Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Using local linear kernel smoothers to test the lack of fit of nonlinear regression models

Herein, we propose a data-driven test that assesses the lack of fit of nonlinear regression models. The comparison of local linear kernel and parametric fits is the basis of this test, and specific boundary-corrected kernels are not needed at the boundary when local linear fitting is used. Under the parametric null model, the asymptotically optimal bandwidth can be used for bandwidth selection. This selection method leads to the data-driven test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The finite-sample property of the proposed data-driven test is illustrated, and the power of the test is compared with that of some existing tests via simulation studies. We illustrate the practicality of the proposed test by using two data sets.     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

Kurtosis modelling by means of the J-transformation

Summary: The H–family of distributions or H–distributions, introduced by Tukey (1960; 1977), are generated by a single transformation of the standard normal distribution and allow for leptokurtosis represented by the parameter h. Alternatively, Haynes et al. (1997) generated leptokurtic distributions by applying the K–transformation to the normal distribution. In this study we propose a third transformation, the so–called J–transformation, and derive some properties of this transformation. Moreover, so-called elongation generating functions (EGFs) are introduced. By means of EGFs we are able to visualize the strength of tail elongation and to construct new transformations. Finally, we compare the three transformations towards their goodness–of–fit in the context of financial return data.     

COMPARISONS AND SELECTION OF TWO-PARAMETER EXPONENTIAL POPULATIONS

For two-parameter exponential populations with the same scale parameter (known or unknown) comparisons are made between the location parameters. This is done by constructing confidence intervals, which can then be used for selection procedures. Comparisons are made with a control, and with the (unknown) “best” or “worst” population. Emphasis is laid on finding approximations to the confidence so that calculations are simple and tables are not necessary. (Since we consider unequal sample sizes, tables for exact values would need to be extensive.)     

WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

In this paper, we establish strong laws for weighted sums of negatively associated (NA) random variables which have a higher‐order moment condition. Some results of Bai Z.D. & Cheng P.E. (2000) [Marcinkiewicz strong laws for linear statistics. Statist. and Probab. Lett. 43, 105–112,] and Sung S.K. (2001) [Strong laws for weighted sums of i.i.d. random variables, Statist. and Probab. Lett. 52, 413–419] are sharpened and extended from the independent identically distributed case to the NA setting. Also, one of the results of Li D.L. et al. (1995) [Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8, 49–76,] is complemented and extended.     

SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

An alternative to model selection in ordinary regression

The weaknesses of established model selection procedures based on hypothesis testing and similar criteria are discussed and an alternative based on synthetic (composite) estimation is proposed. It is developed for the problem of prediction in ordinary regression and its properties are explored by simulations for the simple regression. Extensions to a general setting are described and an example with multiple regression is analysed. Arguments are presented against using a selected model for any inferences.     

基于旅西日本游客旅游选择行为的西安旅游市场分析

根据在全国六大旅游热点城市所做的旅游市场调查的数据结果，对旅西日本游客的旅游选择行为进行了研究，同时进一步有针对性地对西安日本客源市场进行了SWOT分析，在此基础上，对西安旅游业的发展提出了相关对策建议。