Asymptotic Expansions for i.i.d. Sums Via Lower-order Convolutions

In this article, we introduce new asymptotic expansions for probability functions of sums of independent and identically distributed random variables. Results are obtained by efficiently employing information provided by lower-order convolutions. In comparison with Edgeworth-type theorems, advantages include improved asymptotic results in the case of symmetric random variables and ease of computation of main error terms and asymptotic crossing points. The first-order estimate can perform quite well against the corresponding renormalized saddlepoint approximation and, pointwise, requires evaluation of only a single convolution integral. While the new expansions are fairly straightforward, the implications are fortuitous and may spur further related work.     

Testing Normality Using Transformed Data

In this article, we first present a characterization of the normal distribution and then we introduce an exact goodness of fit test for normal distribution. The power of the proposed test under various alternatives is compared with the existing tests, by simulation.     

Empirical likelihood inference for a semiparametric hazards regression model

ABSTRACT

We investigated the empirical likelihood inference approach under a general class of semiparametric hazards regression models with survival data subject to right-censoring. An empirical likelihood ratio for the full 2p regression parameters involved in the model is obtained. We showed that it converged weakly to a random variable which could be written as a weighted sum of 2p independent chi-squared variables with one degree of freedom. Using this, we could construct a confidence region for parameters. We also suggested an adjusted version for the preceding statistic, whose limit followed a standard chi-squared distribution with 2p degrees of freedom.     

On the choice of co-ordinates in simultaneous estimation of normal means under misspecification of normal priors

The problem of choice of coordinates in Stein-type estimators,when simultaneously estimating normal means, is considered. The question of deciding whether to use all coordinates in one combined shrinkage estimators or to separate into groups and use separate shrinkage estimators on each group is considered in the situation in which part of the prior information may be " misspecified". It is observed that the amount of misspecification determines whether to use the combined shrinkage estimator the separate shrinkage estimator.     

Inverse-gaussian acceptance sampling plans by variables

Variable sampling plans to control fraction defective are obtained using the Inverse-Gaussian (IG) distribution. OC curves are obtained and impact of sample size and specification limits on these curves are discussed. Simulation studies are used to investigate sensitivity of the sampling plans under the more commonly used normal distribution.     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

Maximum likelihood estimation in a Weibull regression model with type-1 censoring: a Monte Carlo study

Results of the Monte Carlo study of the performance of a maximum likelihood estimation in a Weibull parametric regression model with two explanatory variables are presented. One simulation run contained 1000 samples censored on the average by the amount of 0-30%. Each simulatedsample was generated in a form of two-factor two-level balanced experiment. The confidence intervals were computed using the large-sample normal approximation via the matrix of observed information. For small sample sizes the estimates of the scale parameter b of the loglifetime were significantly negatively biased, which resulted in a poor quality of confidence intervals for b and the low-level quantiles. All estimators improved their quality when the nominal value of b decreased. A moderate amount of censoring improved the quality of point and confidence estimation. The reparametrization b 7 produced rather accurate confidence intervals. Exact confidence intervals for b in case of non-censoring were obtained using the pivotal quantity b/b.     

Tukey-Type Distributions in the Context of Financial Data

Abstract

In one-parameter (θ) families, we were not aware of explicit hypothesis testing scenarios where maximal invariant statistics failed to distinguish the models. We start with a concrete example (Sec. 2.2) to highlight such a hypothesis testing problem involving markedly different models. In this problem, because of the absence of a nontrivial uniformly most powerful invariant (UMPI) test, we briefly suggest two approaches to test the hypothesis. The first resolution (Sec. 3.1) is frequentist in nature. It utilizes a weight function on the parameter space and compares “average” distributions obtained under the null and alternative models in the sense of Wald (1947 Wald , A. ( 1947 ). Sequential Analysis . New York : Wiley . [Google Scholar] 1950 Wald , A. ( 1950 ). Statistical Decision Functions . New York : Wiley . [Google Scholar]). In contrast, a fully Bayesian resolution (Sec. 3.2) is also included. The note ends with a series of other interesting examples involving one-parameter families where maximal invariant statistics fail to distinguish the hypothesized models. The examples include easy-to-construct families of probability models involving only a single location or scale parameter θ.     

A Simpler Approximation for Areas under the Standard Normal Curve

A simple approximation for areas under the standard normal curve is presented that is suitable for use when tables and/or calculators are not available or not permitted.