Change Point Estimation of Multivariate Linear Profiles Under Linear Drift

In this paper, maximum likelihood estimators (MLE) for both step and linear drift changes in the regression parameters of multivariate linear profiles are developed. Performance of the proposed estimators is compared under linear drift changes in the regression parameters when a combined MEWMA and Chi-square control charts method signals an out-of-control condition. The effect of smoothing parameter of MEWMA control charts, missing data, and multiple drift changes on the performance of the both estimators is also evaluated. The application of the proposed estimators is also investigated thorough a numerical example resulted from a real case.     

Change-Point Detection in Two-Phase Regression with Inequality Constraints on the Regression Parameters

Two-phase regression models with inequality constraints on the regression coefficients and with a small number of measurements is considered. A new test based on the likelihood ratio in linear model with inequality constraints for the presence of a change-point is proposed. Numerical approximations to the powers against various alternatives are given and compared with the powers of the likelihood ratio test in the two-phase regression models without inequality constraints, the backwards CUSUM test, and the k-linear-r-ahead recursive residuals tests. Performance of related likelihood based estimators of the change-point is briefly studied in a Monte Carlo experiment.     

On the small sample properties of norm-restricted maximum likelihood estimators for logistic regression models

This paper develops alternatives to maximum likelihood estimators (MLE) for logistic regression models and compares the mean squared error (MSE) of the estimators. The MLE for the vector of underlying success probabilities has low MSE only when the true probabilities are extreme (i.e., near 0 or 1). Extreme probabilities correspond to logistic regression parameter vectors which are large in norm. A competing “restricted” MLE and an empirical version of it are suggested as estimators with better performance than the MLE for central probabilities. An approximate EM-algorithm for estimating the restriction is described. As in the case of normal theory ridge estimators, the proposed estimators are shown to be formally derivable by Bayes and empirical Bayes arguments. The small sample operating characteristics of the proposed estimators are compared to the MLE via a simulation study; both the estimation of individual probabilities and of logistic parameters are considered.     

On improved estimation of a gamma shape parameter

This paper deals with improved estimation of a gamma shape parameter from a decision-theoretic point of view. First we study the second-order properties of three estimators – (i) the maximum-likelihood estimator (MLE), (ii) a bias corrected version of the MLE, and (iii) an improved version (in terms of mean squared error) of the MLE. It is shown that all the three estimators mentioned above are second-order inadmissible. Next, we obtain superior estimators which are second order better than the above three estimators. Simulation results are provided to study the relative risk improvement of each improved estimator over the MLE.     

A change-point estimator with the hazard ratio

The problem of estimation of parameters in hazard rate change models with a change-point is considered. A change-point estimator using the hazard ratio is suggested and compared with the previously developed change-point estimators. The proposed estimator is shown to be consistent. The performance of the proposed estimator is checked and compared with other change-point estimators via simulation.     

Change-point detection in a shape-restricted regression model

A regression model with a possible structural change and with a small number of measurements is considered. A priori information about the shape of the regression function is used to formulate the model as a linear regression model with inequality constraints and a likelihood ratio test for the presence of a change-point is constructed. The exact null distribution of the test statistic is given. Consistency of the test is proved when the noise level goes to zero. Numerical approximations to the powers against various alternatives are given and compared with the powers of the k-linear-r-ahead recursive residuals tests and CUSUM tests. Performance of four different estimators of the change-point is studied in a Monte Carlo experiment. An application of the procedures to some real data is also presented.     

Linear approximate ML estimation in scaled Type I generalized logistic distribution based on Type-II censored samples

The scaled (two-parameter) Type I generalized logistic distribution (GLD) is considered with the known shape parameter. The ML method does not yield an explicit estimator for the scale parameter even in complete samples. In this article, we therefore construct a new linear estimator for scale parameter, based on complete and doubly Type-II censored samples, by making linear approximations to the intractable terms of the likelihood equation using least-squares (LS) method, a new approach of linearization. We call this as linear approximate maximum likelihood estimator (LAMLE). We also construct LAMLE based on Taylor series method of linear approximation and found that this estimator is slightly biased than that based on the LS method. A Monte Carlo simulation is used to investigate the performance of LAMLE and found that it is almost as efficient as MLE, though biased than MLE. We also compare unbiased LAMLE with BLUE based on the exact variances of the estimators and interestingly this new unbiased LAMLE is found just as efficient as the BLUE in both complete and Type-II censored samples. Since MLE is known as asymptotically unbiased, in large samples we compare unbiased LAMLE with MLE and found that this estimator is almost as efficient as MLE. We have also discussed interval estimation of the scale parameter from complete and Type-II censored samples. Finally, we present some numerical examples to illustrate the construction of the new estimators developed here.     

Estimation of two ordered normal means when a covariance matrix is known

Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67–93] and Peddada et al. [Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703–715]. The estimators are also compared under the Pitman nearness criterion and it is shown that the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error.     

On second-order admissibilities of the estimators of gamma shape vector

Simultaneous estimation problem of gamma shape vector is considered.First, it is shown that the maximum likelihood estimator (MLE), the bias corrected MLE, and the conditional MLE of shape vector are second-order inadmissible. Second, these estimators are improved up to the second order. Finally, we identify whether these improved estimators are second-order admissible or not. Simulation studies are also given.     

Estimating the parameters of a doubly truncated normal distribution

This paper deals with the maximum likelihood estimation of parameters for a doubly truncated normal distribution when the truncation points are known. We prove, in this case, that the MLEs are nonexistent (become infinite) with positive probability. For estimators that exist with probability one, the class of Bayes modal estimators or modified maximum likelihood estimators is explored. Another useful estimating procedure, called mixed estimation, is proposed. Simulations compare the behavior of the MLEs, the modified MLEs, and the mixed estimators which reveal that the MLE, in addition to being nonexistent with positive probability, behaves poorly near the upper boundary of the interval of its existence. The modified MLEs and the mixed estimators are seen to be remarkably better than the MLE     

Change-in-mean problem for long memory time series models with applications

Test and estimation procedures for detecting a change in the mean are proposed in infinite moving average long memory time series models. The asymptotic properties of the test statistics and the change-point estimators are investigated. The method is illustrated through the analysis of real data sets from econometrics and climatology.     

Aalen's linear model for doubly censored data

Double censoring often occurs in registry studies when left censoring is present in addition to right censoring. In this work, we examine estimation of Aalen's nonparametric regression coefficients based on doubly censored data. We propose two estimation techniques. The first type of estimators, including ordinary least squared (OLS) estimator and weighted least squared (WLS) estimators, are obtained using martingale arguments. The second type of estimator, the maximum likelihood estimator (MLE), is obtained via expectation-maximization (EM) algorithms that treat the survival times of left censored observations as missing. Asymptotic properties, including the uniform consistency and weak convergence, are established for the MLE. Simulation results demonstrate that the MLE is more efficient than the OLS and WLS estimators.     

Estimation in the presence of incidental parameters

This paper considers the estimation of “structural” parameters when the number of unknown parameters increases with the sample size. Neyman and Scott (1948) had demonstrated that maximum likelihood estimators (MLE) of structural parameters may be inconsistent in this case. Patefield (1977) further observed that the asymptotic covariance matrix of the MLE is not equal to the inverse of the information matrix. In this paper we establish asymptotic properties of estimators (which include in particular the MLE) obtained via the usual likelihood approach when the incidental parameters are first replaced by their estimates (which are allowed to depend on the structural parameters). Conditions for consistency and asymptotic normality together with a proper formula for the asymptotic covariance matrix are given. The results are illustrated and applied to the problem of estimating linear functional relationships, and mild conditions on the incidental parameters for the MLE (or an adjusted MLE) to be consistent and asymptotically normal are obtained. These conditions are weaker than those imposed by previous authors.     

The LAD estimation of the change-point linear model with randomly censored data

Abstract

In this paper, a change-point linear model with randomly censored data is investigated. We propose the least absolute deviation estimation procedure for regression and change-point parameters simultaneously. The asymptotic properties of the change-point and regression parameter estimators are obtained. We show that the resulting regression parameter estimator is asymptotically normal, and the change-point estimator converges weakly to the minimizer of a given random process. The extensive simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.     

带异质线性趋势的动态二元选择面板模型估计

本文提出了带异质线性趋势的动态二元面板模型的极大似然偏误纠正估计量和近似条件Logit估计量。我们给出了通常极大似然估计量偏误的解析形式,并提供了相应的估计方法。小样本实验表明近似条件似然函数可以很好的消除异质性参数的影响,而偏误纠正估计量可以显著的修正极大似然估计量的偏误。最后我们将本文提出的方法应用到现金红利支付模型。     

Estimating the negative binomial dispersion parameter with highly stratified surveys

We investigate several estimators of the negative binomial (NB) dispersion parameter for highly stratified count data for which the statistical model has a separate mean parameter for each stratum. If the number of samples per stratum is small then the model is highly parameterized and the maximum likelihood estimator (MLE) of the NB dispersion parameter can be biased and inefficient. Some of the estimators we investigate include adjustments for the number of mean parameters to reduce bias. We extend other estimators that were developed for the iid case, to reduce bias when there are many mean parameters. We demonstrate using simulations that an adjusted double extended quasi-likelihood estimator we proposed gives much improved estimates compared to the MLE. Adjusted extended quasi-likelihood and adjusted maximum likelihood estimators also give much-improved results. We illustrate the various estimators with stratified random bottom trawl survey data for cod (Gadus morhua) off the south coast of Newfoundland, Canada.     

C335. Some numerology for the mass ratio of proton to electron,and a partially Bayesian evaluation

Recent small sample studies of estimators for the shape parameter a of the negative binomial distribution (NBD) tend to indicate that the choice of estimator can be reduced to a choice between the method of moments estimator, maximum likelihood estimator (MLE), maximum quasi-likelihood estimator and the conditional likelihood estimator (CLE). In this paper the results of a comprehensive simulation study are reported to assist with the choice from these four estimators. The study includes a traditional procedure for assessing estimators for the shape parameter of the NBD and in addition introduces an alternative assessment procedure. Based on the traditional approach the CLE is considered to perform the best overall for the range of parameter values and sample sizes considered. The alternative assessment procedure indicates that the MLE is the preferred estimator.     

Estimation of the mean of the exponential distribution using moving extremes ranked set sampling

Moving Extremes Ranked Set Sampling (MERSS) is a useful modification of Ranked Set Sampling (RSS). Unlike RSS, MERSS allows for an increase of set size without introducing too much ranking error. The method is considered parametrically under exponential distribution. Maximum likelihood estimator (MLE), and a modified MLE are considered and their properties are studied. The method is studied under both perfect and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE using the usual simple random sampling (SRS).     

Maximum likelihood estimator in a multi-phase random regression model

We consider a random regression model with several-fold change-points. The results for one change-point are generalized. The maximum likelihood estimator of the parameters is shown to be consistent, and the asymptotic distribution for the estimators of the coefficients is shown to be Gaussian. The estimators of the change-points converge, with n ^?1 rate, to the vector whose components are the left end points of the maximizing interval with respect to each change-point. The likelihood process is asymptotically equivalent to the sum of independent compound Poisson processes.     

Optimal rank set sampling estimates for a population proportion

This paper examines two different classes of estimates for a population proportion based on an unbalanced rank set sample. Specifically, the two classes correspond to the maximum likelihood estimator (MLE) and a weighted average (WA) estimate. Both estimators are asymptotically normal, so standard inference procedures can still be implemented. Furthermore, these results can be used to develop optimal allocation schemes for both estimators. The performances of the optimal estimators are studied in terms of both finite sample and asymptotic relative efficiency. In general, the MLE is more efficient than the WA estimate. Lastly, the practicality of the optimal sampling plans is addressed and illustrated via an example.