Construction of neighbor designs of block size 4 for all values of v ≥ 5 by using the method of addition

In this article, a general method of construction of neighbor block designs is given. The designs are constructed using variation of a simple method which we refer to as the method of addition (renamed as the method of cyclic shifts). We give complete solution of neighbor balanced designs for k = 4 for any value of v. We also give many series of generalized neighbor designs (GNDs). In the last section, we have constructed GNDs in a sequential manner (as Did John 1981) for v ≤ 50 and r is multiple of k.     

REDUCED RESIDUE CLASSES CYCLIC PBIB DESIGNS

A new general class of m-class cyclic association scheme is defined for v treatments, where v is a composite number. A simple method of construction of PBIB designs having this association scheme using more than one initial block and some methods using only one initial block are proposed. A complete analysis of this type of PBIB designs is given. Also given is a list of 39 useful PBIB designs of this type having v≤15 and r≤10 and having only three associate classes together with their efficiency factors for all types of comparisons and over all efficiency factors.     

Accurate unconditional p-values for a two-arm study with binary endpoints

Unconditional exact tests are increasingly used in practice for categorical data to increase the power of a study and to make the data analysis approach being consistent with the study design. In a two-arm study with a binary endpoint, p-value based on the exact unconditional Barnard test is computed by maximizing the tail probability over a nuisance parameter with a range from 0 to 1. The traditional grid search method is able to find an approximate maximum with a partition of the parameter space, but it is not accurate and this approach becomes computationally intensive for a study beyond two groups. We propose using a polynomial method to rewrite the tail probability as a polynomial. The solutions from the derivative of the polynomial contain the solution for the global maximum of the tail probability. We use an example from a double-blind randomized Phase II cancer clinical trial to illustrate the application of the proposed polynomial method to achieve an accurate p-value. We also compare the performance of the proposed method and the traditional grid search method under various conditions. We would recommend using this new polynomial method in computing accurate exact unconditional p-values.     

A-optimal designs for mixture central polynomial model with qualitative factors

Mixture central polynomial models with qualitative factors are widely applied in many fields of research. In this paper, a method of finding A-optimal design for two degree mixture central polynomial model with qualitative factors will be proposed. The variance function will be given for getting the support points of the design. The A-optimality is confirmed by the equivalence theorem. In addition, this method also works effectively with higher degree models.     

Improved estimation of the mean in one-parameter exponential families with known coefficient of variation

The value for which the mean square error of a biased estimatoraT for the mean μ is less than the variance of an unbiased estimatorT is derived by minimizingMSE(aT). The resulting optimal value is 1/[1+c(n)v ²], wherev=σ/μ, is the coefficient of variation. WhenT is the UMVUE , thenc(n)=1/n, and the optimal value becomes 1/(n+v ²) (Searls, 1964). Whenever prior information about the size ofv is available the shrinkage procedure is useful. In fact for some members of the one-parameter exponential families it is known that the variance is at most a quadratic function of the mean. If we identify the pertinent coefficients in the quadratic function, it becomes easy to determinev.     

Balanced treatment incomplete block designs through integer programming

An algorithm is presented to construct balanced treatment incomplete block (BTIB) designs using a linear integer programming approach. Construction of BTIB designs using the proposed approach is illustrated with an example. A list of efficient BTIB designs for 2 ? v ? 12, v + 1 ? b ? 50, 2 ? k ? min(10, v), r ? 10, r₀ ? 20 is provided. The proposed algorithm is implemented as part of an R package.     

D-optimal designs for covariate models

The problem of finding D-optimal or D-efficient designs in the presence of covariates is considered under a completely randomized design set-up with v treatments, k covariates and N experimental units. In contrast to Lopes Troya [Lopes Troya, J., 1982, Optimal designs for covariates models. Journal of Statistical Planning and Inference, 6, 373–419.], who considered this problem in the equireplicate case, we do not assume that N/v is an integer, and this allows us to study situations where no equireplicate design exists. Even when N/v is an integer, it is seen quite counter-intuitively that there are situations where a non-equireplicate design outperforms the best equireplicate design under the D-criterion.     

Joint detection for functional polynomial regression with autoregressive errors

In this article, we are concerned with detecting the true structure of a functional polynomial regression with autoregressive (AR) errors. The first issue is to detect which orders of the polynomial are significant in functional polynomial regression. The second issue is to detect which orders of the AR process in the AR errors are significant. We propose a shrinkage method to deal with the two problems: polynomial order selection and autoregressive order selection. Simulation studies demonstrate that the new method can identify the true structure. One empirical example is also presented to illustrate the usefulness of our method.     

An iterative algorithm for solving sparse linear equations

This article introduces a new iterative technique for solving systems of linear equations of the kind Ax = b. Convergence, and with a given rate, is guaranteed with the square nonsingular matrix A being non-negative. The iterative algorithm depends on a scheme derived from Bayesian updating. The algorithm is shown to compare very favorably with the wisely used GMRES routine. With the algorithm being easy to code, it has the potential to be highly useable.     

Some important classes of generalized neighbor designs for linear blocks

In this paper, some infinite series of generalized neighbor designs are constructed for the linear blocks which are useful to balance out the neighbor effects for the cases where (a) one of the v treatments has some neighbor effects with other treatments, while remaining (v – 1) treatments have half of that neighbor effect among selves, (b) some of the v treatments have some neighbor effect with other treatments, while remaining treatments have half of that neighbor effect among themselves, (c) one of the v treatments has some neighbor effect with other treatments, while remaining (v – 1) treatments have double of that effect among themselves, and (d) some of the v treatments have some neighbor effect with other, while remaining treatments have double of it among themselves.     

Polynomial approximation of nonlinear regression functions

In the present paper a nonlinear regression function is approximated by a polynomial estimator according to the expectation of the quadratic L ²-distance as risk is given. For special experimental designs with repeating experimental points this estimator coincides with the estimator by the method of the reproducing kernel.

Considerations about the relation for the sample size and the degree of the approximation polynomial and about the quadratic mean are given.     

Estimation of regression parameters in missing data problems

Let Y be a response variable, possibly multivariate, with a density function f (y|x, v; β) conditional on vectors x and v of covariates and a vector β of unknown parameters. The authors consider the problem of estimating β when the values taken by the covariate vector v are available for all observations while some of those taken by the covariate x are missing at random. They compare the profile estimator to several alternatives, both in terms of bias and standard deviation, when the response and covariates are discrete or continuous.     

On computer generation of gamma random variables by rejection and composition procedures 2

The paper presents various algorithms for generating gamma random variables, by combining rejection and composition procedures. Two efficient algorithms are given for the case when the parameter of the gamma distribution is 0<v<l. For the case vl, several algorithms are given but they (except one), work reliably only for small values of v. Results of some computer tests together with FORTRAN subroutines are also presented.     

D-Optimal Designs for Covariate Parameters in Block Design Set Up

The problem considered is that of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non stochastic controllable covariates, when N = 2(mod 4), N being the total number of observations. It is clear that when N ≠ 0 (mod 4), it is not possible to find designs attaining minimum variance for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters were established when each of the covariates belongs to the interval [?1, 1]. Some constructions of D-optimal design have been provided for symmetric balanced incomplete block design (SBIBD) with parameters b = v, r = k = v ? 1, λ =v ? 2 when k = 2 (mod 4) and b is an odd integer.     

Non binary partially neighbor balanced designs for circular blocks

ABSTRACT

Neighbor designs are recommended for the cases where the performance of treatment is affected by the neighboring treatments as in biometrics and agriculture. In this paper we have constructed two new series of non binary partially neighbor balanced designs for v = 2n and v = 2n+1 number of treatments, respectively. The blocks in the design are non binary and circular but no treatment is ever a neighbor to itself. The designs proposed here are partially balanced in terms of nearest neighbors. No such series are known in the literature.     

Hypercubic designs and applications

In this paper we develop relatively easy methods for constructing hypercubic designs from symmetrical factorial experiments for t=v ^m treatments with v=2, 3. The proposed methods are easy to use and are flexible in terms of choice of possible block sizes.     

ON THE CHOICE OF ESTIMATOR IN SURVERY SAMPLING*

We re-examine the criteria of “hyper-admissibility” and “necessary bestness”, for the choice of estimator, from the point of view of their relevance to the design of actual surveys. Both these criteria give rise to a unique choice of estimator (viz. the Horvitz-Thompson estimator ?_HT) whatever be the character under investigation or sample design. However, we show here that the “principal hyper-surfaces” (or “domains”) of dimension one (which are practically uninteresting)play the key role in arriving at the unique choice. A variance estimator v₁(?_HT) (due to Horvitz-Thompson), which takes negative values “often”, is shown to be uniquely “hyperadmissible” in a wide class of unbiased estimators of the variance of ?_HT. Extensive empirical evidence on the superiority of the Sen-Yates-Grundy variance estimator v₂(?_HT) over v₁(?_HT) is presented.     

Bootstrap inference in local polynomial regression of time series

In this paper we consider the inferential aspect of the nonparametric estimation of a conditional function , where X _t,m represents the vector containing the m conditioning lagged values of the series. Here is an arbitrary measurable function. The local polynomial estimator of order p is used for the estimation of the function g, and of its partial derivatives up to a total order p. We consider α-mixing processes, and we propose the use of a particular resampling method, the local polynomial bootstrap, for the approximation of the sampling distribution of the estimator. After analyzing the consistency of the proposed method, we present a simulation study which gives evidence of its finite sample behaviour.     

The Asymptotic Distributions of Unified Process Capability Indices

Abstract

This paper derives the asymptotic distributions of the estimators of the unified process capability indices C _p (u, v) and C _pa (u, v) for arbitrary population under general, regularity conditions, assuming that the fourth moment about the mean exists.     

Visualizing main effects and interaction in multiple non-symmetric correspondence analysis

Non-symmetric correspondence analysis (NSCA) is a useful technique for analysing a two-way contingency table. Frequently, the predictor variables are more than one; in this paper, we consider two categorical variables as predictor variables and one response variable. Interaction represents the joint effects of predictor variables on the response variable. When interaction is present, the interpretation of the main effects is incomplete or misleading. To separate the main effects and the interaction term, we introduce a method that, starting from the coordinates of multiple NSCA and using a two-way analysis of variance without interaction, allows a better interpretation of the impact of the predictor variable on the response variable. The proposed method has been applied on a well-known three-way contingency table proposed by Bockenholt and Bockenholt in which they cross-classify subjects by person's attitude towards abortion, number of years of education and religion. We analyse the case where the variables education and religion influence a person's attitude towards abortion.