On kernel density derivative estimation

Estimators of derivatives of a density function based on polynomial multiples of kernels are compared with those based on differentiated kernels.     

Change points in nonparametric regresion functions

Estimators of location and size of jumps or discontinuities in a regression function and/or its derivatives are proposed. The estimators are based on the analysis of residuals obtained from the locally weighted least squares regression. The proposed estimators adapt to both fixed and random designs. The asymptotic properties of the estimators are investigated. The method is illustrated through simulation studies.     

Exponentiated Teissier distribution with increasing,decreasing and bathtub hazard functions

This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress–strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions.     

复杂抽样推断方法体系的比较研究

对复杂样本进行推断通常有两种体系,一种是传统的基于随机化理论的统计推断,另一种是基于模型的统计推断。传统的抽样理论以随机化理论为基础,将总体取值视为固定,随机性仅体现在样本的选取上,对总体的推断依赖于抽样设计。该方法在大样本情况下具有稳健估计量,但在小样本、数据缺失等情况下失效。基于模型的抽样推断认为总体是超总体模型中抽取的一个随机样本,对总体的推断取决于模型的建立,但在不可忽略抽样设计下估计量是有偏估计。在对这两类推断方法分析的基础上,提出抽样设计辅助的模型推断,并指出该方法在复杂抽样中具有重要的应用价值。     

Maximum likelihood estimation in convex hull models

In this paper we consider models involving the convex hull operation of the parameter and the noise i.e. Y_i = CH(A, X_X). Then we generalize the basic models to ANOVA models; i.e. Y_ij=CH(A∪B_j,X_ij). In some cases the consistent estimators for the J U new parameters are derived. Assuming the existence of density forrandom convex sets, we derive the likelihood for the convex hull model. We then find the maximum Likelihood Estimators for the parameters. Examples for some random convex sets with finite dimensional distributions are derived to show how good these estimators are.     

Wahrscheinlichkeitstransformationen in Entscheidungsmodellen bei linearer partieller Information

In decision models with linear partial information the incomplete knowledge of probabilities is expressed by means of convex polyhedra. The transformation of incompletely specified probabilities by Bayes' theorem, the law of total probabilities, and the multiplication law for independent events is analysed with reference to recent results on this topic. As a new result the incorrectness of a central theorem in Kofler/Menges (1976) is shown. But the theory is partly reestablished by an equivalence between two optimization problems, which is derived from bilinearity.     

Robust Estimation and Hypothesis Testing of Linear Contrasts in Analysis of Covariance with Stochastic Covariates

Estimators of parameters are derived by using the method of modified maximum likelihood (MML) estimation when the distribution of covariate X and the error e are both non-normal in a simple analysis of covariance (ANCOVA) model. We show that our estimators are efficient. We also develop a test statistic for testing a linear contrast and show that it is robust. We give a real life example.     

Bayesian estimation of the difference between two proportions

This paper is concerned with the problem of allocating a fixed number of trials between two independent binomial populations with unknown success probabilities θ₁ and θ₂, in order to estimate θ₁ - θ₂ with squared error loss. Introducing independent beta priors on θ₁ and θ₂, a heuristic allocation procedure is introduced and compared both with the optimal and with the best fixed allocation procedure. Numerical and asymptotic results of these comparisons are given and seem to indicate that there are situations when the best fixed allocation procedure performs almost as well as the optimal procedure.     

Pitman Closeness of kth Records Based on a Two-Sequence Case

Suppose upper kth records were observed from an X-sequence of iid continuous random variables, and kth upper records from another independent Y-sequence of iid variables from the same distribution are to be observed. The Pitman closeness probabilities of these statistics are derived. For symmetric distribution, the Pitman closeness probabilities of kth record statistics to the population median, are also examined and it is shown that these probabilities are distribution free. Numerical computations are conducted to illustrate the results developed here.     

A representation in beta series for the exact density of some random volume contents

Consider r independent and identically distributed random points in a unit n-ball of which p are in the interior and rp are on the surface. These r points, via their convex hull, generate an r-simplex. This article deals with the exact density of the r-content when the points are uniformly distributed. The exact density of the r-content is obtained for the general values of the parameters r, n and p. A representation of the density is given as a mixture of beta type-1 densities so that one can evaluate various types of probabilities by using incom-plete beta tables.     

Combined Density Nowcasting in an Uncertain Economic Environment

We introduce a combined density nowcasting (CDN) approach to dynamic factor models (DFM) that in a coherent way accounts for time-varying uncertainty of several model and data features to provide more accurate and complete density nowcasts. The combination weights are latent random variables that depend on past nowcasting performance and other learning mechanisms. The combined density scheme is incorporated in a Bayesian sequential Monte Carlo method which rebalances the set of nowcasted densities in each period using updated information on the time-varying weights. Experiments with simulated data show that CDN works particularly well in a situation of early data releases with relatively large data uncertainty and model incompleteness. Empirical results, based on U.S. real-time data of 120 monthly variables, indicate that CDN gives more accurate density nowcasts of U.S. GDP growth than a model selection strategy and other combination strategies throughout the quarter with relatively large gains for the two first months of the quarter. CDN also provides informative signals on model incompleteness during recent recessions. Focusing on the tails, CDN delivers probabilities of negative growth, that provide good signals for calling recessions and ending economic slumps in real time.     

A comparioson of nonparametric unweighited and length-biased density estimation of fibres

Two sampling procedures used to estimate the distribution of the length of textile fibres are studied . Estimators of the density function of fibre length and the asymptotic propertiesof these estimators are discussed. Simulations were undertaken to compare mean square errors of the estimators for various saniple sizes.     

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).     

Classification of dichotomous and continuous variables with incomplete samples

This Article Considers the problem of classifiying an observation consisting of both binary and continuous variables based on two general incomplete training samples one from each of the two given populations. The location linear model adopted by krzanowski 1975 forms the basis of our inverstigation. For a given location, When the common dispersion matrix as Well as the corresponding cell probabilities for the underlying populations are known, exact distribution of the conditional maximum likelihood classification rule is derived. The overall error rate can be obtained and is based on linear cominations of independent non– Chi– Distributions. large sample result for the case where the cell probabilities are unknown is also available.     

A new geometric first-order integer-valued autoregressive (NGINAR(1)) process

A new stationary first-order integer-valued autoregressive process with geometric marginal distributions is introduced based on negative binomial thinning. Some properties of the process are established. Estimators of the parameters of the process are obtained using the methods of conditional least squares, Yule–Walker and maximum likelihood. Also, the asymptotic properties of the estimators are derived involving their distributions. Some numerical results of the estimators are presented with a discussion to the obtained results. Real data are used and a possible application is discussed.     

Maximum likelihood analysis of masked series system lifetime data

Component lifetime parameters of a series system are estimated from system lifetimes and masked cause of failure observations. The time and cause of system failures are assumed to follow a competing risks model. The masking probabilities of the minimum random subsets are not subjected to the symmetry assumption. Sufficient regularity conditions are provided, justifying the maximum likelihood analysis. Maximum likelihood estimates of both the lifetime parameters and masking probabilities are generically computed via an EM algorithm. An appropriate set of asymptotically pivotal quantities are also derived. Such maximum likelihood based estimates are further refined by bootstrap. The developed techniques are illustrated by numerical examples of independent Weibull component lifetimes with distinct scale and shape parameters.     

Small-sample estimators of the quantiles of the normal,log-normal and Pareto distributions

Estimators of the quantiles of the normal and log-normal distributions are derived. They are more efficient than the established estimators by a wide margin for small samples and high quantiles of the log-normal distribution. Although their evaluation is iterative, it requires only moderate amount of computing, which is not related to the sample size. The method is also applied to the quantiles of the Pareto distribution, but the resulting estimator is more efficient only in some settings. An application to financial statistics, estimating the return on a unit investment in equity markets over a long term, is presented.     

Generalized RCINAR(1) Process with Signed Thinning Operator

A generalized random coefficient first-order integer-valued autoregressive process with signed thinning operator is introduced, this kind of process is appropriate for modeling negative integer-valued time series. Strict stationarity and ergodicity of process are established. Estimators of the parameters of interest are derived and their properties are studied via simulation. At last, we use bootstrap method in the real data analysis.     

Confidence intervals for the comparison of two poisson distributions

Confidence interval construction the difference in mean event rates for two Index independent , Poisson samples is discussed. Intervals are derived by considering Bayes estimates of the mean event rates using a family of noninformative priors. The coverage probabilities of the proposed are compared to those of the standard Wald interval for of observed events. A compromise method of constructing interval based on the data is suggested and its properties are evaluated. The method is illustrated in several examples.     

Improved unbiased estimators in adaptive cluster sampling

Summary.  The usual design-unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved. Improved unbiased estimators obtained by conditioning on sufficient statistics—not necessarily minimal—are described. First, estimators that are as easy to compute as the usual design-unbiased estimators are given. Estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed. Estimators are compared in examples.