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The mean residual life of a non negative random variableXwith a finite mean is defined byM(t) =E[X−t|X>t] fort⩾ 0. A popular nonparametric model of aging is new better than used in expectation (NBUE), whenM(t) ⩽M(0) for allt⩾ 0. The exponential distribution lies at the boundary. There is a large literature on testing exponentiality against NBUE alternatives. However, comparisons of tests have been made only for alternatives much stronger than NBUE. We show that a new Kolmogorov-Smirnov type test is much more powerful than its competitors in most cases. [ABSTRACT FROM AUTHOR]

If X1 and X2 are random variables with distribution functions F1 and F2, then X1 is said to be stochastically larger than X2 if F1 ≤ F2. Statistical inferences under stochastic ordering for the two-sample case has a long and rich history. In this article we consider the k-sample case; that is, we have k populations with distribution functions F1, F2,..., Fk, k ≥ 2, and we assume that F1 ≤ F2 ≤,...,≤ Fk. For k = 2, the nonparametric maximum likelihood estimators of F1 and F2 under this order restriction have been known for a long time; their asymptotic distributions have been derived only recently. These results have very complicated forms and are hard to deal with when making statistical inferences. We provide simple estimators when k ≥ 2. These are strongly uniformly consistent, and their asymptotic distributions have simple forms. If &Fcirc;i and &Fcirci* are the empirical and our restricted estimators of Fi, then we show that, asymptotically, P(\ &Fcirci* (x) - Fi (x)\ ≤ u) &ge P (\ &Fcirc;i (x) \ ≤ u) for all x and all u > 0, with strict inequality in some cases. This clearly shows a uniform improvement of the restricted estimator over the unrestricted one. We consider simultaneous confidence bands and a test of hypothesis of homogeneity against the stochastic ordering of the k distributions. The results have also been extended to the case of censored observations. Examples of application to real life data are provided. [ABSTRACT FROM AUTHOR]

Regression analysis constitutes a large portion of the statistical repertoire in applications. In cases where such analysis is used for exploratory purposes with no previous knowledge of the structure, one would not wish to impose any constraints on the problem. But in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure. An important example of this occurs when the experimenter has a strong belief that the regression function changes monotonically with some or all of the predictor variables in a region of interest. The analyses needed for statistical inferences under such constraints are nonstandard. Considering the present body of knowledge developed for unconstrained regression, it will be an enormous task to derive the analogs of even a small fraction of this for the restricted case. In this article we initiate the study with simple linear regression on a single variable. The estimators of the regression parameters may be intuitively obvious in this case, but, as discussed, very little else is. [ABSTRACT FROM AUTHOR]

A problem frequently encountered in the practice of statistics is the comparison of several treatments with a control or standard. We consider an experimental situation where prior knowledge indicates that all of the treatments are at least as effective as the control and the problem is to determine if any are significantly better than the control. A number of statistical procedures have been proposed for this situation, of which the best known is Dunnett's (1955) multiple comparison procedure. Dunnett's test rejects equality of the treatments and the control for a large value of the maximum contrast of the data vector with several vectors that are located "symmetrically" within the alternative region. We study a large class of such tests, which includes Dunnett's test as a particular case. One of these tests, which is based on the maximum contrast of the data vector with several orthogonal vectors, is very easy to implement and has an uncomplicated, good, and fairly uniform power function over the entire alternative region. In fact, a small Monte Carlo power study suggests that this orthogonal contrast test is approximately "maximin" within this class of tests. Moreover, the simplicity of the power function of the orthogonal contrast test enables the experimenter to determine sample sizes for designed experiments with specific power characteristics. Such sample size determinations can be difficult, if not impossible, using other procedures. Abelson and Tukey (1963) suggested tests for a large class of restricted problems that are based on contrasts of the data vector with a single vector that is "centrally" located within the alternative region. These single contrast tests have the advantage that their distributions under the null hypotheses (a t distribution) and under the alternative (a... [ABSTRACT FROM AUTHOR]