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1.
On locally optimal invariant unbiased tests for the variance components ratio in mixed linear models
Andrzej Michalski 《Statistical Papers》2009,50(4):855-868
In the paper the problem of testing of two-sided hypotheses for variance components in mixed linear models is considered.
When the uniformly most powerful invariant test does not exist (see e.g. Das and Sinha, in Proceedings of the second international
Tampere conference in statistics, 1987; Gnot and Michalski, in Statistics 25:213–223, 1994; Michalski and Zmyślony, in Statistics
27:297–310, 1996) then to conduct the optimal statistical inference on model parameters a construction of a test with locally
best properties is desirable, cf. Michalski (in Tatra Mountains Mathematical Publications 26:1–21, 2003). The main goal of
this article is the construction of the locally best invariant unbiased test for a single variance component (or for a ratio
of variance components). The result has been obtained utilizing Andersson’s and Wijsman’s approach connected with a representation
of density function of maximal invariant (Andersson, in Ann Stat 10:955–961, 1982; Wijsman, in Proceedings of fifth Berk Symp
Math Statist Prob 1:389–400, 1967; Wijsman, in Sankhyā A 48:1–42, 1986; Khuri et al., in Statistical tests for mixed linear models, 1998) and from generalized Neyman–Pearson Lemma
(Dantzig and Wald, in Ann Math Stat 22:87–93, 1951; Rao, in Linear statistical inference and its applications, 1973). One
selected real example of an unbalanced mixed linear model is given, for which the power functions of the LBIU test and Wald’s
test (the F-test in ANOVA model) are computed, and compared with the attainable upper bound of power obtained by using Neyman–Pearson
Lemma. 相似文献
2.
On MSE of EBLUP 总被引:1,自引:1,他引:0
Tomasz Ża̧dło 《Statistical Papers》2009,50(1):101-118
We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general
mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes
unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed
by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called
the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat
Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator
of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta
and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed
by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp
2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation
of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the
formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive
the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate
to terms o(D
−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D
−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using
our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE
and estimators of its MSE and their performance in Monte Carlo simulation study.
相似文献
3.
Arijit Chaudhuri Tasos C. Christofides Amitava Saha 《Statistical Methods and Applications》2009,18(3):389-418
In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response
(RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a
respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion,
testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976),
Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994)
among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities
the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of
an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large
scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is
essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented
here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible
in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika
57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is
device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants
before they agree to use the randomization device.
The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported
by CSIR Grant No. 21(0539)/02/EMR-II. 相似文献
4.
We introduce a new family of skew-normal distributions that contains the skew-normal distributions introduced by Azzalini
(Scand J Stat 12:171–178, 1985), Arellano-Valle et al. (Commun Stat Theory Methods 33(7):1465–1480, 2004), Gupta and Gupta
(Test 13(2):501–524, 2008) and Sharafi and Behboodian (Stat Papers, 49:769–778, 2008). We denote this distribution by GBSN
n
(λ1, λ2). We present some properties of GBSN
n
(λ1, λ2) and derive the moment generating function. Finally, we use two numerical examples to illustrate the practical usefulness
of this distribution. 相似文献
5.
The concept of fractional cointegration (Cheung and Lai in J Bus Econ Stat 11:103–112, 1993) has been introduced to generalize
traditional cointegration (Engle and Granger in Econometrica 55:251–276, 1987) to the long memory framework. In this work
we propose a test for fractional cointegration with the sieve bootstrap and compare by simulations the performance of our
proposal with other semiparametric methods existing in literature: the three steps technique of Marinucci and Robinson (J
Econom 105:225–247, 2001) and the procedure to determine the fractional cointegration rank of Robinson and Yajima (J Econom
106:217–241, 2002). 相似文献
6.
In this paper, we introduce an alternative stochastic restricted Liu estimator for the vector of parameters in a linear regression
model when additional stochastic linear restrictions on the parameter vector are assumed to hold. The new estimator is a generalization
of the ordinary mixed estimator (OME) (Durbin in J Am Stat Assoc 48:799–808, 1953; Theil and Goldberger in Int Econ Rev 2:65–78,
1961; Theil in J Am Stat Assoc 58:401–414, 1963) and Liu estimator proposed by Liu (Commun Stat Theory Methods 22:393–402,
1993). Necessary and sufficient conditions for the superiority of the new stochastic restricted Liu estimator over the OME,
the Liu estimator and the estimator proposed by Hubert and Wijekoon (Stat Pap 47:471–479, 2006) in the mean squared error
matrix (MSEM) sense are derived. Furthermore, a numerical example based on the widely analysed dataset on Portland cement
(Woods et al. in Ind Eng Chem 24:1207–1241, 1932) and a Monte Carlo evaluation of the estimators are also given to illustrate
some of the theoretical results. 相似文献
7.
We provide some unifying definitions, make some corrections to articles by Faraz and Parsian (J Stat Pap 47:569–593, 2006)
and Costa (J Qual Technol 26:155–163, 1994; 29:197–204, 1997), and using these provide more accurate tables of results and
comparisons of control charts. We also investigate the impact of an incorrectly specified process shift on signal frequency. 相似文献
8.
Summary We extend to masses on a real interval the notion of ϕ-mean, usually considered in the context of σ-additive probabilities
or probability distribution functions, and consider some axiomatic treatments of it at different levels of masses (simple
masses, compact support masses, tight masses, arbitrary masses). Moreover, as an important special case, we get axiomatic
systems for general means, as well. We also prove that the usual axiomatic system “Consistency with Certainty+Associativity+Monotonicity”
characterizes the ϕ-mean of masses with arbitrary compact support and that, already at tight masses level, this system is
not adequate. We note that the analytical tool used to define the ϕ-mean is the Choquet integral.
Work performed under the auspices of the National Group: “Inferenza Statistica: basi probabilistiche e sviluppi metodologici”
(MURST 40%). 相似文献
9.
The multivariate skew-t distribution (J Multivar Anal 79:93–113, 2001; J R Stat Soc, Ser B 65:367–389, 2003; Statistics 37:359–363,
2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew–normal ones as limiting cases. In this paper,
we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test
data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763–771, 2003) where the random errors
and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of
dentistry. 相似文献
10.
Matthias Fischer 《Statistical Papers》2010,51(1):41-56
Constructing skew and heavy-tailed distributions by transforming a standard normal variable goes back to Tukey (Exploratory
data analysis. Addison-Wesley, Reading, 1977) and was extended and formalized by Hoaglin (In: Data analysis for tables, trends,
and shapes. Wiley, New York, 1983) and Martinez and Iglewicz (Commun Statist Theory Methods 13(3):353–369, 1984). Applications
of Tukey’s GH distribution family—which are composed by a skewness transformation G and a kurtosis transformation H—can be found, for instance, in financial, environmental or medical statistics. Recently, alternative transformations emerged
in the literature. Rayner and MacGillivray (Statist Comput 12:57–75, 2002b) discuss the GK distributions, where Tukey’s H-transformation is replaced by another kurtosis transformation K. Similarly, Fischer and Klein (All Stat Arch, 88(1):35–50, 2004) advocate the J-transformation which also produces heavy tails but—in contrast to Tukey’s H-transformation—still guarantees the existence of all moments. Within this work we present a very general kurtosis transformation which nests H-, K-and an approximation to the J-transformation and, hence, permits to discriminate between them. Applications to financial and teletraffic data are given. 相似文献
11.
The Fisher information matrix for a mixture of two Laplace distributions is derived. Numerical tabulations of the matrix and
a computer program are provided for practical purposes. The work is motivated by two real–life examples discussed in Hsu (Appl
Stat 28:62–72, 1979) and Bhowmick et al. (Biostatistics 7:630–641, 2006).
相似文献
12.
Joachim Wilde 《Statistical Papers》2008,49(3):471-484
Dagenais in (Econ Lett 63:19–21, 1999) and Lucchetti in (Econ Lett 75:179–185, 2002) have demonstrated that the naive GMM
estimator of Grogger in (Econ Lett 33:329–332, 1990) for the probit model with an endogenous regressor is not consistent.
This paper completes their discussion by explaining the reason for the inconsistency and presenting a natural solution. Furthermore,
the resulting GMM estimator is analyzed in a Monte-Carlo simulation and compared with alternative estimators. 相似文献
13.
In this paper we introduce a new extension for the Birnbaum–Saunder distribution based on the family of the epsilon-skew-symmetric
distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427–443, 2005). The extension allows generating
Birnbaun–Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab
47:88–95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application
are reported illustrating good fitting properties of the proposed model. 相似文献
14.
S. Huschens 《Statistical Papers》1990,31(1):155-159
For the characteristic values T1 of the matrix V:=Diag(p)-ppT with p=(p1,...,pk), p1≥p2≥...≥pk≥pk+1>0 and p1+p2+...+pk+pk+1=1 the inequalities p1≥τ1≥p2≥τ2≥...≥pk≥τk>0 are given by RONNING
(1982). These inequalities give, if p and pk+1 are unknown, the upper bound 1≥T1. However, in this note the bound 1/2≥T1 is
derived. V is proportional to the covariance matrix for multinomial, Dirichlet and multivariate hypergeometric distributions.
A statistical application for the multinomial distribution is given. 相似文献
15.
This note provides the asymptotic distribution of a Perron-type innovational outlier unit root test developed by Popp (J Stat
Comput Sim 78:1145–1161, 2008) in case of a shift in the intercept for non-trending data. In Popp (J Stat Comput Sim 78:1145–1161,
2008), only critical values for finite samples based on Monte Carlo techniques are tabulated. Using similar arguments as in
Zivot and Andrews (J Bus Econ Stat 10:251–270, 1992), weak convergence is shown for the test statistics. 相似文献
16.
Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data,
2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest
(Ghosh and Lin, Biometrics 56:554–562, 2000; Wang et al., J Am Stat Assoc 96:1057–1065, 2001; Huang and Wang, J Am Stat Assoc
99:1153–1165, 2004; Ye et al., Biometrics 63:78–87, 2007). In addition, sometimes there may exist more than one type of recurrent
events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics
5:129–143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among
different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling
approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown
parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of
leukemia patients. 相似文献
17.
Amitava Saha 《Statistical Papers》2010,51(2):349-355
Singh et al. (Stat Trans 6(4):515–522, 2003) proposed a modified unrelated question procedure and they also demonstrated that
the modified procedure is capable of producing a more efficient estimator of the population parameter π
A
, namely, the proportion of persons in a community bearing a sensitive character A when π
A
< 0.50. The development of Singh et al. (Stat Trans 6(4):515–522, 2003) is based on simple random samples with replacement
and on the assumption that π
B
, namely, the proportion of individuals bearing an unrelated innocuous character B is known. Due to these limitations, Singh et al.’s (Stat Trans 6(4):515–522, 2003) procedure cannot be used in practical
surveys where usually the sample units are chosen with varying selection probabilities. In this article, following Singh et
al. (Stat Trans 6(4):515–522, 2003) we propose an alternative RR procedure assuming that the population units are sampled
with unequal selection probabilities and that the value of π
B
is unknown. A numerical example comparing the performance of the proposed RR procedure under alternative sampling designs
is also reported. 相似文献
18.
As GARCH models and stable Paretian distributions have been revisited in the recent past with the papers of Hansen and Lunde
(J Appl Econom 20: 873–889, 2005) and Bidarkota and McCulloch (Quant Finance 4: 256–265, 2004), respectively, in this paper
we discuss alternative conditional distributional models for the daily returns of the US, German and Portuguese main stock
market indexes, considering ARMA-GARCH models driven by Normal, Student’s t and stable Paretian distributed innovations. We find that a GARCH model with stable Paretian innovations fits returns clearly
better than the more popular Normal distribution and slightly better than the Student’s t distribution. However, the Student’s t outperforms the Normal and stable Paretian distributions when the out-of-sample density forecasts are considered. 相似文献
19.
We study two sequential, response-adaptive randomized designs for clinical trials; one has been proposed in Bandyopadhyay
and Biswas (Biometrika 88: 409–419, 2001) and in Biswas and Basu (Sankhya Ser B 63:27–42, 2001), the other stems from the
randomly reinforced urn introduced and studied in Muliere et al. (J Stat Plan Inference 136:1853–1874, 2006a). Both designs
can be used in clinical trials where the response from each patient is a continuous variable. Comparison is conducted through
numerical studies and along a new guideline for the evaluation of a response-adaptive design. 相似文献
20.
Sasabuchi et al. (Biometrika 70(2):465–472, 1983) introduces a multivariate version of the well-known univariate isotonic
regression which plays a key role in the field of statistical inference under order restrictions. His proposed algorithm for
computing the multivariate isotonic regression, however, is guaranteed to converge only under special conditions (Sasabuchi
et al., J Stat Comput Simul 73(9):619–641, 2003). In this paper, a more general framework for multivariate isotonic regression
is given and an algorithm based on Dykstra’s method is used to compute the multivariate isotonic regression. Two numerical
examples are given to illustrate the algorithm and to compare the result with the one published by Fernando and Kulatunga
(Comput Stat Data Anal 52:702–712, 2007). 相似文献