Consistent deconvolution in density estimation

Suppose we have n observations from X = Y + Z, where Z is a noise component with known distribution, and Y has an unknown density f. When the characteristic function of Z is nonzero almost everywhere, we show that it is possible to construct a density estimate f_n such that for all f, Iim_n| |=0.     

A Comparison of the Performance of Phase II Simple Linear Profile Control Charts when Parameters are Estimated

The standard deviation of the average run length (SDARL) is an important performance metric in studying the performance of control charts with estimated in-control parameters. Only a few studies in the literature, however, have considered this measure when evaluating control chart performance. The current study aims at comparing the in-control performance of three phase II simple linear profile monitoring approaches; namely, those of Kang and Albin (2000), Kim et al. (2003), and Mahmoud et al. (2010). The comparison is performed under the assumption of estimated parameters using the SDARL metric. In general, the simulation results of the current study show that the method of Kim et al. (2003) has better overall statistical performance than the competing methods in terms of SDARL values. Some of the recommended approaches based solely on the usual average run length properties can have poor SDARL performance.     

The General Segmented Distribution

We develop a distribution supported on a bounded interval with a probability density function that is constructed from any finite number of linear segments. With an increasing number of segments, the distribution can approach any continuous density function of arbitrary form. The flexibility of the distribution makes it a useful tool for various modeling purposes. We further demonstrate that it is capable of fitting data with considerable precision—outperforming distributions recommended by previous studies. We suggest that this distribution is particularly effective in fitting data with sufficient observations that are skewed and multimodal.     

Out-of-Sample Performance of Discrete-Time Spot Interest Rate Models

We provide a comprehensive analysis of the out-of-sample performance of a wide variety of spot rate models in forecasting the probability density of future interest rates. Although the most parsimonious models perform best in forecasting the conditional mean of many financial time series, we find that the spot rate models that incorporate conditional heteroscedasticity and excess kurtosis or heavy tails have better density forecasts. Generalized autoregressive conditional heteroscedasticity significantly improves the modeling of the conditional variance and kurtosis, whereas regime switching and jumps improve the modeling of the marginal density of interest rates. Our analysis shows that the sophisticated spot rate models in the existing literature are important for applications involving density forecasts of interest rates.     

Noninformative priors for the normal variance ratio

In this paper, we consider noninformative priors for the ratio of variances in two normal populations. We develop first and second order matching priors. We find that the second order matching prior matches alternative coverage probabilities up to the second order and is also a HPD matching prior. It turns out that among the reference priors, only one-at-a-time reference prior satisfies a second order matching criterion. Our simulation study indicates that the one-at-a-time reference prior performs better than other reference priors in terms of matching the target coverage probabilities in a frequentist sense. This work is supported by Korea Research Foundation Grant (KRF-2004-002-C00041).     

Smoothed Histograms for Frequency Data on Irregular Intervals

Frequency tables are often constructed on intervals of irregular width. When plotted as bar charts, the underlying true density information may be quite distorted. The majority of introductory statistics texts recommend tabulating data into intervals of equal width, but seldom caution the consequences of failing to do so. An occasional introductory text correctly emphasizes that area rather than frequency should be plotted. Nevertheless, the correctly scaled density figure is often visually less informative than one might expect, with wide bins at constant height. In many cases, the right most bin interval has no well-defined end point, making its depiction some what arbitrary. In this note, we introduce a regular histogram approximation that matches the frequencies and also minimizes a roughness criterion for visual and exploratory appeal. The resulting estimate can reveal the density structure much more clearly. We also formulate an alternative criterion that explicitly takes account of the uncertainty in the bin frequencies.     

Design priorities and disciplinary perspectives: the case of the US National Children's Study

Summary.  The National Children's Study (NCS), which was undertaken in 2000 by collaboration between several US federal government agencies, is one of the largest and boldest longitudinal studies of children's health ever undertaken. One of the key design issues has been the nature of the NCS sample. The paper describes the nature of the choices and the reasons for the decision that the NCS be based on a national probability sample. Designed as a study of the environmental influences on children's health and development, the NCS is expected to identify, enrol and follow about 100000 children from their birth to the age of 21 years. A broad definition of relevant environments of interest, and a full partnership between government, university and medical scientists, introduces considerable challenges in the design of the study.     

Bandwidth-based nonparametric inference

Nonparametric curve estimation is an extremely common statistical procedure. While its primary purpose has been exploratory, some advances in inference have been made. This paper provides a critical review of inferential tests that make fundamental use of a key element of nonparametric smoothing, the bandwidth, to determine the significance of certain features. A major focus is on two important problems that have been tackled using bandwidth-based inference: testing for the multimodality of a density and testing for the monotonicity of a regression curve. Early research in bandwidth-based inference is surveyed, as well as recent theoretical advances. Possible future directions in bandwidth-based inference are discussed.     

关于非中心Laplace分布的密度函数

在本文中,对文[1]提出的广义Laplace分布进行了讨论,给出了广义Laplace分布的密度函数的解析表达式,同时进一步推导了非中心Laplace分布的密度函数表达式,最后对这类分布重要的数字特征在文中也被给出.