Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval

This paper investigates nonparametric estimation of density on [0, 1]. The kernel estimator of density on [0, 1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0, 1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0, 1] are presently estimated.     

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.     

Estimating population size with truncated sampling

Let X₁, X₂,…,X_n be independent, indentically distributed random variables with density f(x,θ) with respect to a σ-finite measure μ. Let R be a measurable set in the sample space X. The value of X is observable if X ? (X?R) and not otherwise. The number J of observable X’s is binomial, N, Q, Q = 1?P(X ? R). On the basis of J observations, it is desired to estimate N and θ. Estimators considered are conditional and unconditional maximum likelihood and modified maximum likelihood using a prior weight function to modify the likelihood before maximizing. Asymptotic expansions are developed for the [Ncirc]’s of the form [Ncirc] = N + α√N + β + o_p(1), where α and β are random variables. All estimators have the same α, which has mean 0, variance σ² (a function of θ) and is asymptotically normal. Hence all are asymptotically equivalent by the usual limit distributional theory. The β’s differ and Eβ can be considered an “asymptotic bias”. Formulas are developed to compare the asymptotic biases of the various estimators. For a scale parameter family of absolutely continuous distributions with X = (0,∞) and R = (T,∞), special formuli are developed and a best estimator is found.     

Equality of two blues and ridge-type estimates

Equality is shown of the g-inverse and Moore-Penrose inverse representation of the BLUE in the general linear model. The proof is based on a matrix identity which allows also to establish a functional relationship between the BLUE and Ridge-type estimates.     

The maximum likelihood estimators of the parameters of the gamma distribution are always positively biased

Several authors have conjectured, on the basis of their numerical work, that the maximum likelihood estimators of the shape and scale parameters of the Gamma distribution are positively biased. It is proved that their conjecture is always true.     

Maximum likelihood estimation for the generalized poisson distribution

The generalized Poisson distribution;containing two

parameters and studied by many researchers; describes the distribution of busy periods under a queueing system and has very interesting properties; The probabilities for successive classes depend upon the previous occurrences; The problem of admissible maximum likelihood estimators for for the parameters Is discussed and a necessary and sufficient condition is derived for which unique admissible maximum likelihood estimators exist; The first; order terms in the biases; variances and the covariance of these maximum likelihood estimators are obtained.     

Estimation of Mode Using Two-phase Sampling

In this article, we consider the problem of estimation of mode using two-phase sampling. Ratio- and difference-type estimators in two-phase sampling are proposed. The asymptotic properties of the proposed estimators are studied analytically as well as empirically for different situations for the given cost of surveys. The use of two-phase sampling has been found to be cost saving design while estimating mode by making a proper use of auxiliary information.     

ALL-BIAS DESIGNS FOR POLYNOMIAL SPLINE REGRESSION MODELS

Polynomial spline regression models of low degree have proved useful in modeling responses from designed experiments in science and engineering when simple polynomial models are inadequate. Where there is uncertainty in the number and location of the knots, or breakpoints, of the spline, then designs that minimize the systematic errors resulting from model misspecification may be appropriate. This paper gives a method for constructing such all‐bias designs for a single variable spline when the distinct knots in the assumed and true models come from some specified set. A class of designs is defined in terms of the inter‐knot intervals and sufficient conditions are obtained for a design within this class to be all‐bias under linear, quadratic and cubic spline models. An example of the construction of all‐bias designs is given.     

Estimation of location extremes within general families of scale mixtures

In this paper, we study the estimation of the minimum and maximum location parameters, respectively, representing the minimum guaranteed lifetime of series and parallel systems of components, within a general class of scale mixtures. The conditional or underlying distribution has only the primary restriction of being a location-scale family with positive support. The mixing distribution is also quite general in that we only assume that it has positive support and finite second moment. For demonstrative purposes several special cases are highlighted such as the gamma, inverse-Gaussian, and discrete mixture. Various estimators, including bootstrap bias corrected estimators, are compared with respect to both mean-squared-error and Pitman's measure of closeness.     

投射偏差视角下的服务类品牌消费--以农村信息消费支付意愿为例

现将投射偏差模型框架引入服务类耐用品消费者均衡中,从理论上阐述投射偏差如何会导致消费者在服务类商品消费时无法达到效用最大化。研究采用实验和实地调研的方法,一共有251名人员参与了实验与调研,分析上网体验对于未来一年宽带的支付意愿影响。研究结果发现,人们在体验上网前后对于信息的认知状态有显著差异,没有上过网的人会基于当前的认知状态而低估未来一年宽带的效用,其支付意愿明显低于上过网的人,投射偏差在服务类耐用品的消费均衡中发挥了重要作用。