a weighted average of two-order statistics, are not necessarily asymptotically normal. Our main result is that when using the Harrell–Davis estimator, good control over the Type I error probability can be achieved in simulations via a standard percentile bootstrap method, even when there are tied values, provided the sample sizes are not too small. In addition, the two methods considered here can have substantially higher power than alternative procedures. Using real data, we illustrate how quantile comparisons can be used to gain a deeper understanding of how groups differ.     

Semiparametric test for multiple change-points based on empirical likelihood

In the dynamic financial market, the change of financial asset prices is always described as a certain random events which result in abrupt changes. The random time when the event occurs is called a change point. As the event happens, in order to mitigate property damage the government should increase the macro-control ability. As a result, we need to find a valid statistical model for change point problem to solve it effectively. This paper proposes a semiparametric model for detecting the change points. According to the research of empirical studies and hypothesis testing we acquire the maximum likelihood estimators of change points. We use the loglikelihood ratio to test the multiple change points. We obtain some asymptotic results. The estimated change point is more efficient than the non parametric one through simulation experiments. Real data application illustrates the usage of the model.     

A comparison of stein-like procedures for estimating linear regression models with multicollinear data

This paper compares several Stein-like estimation methods for estimating regression parameters. The criterion function was the mean-squared error of prediction and the parameter of interest was the mean of the response variable at the sampled values of the control variables. Large sample simulation techniques were used to evaluate the mean-squared error of the predictions. The parameters of interest were varied systematically over wide ranges.     

Decision-theoretic estimation of generalized variance and generalized precision

Consider a random data matrix X=(X₁,...,X_k):pXk with independent columns [sathik] and an independent p X p Wishart matrix [sathik]. Estimators dominating the best affine equivariant estimators of [sathik] are obtained under four types of loss functions. Improved estimators (Testimators) of generalized variance and generalized precision are also considered under convex entropy loss (CEL).     

A Nonparametric Estimator of Survival Functions for Arbitrarily Truncated and Censored Data

It is well-known that the nonparametric maximum likelihood estimator (NPMLE) may severely under-estimate the survival function with left truncated data. Based on the Nelson estimator (for right censored data) and self-consistency we suggest a nonparametric estimator of the survival function, the iterative Nelson estimator (INE), for arbitrarily truncated and censored data, where only few nonparametric estimators are available. By simulation we show that the INE does well in overcoming the under-estimation of the survival function from the NPMLE for left-truncated and interval-censored data. An interesting application of the INE is as a diagnostic tool for other estimators, such as the monotone MLE or parametric MLEs. The methodology is illustrated by application to two real world problems: the Channing House and the Massachusetts Health Care Panel Study data sets.     

Some Estimates for the Rate of Convergence in the Multidimensional Central Limit Theorem for Homogeneous Markov Chains

This paper obtains some estimates for the rate of convergence in the multi-dimensional central limit theorem for vector-valued functions of a homogeneous Markov chain without assuming the finiteness of their absolute third moment. These estimates have a universal character and generalize the results that hold when the third moments are finite.     

Distribution of the product of a pair of independent two-sided power variates

ABSTRACT

The distributions of algebraic functions of random variables are important in theory of probability and statistics and other areas such as engineering, reliability, and actuarial applications, and many results based on various distributions are available in the literature. The two-sided power distribution is defined on a bounded range, and it is a generalization of the uniform, triangular, and power-function probability distributions. This paper gives the exact distribution of the product of two independent two-sided power-distributed random variables in a computable representation. The percentiles of the product are then computed, and a real data application is given.     

Incorporating regulatory focus theory in product recall communications to increase compliance with a product recall

Product recall communications with consumers is an important yet under-researched area of crisis management. This study examines whether applying regulatory focus theory in product recall communications can help companies involved in a product recall. This study examines the issue with a product recall message related to laptop computers. We find that creating regulatory fit through the product recall message increases intentions to comply with a product recall request, however future purchase intentions are also adversely impacted. We believe that the benefits of increased compliance greatly outweigh the small decrease in future purchase intentions, and companies should seriously consider incorporating regulatory focus theory in their product recall communications.     

Stabilized Sieve Sampling: A Point-Estimator Analysis

A modification of sieve sampling is proposed that returns a constant sample size. It is a scheme that selects line items with probability proportional to size (PPS) and nearly without replacement. An unbiased estimator of the total error amount is presented and its variance derived. Conditions under which the scheme is more efficient than sieve sampling and than PPS with replacement sampling are given.