On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function

Summary Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ^-r of unknown parameter λ of gamma distribution with density ,x> 0, whereb-known parameter, for loss function . Goodmann in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ² of the normal distribution. In particular for quadratic loss function he took weight of the formK(σ²)=C andK(σ²)=(σ²)^-2 only. In this work we obtained the class of all unbiased Lehmanns-estimators of the variance λ² of the exponential distribution, among estimators of the form functions of the sufficient statistics-with quadratic loss function with weight of the form ,C>0.

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Resumen Lehmann en su trabajo [4] generalizó la idea del estimador sin vías en relación a la aceptación de la función de pérdidas. En el trabajo [5] Singh considera de estimadores admisibles para la función λ^-r parámetro desconocido λ de la distribución de gamma, de densidad ,x>0,b>0 parámetro conocido, de la función de pérdidas resulta . Goodman en su trabajo [1] acumulando 3 formas diferentes de funciones de pérdidas encontró estimadores sin biases en el sentido de Lehmann de la variancia de σ² de una distribución normal, en particular para la función de pérdidas con los pesos, solo de la formaK(σ²)=C,K(σ²)=(σ²)^-2. En su trabajo distinguida la clase de todos los estimadores sin biases obtenidos en el sentido de Lehmann de la variancia λ² en la distribución exponencial, entre los estimadores de forma así pues de la función estadística suficiente— por una función de pérdidas al cuadrado con los pesos de la forma ,C>0. Palabras y frases. Estimador sin vías en el sentido de Lehmann, función de pérdidas, riesgo mínimo, suficiente estadística.

     

Bin width selection in multivariate histograms by the combinatorial method

We present several multivariate histogram density estimates that are universallyL ₁-optimal to within a constant factor and an additive term . The bin widths are chosen by the combinatorial method developed by the authors inCombinatorial Methods in Density Estimation (Springer-Verlag, 2001). The present paper solves a problem left open in that book.     

Experimentelle und analytische Untersuchungen zum Zündverhalten stark verdünnter C2H2/O2-Gemische

Zusammenfassung Das Zündverhalten homogener Gasgemische bestehend aus Argon mit C₂H₂+O₂-Anteilen von 2% wird bei ?quivalenzverh?ltnissen von ϕ=0,2; 0,5; 1,0 und 2,0 hinter Sto?wellen experimentell untersucht. Kriterium für das Ende der Induktionsperiode ist das starke Ansteigen der OH-Konzentration, die durch Absorptions- oder Emissionsverfahren gemessen wird. Die Gaszust?nde sind in einem Temperaturbereich 1000 K≦T≦1560 K bei Drücken zwischen 0,6 und 1,3 bar variiert worden. Die Me?werte lassen sich durch eine Korrelationsgleichung darstellen mit τ in μs und Konzentrationen in mol cm⁻³. Mit Hilfe eines reaktionskinetischen Modells bestehend aus 29 Elementarreaktionen werden Computersimulationen des Zündverhaltens der verschiedenen Gemische durchgeführt. Die übereinstimmung zwischen berechneten und gemessenen OH-Induktionszeiten erscheint zufriedenstellend, wenn man bedenkt, da? keine kinetische Anpassung vorgenommen worden ist.     

Three oxidation states and atomic-scale <Emphasis Type="Italic">p–n</Emphasis> junctions in manganese perovskite oxide from hydrothermal systems

Perovskite oxides have provided magical structural models for superconducting and colossal magnetoresistance, and the search for nano-scale and/or atomic-scale devices with particular property by specific preparations in the same systems has been extensively conducted. We present here the three oxidation states of manganese (Mn³⁺, Mn⁴⁺, Mn⁵⁺) in the perovskite oxide, La_0.66Ca_0.29K_0.05MnO₃, which most interestingly shows the rectifying effect as atomic-scale p–n junctions (namely FY-Junctions) of single crystals and films. The family of cubic perovskite oxides were synthesised by the so-called hydrothermal disproportionation reaction of MnO₂ under the condition of strong alkali media. The new concept of the atomic-scale p–n junctions, based on the ideal rectification characteristic of the p–n junctions in the single crystal, basically originates from the structural linkages of [Mn³⁺–O–Mn⁴⁺–O–Mn⁵⁺], where Mn³⁺ and Mn⁵⁺ in octahedral symmetry serve as a donor and an acceptor, respectively, corresponding to the localized Mn⁴⁺ .     

Generalizacion del teorema de Hanson y Russo para B-variables aleatorias

Resumen En este trabajo se presenta una generalización de un teorema de D. L. Hanson y R. P. Russo (1981) para variables aleatorias i.i.d. que toman valores en un espacio de Banach separable (B-variables), en el esquema más general de la ley de Marcinkiewicz y Zygmund. Imponiendo condiciones sobre los momentos y el tipo Rademacher del espacio se obtienen resultados de la forma:      

Some multiple comparisons using sample quasi ranges on censored data

We considerk(k)≥2 independent populations (treatments or systems) and an solutely continuous member of location-scale family of distributions, index by the location parameter μ _i (-∞ < μ _i < ∞) and scale parameter θ _i (θ _i > 0), is used to model the observations from the ith population,i=1,...k. The problem of simultaneous selection of two subsets, one containing population associated with the smallest ϕ-value and other containing population with the largest ϕ-value with probability at least a pre-specified value is considered when the data are censored. We also construct 100P ^*% simultaneous upper and two-sided confidence intervals for where θ_[1] ≤ ... ≤ θ_[k] denotes the ordered values of ϕs. The proposed procedures, based on sample quasi ranges, are useful when the experimenter has smaller samples or censored samples or there is suspicion of outliers in the samples. The results are applied to exponential populations model and, for thes casi: (i) the constants have been computed to apply the proposed multiple comparisons; (ii) two members of the proposed class have been compared with the existing procedure. A numerical example is also given.     

Estimacion no parametrica de curvas notables para datos dependientes

Resumen Sea {X _t :t∈Z} una serie de tiempo estacionaria, con valores en ℝ ^p , verificando la condición de ser α-mixing oL ²-estable. A partir de una muestra de tama?on se define una amplia clase de estimadores no paramétricos de la función de densidadf(x) asociada al proceso, y de la función de autorregresión de ordenk: siendog una función real. Se estudian las siguientes propiedades asintóticas de estos estimadores: consistencia puntual (casi segura y en mediar-ésima); consistencia global con norma uniforme casi segura; sesgo, varianza y normalidad asintótica. El presente trabajo es un resumen que contiene parte de los resultados obtenidos por el autor en su Tesis Doctoral.     

Turbidity Data of Weightless SF<Subscript>6</Subscript> Near its Liquid–Gas Critical Point

Light transmission measurements performed in SF₆ close to its liquid–gas critical point are used to obtain turbidity data in the reduced temperature range (T is temperature, T _c is the critical temperature). Automatic experiments (ALICE 2 facility) were made at a near critical density, i.e., , in the one-phase homogeneous region, under the microgravity environment of the Mir Space Station ( is the average density, ρ _c is the critical density). The turbidity data analysis verifies the theoretical crossover formulations for the isothermal compressibility and the correlation length ξ. These latter formulations are also used to analyze very near T _c thermal diffusivity data obtained under microgravity conditions by Wilkinson et al. (Phys. Rev. E 57 436, 1998).     

On the theory of flux gates with output at fundamental frequency

A parametric theory is developed of flux gates with an output at the fundamental frequency. General and particular design expressions were derived. Special emphasis is focussed on the effect of internal parametric amplification of the useful signal that makes possible detection and measurement of weak magnetic fields. The sources of internal flux gate noise were established and ways for their reduction are indicated. The practically achievable noise level was found to be . Translated from Izmeritel'naya Tekhnika, No. 3, pp. 54–60, March, 1999.